4326:
conspire to make the behavior of heat flow quite unlike the flow of electricity in normal situations. Unfortunately, although the electrical and thermal differential equations are analogous, it is erroneous to conclude that there is any practical analogy between electrical and thermal resistance. This is because a material that is considered an insulator in electrical terms is about 20 orders of magnitude less conductive than a material that is considered a conductor, while, in thermal terms, the difference between an "insulator" and a "conductor" is only about three orders of magnitude. The entire range of thermal conductivity is then equivalent to the difference in electrical conductivity of high-doped and low-doped silicon."
4836:
5390:
38:
4502:
4339:
2213:
3760:
544:
3174:
2978:
4325:
A 2008 review paper written by
Philips researcher Clemens J. M. Lasance notes that: "Although there is an analogy between heat flow by conduction (Fourier's law) and the flow of an electric current (Ohm’s law), the corresponding physical properties of thermal conductivity and electrical conductivity
2417:
Given all this information, the designer can construct a model of the heat flow from the semiconductor junction, where the heat is generated, to the outside world. In our example, the heat has to flow from the junction to the case of the transistor, then from the case to the metalwork. We do not
2363:). The specification for the design should include a maximum temperature at which the circuit should function correctly. Finally, the designer should consider how the heat from the transistor will escape to the environment: this might be by convection into the air, with or without the aid of a
2191:
The heat flow can be modelled by analogy to an electrical circuit where heat flow is represented by current, temperatures are represented by voltages, heat sources are represented by constant current sources, absolute thermal resistances are represented by resistors and thermal capacitances by
740:
The thermal resistance of materials is of great interest to electronic engineers because most electrical components generate heat and need to be cooled. Electronic components malfunction or fail if they overheat, and some parts routinely need measures taken in the design stage to prevent this.
1894:
3576:
626:: In spacecraft and aircraft, thermal resistance and conductance are critical for managing temperature variations in extreme environments. Designing spacecraft and aviation systems require considerations of thermal conductance and resistance to manage temperature extremes.
6083:
The logarithmic distribution of the temperature is sketched in the inset of the thumbnail figure. Assuming that the temperature distribution, equation 7, is used with
Fourier's law in equation 5, the heat transfer rate can be expressed in the following form
602:: Thermal resistance is crucial for designing heat sinks and thermal management systems in electronic devices to prevent overheating. Calculating thermal conductance is crucial for designing effective heat sinks and cooling systems in electronic devices.
4095:
6069:
4369:
The junction-to-air thermal resistance can vary greatly depending on the ambient conditions. (A more sophisticated way of expressing the same fact is saying that junction-to-ambient thermal resistance is not
Boundary-Condition Independent (BCI).)
608:: Automotive engineers use thermal resistance to optimize the cooling system and prevent overheating in engines and other vehicle components. Evaluating thermal resistance helps in designing engine components and automotive cooling systems.
4973:
in the radial direction. The standard method can be used for analyzing radial systems under steady state conditions, starting with the appropriate form of the heat equation, or the alternative method, starting with the appropriate form of
2990:
667:: Thermal resistance is considered in climate studies to understand heat transfer in Earth's atmosphere and oceans. Evaluating thermal resistance is useful in studying soil temperature profiles for environmental and agricultural research.
335:
211:
2795:
465:
Objects made of insulators like rubber tend to have very high resistance and low conductance, while objects made of conductors like metals tend to have very low resistance and high conductance. This relationship is quantified by
4392:
A JEDEC standard for measuring the junction-to-case thermal resistance (JESD51-14) is relatively newcomer, having been published in late 2010; it concerns only packages having a single heat flow and an exposed cooling surface.
6224:
1876:
530:. The higher the thermal insulance, the better a material insulates against heat transfer. It is commonly used in construction to assess the insulation properties of materials such as walls, roofs, and insulation products.
3417:
3489:
4599:
3865:
3564:
6336:
5067:
614:
design: Thermal conductance is important for designing cookware to ensure even heat distribution and cooking efficiency. Assessing thermal conductance is important in designing cookware for even heat distribution.
3755:{\displaystyle {\dot {Q}}={{125\ ^{\circ }{\text{C}}-(21\ ^{\circ }{\text{C}})} \over {1.5\ ^{\circ }{\text{C}}/{\text{W}}+0.1\ ^{\circ }{\text{C}}/{\text{W}}+4\ ^{\circ }{\text{C}}/{\text{W}}}}=18.6\ {\text{W}}}
3772:
This method can be generalized to include any number of layers of heat-conducting materials, simply by adding together the absolute thermal resistances of the layers and the temperature drops across the layers.
2648:
5236:
4707:
4816:
4843:
It is often suitable to assume one-dimensional conditions, although the heat flow is multidimensional. Now, two different circuits may be used for this case. For case (a) (shown in picture), we presume
2515:
3288:
503:) is a measure of a material's resistance to the heat current. It quantifies how effectively a material can resist the transfer of heat through conduction, convection, and radiation. It has the units
6596:
Schweitzer, D.; Pape, H.; Chen, L.; Kutscherauer, R.; Walder, M. (2011). "Transient dual interface measurement — A new JEDEC standard for the measurement of the junction-to-case thermal resistance".
1822:
3346:
4492:
2282:
Consider a component such as a silicon transistor that is bolted to the metal frame of a piece of equipment. The transistor's manufacturer will specify parameters in the datasheet called the
2783:
645:(MRI) machines and laser systems to maintain precise operating temperatures. Ensuring proper thermal management is crucial for the safety and performance of medical devices and laser systems.
5839:
5762:
4229:
2554:
is the absolute thermal resistance of the bond between the transistor's case and the metalwork. This figure depends on the nature of the bond - for example, a thermal bonding pad or
5492:
3221:
2321:
2182:
2143:
2104:
423:) measures the ability of a material or system to conduct heat. It provides insights into the ease with which heat can pass through a particular system. It is measured in units of
2552:
1682:
4005:
2451:
2408:
5679:
5622:
635:
Energy efficiency: In the energy sector, thermal resistance and conductance play a role in designing efficient heat exchangers for power plants and energy-efficient appliances.
6378:
5910:
2361:
4959:
2234:
2065:
1601:
1210:
1184:
1158:
5333:
5285:
4128:
3898:
3765:
This means that the transistor can dissipate about 18 watts before it overheats. A cautious designer would operate the transistor at a lower power level to increase its
2702:
2028:
1997:
1962:
1718:
1637:
2731:
1931:
1077:
4885:
4182:
3169:{\displaystyle {\dot {Q}}_{\rm {max}}={{T_{J{\rm {max}}}-(T_{\rm {amb}}+\Delta T_{\rm {HS}})} \over {R_{\theta {\rm {JC}}}+R_{\theta {\rm {B}}}+R_{\theta {\rm {HA}}}}}}
6803:
6718:
There is a large amount of literature on this topic. In general, works using the term "thermal resistance" are more engineering-oriented, whereas works using the term
6657:
4280:
4153:
3923:
2675:
5900:
5871:
5562:
5533:
5384:
1555:
1132:
1473:
5421:
5355:
5123:
5101:
4907:
1779:
1751:
1439:
1328:
6683:
4306:
4255:
3989:
3967:
3945:
3223:, the maximum power that the transistor can be allowed to dissipate, so they can design the circuit to limit the temperature of the transistor to a safe level.
1531:
1502:
1400:
1376:
1352:
1295:
1271:
1249:
1101:
1044:
1022:
990:
966:
942:
918:
887:
863:
839:
815:
2973:{\displaystyle T_{J{\rm {max}}}-(T_{\rm {amb}}+\Delta T_{\rm {HS}})={\dot {Q}}_{\rm {max}}(R_{\theta {\rm {JC}}}+R_{\theta {\rm {B}}}+R_{\theta {\rm {HA}}})\,}
268:
144:
670:
6090:
2418:
need to consider where the heat goes after that, because we are told that the metalwork will conduct heat fast enough to keep the temperature less than
1831:
763:
and so often use it as an analogy when doing calculations involving thermal resistance. Mechanical and structural engineers are more familiar with
454:
difference (in kelvins) is required to transfer a unit of heat current (in watts) through the material or object. It is essential to optimize the
3353:
3428:
450:) measures the opposition to the heat current in a material or system. It is measured in units of kelvins per watt (K/W) and indicates how much
4520:
3799:
3500:
6235:
6774:
6755:
6736:
6613:
6566:
6541:
6516:
4986:
661:: Researchers use thermal conductance data to develop new materials for various applications, including energy storage and advanced coatings.
596:: Understanding thermal resistance helps in designing energy-efficient buildings with effective insulation materials to reduce heat transfer.
487:
4835:
673:(HVAC): Understanding thermal resistance aids in optimizing heating, ventilation, and air conditioning systems for better energy efficiency.
2565:
59:
2456:
Suppose the engineer wishes to know how much power can be put into the transistor before it overheats. The calculations are as follows.
5133:
620:: In industries like HVAC and chemical processing, heat exchangers use thermal conductance to efficiently transfer heat between fluids.
6641:
483:
3793:, the following equation can be derived, and is valid as long as all of the parameters (x and k) are constant throughout the sample.
4621:
2260:
81:
4729:
397:. Knowledge of these principles is crucial in various scientific, engineering, and everyday applications, from designing efficient
676:
Thermal packaging: Ensuring proper thermal conductance and resistance is crucial for protecting sensitive goods during transport.
632:: Understanding thermal properties is vital for the design of cryogenic systems used in superconductors and medical applications.
406:
2463:
6824:
3232:
5125:
as a variable becomes evident when the rate at which energy is conducted across a cylindrical surface, this is represented as
2238:
1788:
5389:
1605:
682:
systems: Understanding thermal resistance is important in the design of solar collectors and thermal energy storage systems.
3295:
6702:
4509:
Similarly to electrical circuits, the total thermal resistance for steady state conditions can be calculated as follows.
4411:
6582:
754:
5397:
In order to determine the temperature distribution in the cylinder, equation 4 can be solved applying the appropriate
4978:. For a hollow cylinder in steady state conditions with no heat generation, the appropriate form of heat equation is
2739:
700:: Infrared cameras and thermal imaging devices use principles of thermal conductance to detect temperature variations.
2223:
688:
processes: Controlling thermal conductance is essential in processes like welding, heat treatment, and metal casting.
52:
46:
6431:
5767:
5690:
5287:
is the area that is normal to the direction of where the heat transfer occurs. Equation 1 implies that the quantity
4374:
has a standard (number JESD51-2) for measuring the junction-to-air thermal resistance of electronics packages under
5103:
is treated as a variable. Considering the appropriate form of
Fourier's law, the physical significance of treating
1641:
642:
4197:
2242:
2227:
6797:
63:
6819:
4909:. When the multidimensional effects becomes more significant, these differences are increased with increasing
4386:
5431:
4090:{\displaystyle R_{\theta }={\frac {\Delta x}{A\phi _{q}}}{\frac {\Delta T}{\Delta x}}={\frac {\Delta T}{q}}}
3766:
3182:
1535:
2289:
2150:
2111:
2072:
2523:
1646:
1453:
1380:
386:
6709:, Fort Collins, Colorado. Example thermal resistance and power dissipation calculation in semiconductors.
6670:, F. Molaei. “Interfacial thermal resistance engineering for polyaniline (C3N)-graphene heterostructure”,
6064:{\displaystyle {T(r)={T_{s,1}-T_{s,2} \over {\ln(r_{1}/r_{2})}}\ln \left({r \over r_{2}}\right)+T_{s,2}}}
2421:
2378:
2371:. For simplicity, let us assume that the designer decides to bolt the transistor to a metal surface (or
5627:
5570:
2368:
1506:
1275:
1081:
898:
664:
611:
6791:
1443:
6341:
2326:
6719:
6463:
6452:"Ten Years of Boundary-Condition- Independent Compact Thermal Modeling of Electronic Parts: A Review"
6394:
4970:
4912:
1965:
1511:
1356:
722:
523:
497:
471:
370:
261:
137:
6399:
6389:
2035:
1448:
599:
593:
467:
455:
398:
347:
6722:
are more physics-oriented. The following books are representative, but may be easily substituted.
1569:
1193:
1167:
1141:
6651:
6481:
5398:
5290:
5253:
4375:
4106:
3876:
2680:
2004:
1973:
1938:
1691:
1610:
1112:
1048:
970:
694:: Assessing thermal conductance is important in geothermal heat exchangers and energy production.
436:
410:
402:
17:
4852:
surfaces parallel to the x- direction. We may obtain different results for the total resistance
2707:
1907:
1893:
1053:
6508:
4855:
4160:
6770:
6751:
6732:
6637:
6609:
6562:
6537:
6512:
4501:
4379:
4309:
4262:
4135:
3905:
2657:
1332:
795:
750:
691:
658:
605:
515:
394:
382:
6418:
Tony Abbey. "Using FEA for
Thermal Analysis". Desktop Engineering magazine. 2014 June. p. 32.
5876:
5847:
5538:
5509:
5360:
1540:
1117:
6601:
6500:
6471:
6229:
Finally, for radial conduction in a cylindrical wall, the thermal resistance is of the form
4975:
1783:
1229:
655:
and cooking and design equipment for food processing, such as ovens and refrigeration units.
6676:
1458:
486:. The relationship between thermal conductance and resistance is analogous to that between
6435:
4257:
is the cross-sectional area (m) perpendicular to the path of heat flow through the sample,
3790:
3786:
1188:
867:
730:
648:
589:
Thermal conductance and resistance have several practical applications in various fields:
432:
378:
6632:
Incropera, Dewitt, Bergman, Lavine, Frank P., David P., Theodore L., Adrienne S. (2013).
5404:
5338:
5106:
5084:
4890:
1758:
1730:
1416:
1307:
6467:
767:
and so often use it as an analogy when doing calculations involving thermal resistance.
330:{\displaystyle {\mathsf {L}}^{-2}{\mathsf {M}}^{-1}{\mathsf {T}}^{3}{\mathsf {\Theta }}}
206:{\displaystyle {\mathsf {L}}^{2}{\mathsf {M}}{\mathsf {T}}^{-3}{\mathsf {\Theta }}^{-1}}
4291:
4240:
3974:
3952:
3930:
2555:
1564:
1516:
1487:
1385:
1361:
1337:
1280:
1256:
1234:
1086:
1029:
1007:
975:
951:
927:
903:
872:
848:
824:
800:
764:
652:
638:
617:
527:
351:
4385:
A JEDEC standard for measuring the junction-to-board thermal resistance (relevant for
4338:
381:. Furthermore, these principles find applications in a multitude of fields, including
361:
are fundamental concepts that describe the ability of materials or systems to conduct
6813:
6501:
6485:
685:
651:: The food industry uses knowledge of thermal conductance to optimize processes like
474:. However, the nature of a material is not the only factor as it also depends on the
374:
343:
4406:
When resistances are in series, the total resistance is the sum of the resistances:
1107:
697:
679:
569:
504:
439:, and various engineering systems where the controlled movement of heat is vital.
366:
249:
125:
6219:{\displaystyle {{\dot {Q}}_{r}={2\pi Lk(T_{s,1}-T_{s,2}) \over \ln(r_{2}/r_{1})}}}
4155:
is the thickness (m) of the sample (measured on a path parallel to the heat flow),
2195:
The diagram shows an equivalent thermal circuit for a semiconductor device with a
1897:
The diagram shows an equivalent thermal circuit for a semiconductor device with a
1826:
1686:
760:
3925:
is the thickness (m) of the sample (measured on a path parallel to the heat flow)
1871:{\displaystyle \mathbf {J} =\sigma \mathbf {E} =-\sigma {\boldsymbol {\nabla }}V}
6605:
6598:
2011 27th Annual IEEE Semiconductor
Thermal Measurement and Management Symposium
4969:
Spherical and cylindrical systems may be treated as one-dimensional, due to the
2323:), and the maximum allowable temperature of the semiconductor junction (symbol:
2212:
1411:
1406:
1219:
946:
729:
unit of absolute thermal resistance is kelvins per watt (K/W) or the equivalent
710:
512:
458:, evaluate the efficiency of electronic devices, and enhance the performance of
451:
390:
4848:
surfaces for those normal to the x- direction, whereas for case (b) we presume
6476:
6451:
4845:
629:
459:
4849:
4185:
4130:
is the absolute thermal resistance (K/W) across the thickness of the sample,
3996:
3492:
2372:
2364:
2196:
1898:
1482:
1162:
893:
623:
558:
3900:
is the absolute thermal resistance (K/W) across the thickness of the sample
3412:{\displaystyle R_{\theta {\rm {JC}}}=1.5\ ^{\circ }{\text{C}}/{\text{W}}\,}
4887:
and the actual corresponding values of the heat transfer are bracketed by
3484:{\displaystyle R_{\theta {\rm {B}}}=0.1\ ^{\circ }{\text{C}}/{\text{W}}\,}
6687:
6627:
6625:
6427:
4594:{\displaystyle {{1 \over R_{\rm {tot}}}={1 \over R_{B}}+{1 \over R_{C}}}}
3860:{\displaystyle R_{\theta }={\frac {\Delta x}{Ak}}={\frac {\Delta xr}{A}}}
3559:{\displaystyle R_{\theta {\rm {HA}}}=4\ ^{\circ }{\text{C}}/{\text{W}}\,}
1223:
1136:
922:
790:
554:
508:
369:. The ability to manipulate these properties allows engineers to control
6331:{\displaystyle {R_{t,\mathrm {cond} }={\ln(r_{2}/r_{1}) \over 2\pi Lk}}}
5393:
Hollow cylinder with convective surface conditions in thermal conduction
6695:
5062:{\displaystyle {{1 \over r}{d \over dr}\left(kr{dT \over dr}\right)=0}}
3991:
is the cross-sectional area (m) perpendicular to the path of heat flow.
733:
per watt (°C/W) – the two are the same since the intervals are equal: Δ
238:
114:
6691:
4283:
4232:
3420:
819:
428:
2643:{\displaystyle T_{J{\rm {max}}}-(T_{\rm {amb}}+\Delta T_{\rm {HS}})}
5388:
4834:
4500:
4371:
2106:
is the device's absolute thermal resistance from junction to case.
1892:
1002:
479:
6767:
Advanced
Materials for Thermal Management of Electronic Packaging
5231:{\displaystyle {q_{r}=-kA{dT \over dr}=-k(2\pi rL){dT \over dr}}}
2145:
is the absolute thermal resistance from the case to the heatsink.
4313:
4189:
996:
843:
718:
714:
519:
475:
424:
362:
4839:
Equivalent thermal circuits for series-parallel composite wall
4702:{\displaystyle {R_{\rm {tot}}={R_{B}R_{C} \over R_{B}+R_{C}}}}
4333:
2206:
537:
31:
6682:
Michael Lenz, GĂĽnther
Striedl, Ulrich Fröhler (January 2000)
4811:{\displaystyle {R_{t,{\rm {cond}}}={L \over (k_{b}+k_{c})A}}}
4721:
With terms for the thermal resistance for conduction, we get
4378:
and another standard (number JESD51-6) for measurement under
2460:
Total absolute thermal resistance from junction to ambient =
3995:
In terms of the temperature gradient across the sample and
726:
641:: Thermal management is crucial for medical equipment like
6729:
5357:, it follows from equation 5 that the heat transfer rate,
2510:{\displaystyle R_{\theta {\rm {JC}}}+R_{\theta {\rm {B}}}}
3283:{\displaystyle T_{J{\rm {max}}}=125\ ^{\circ }{\text{C}}}
2558:
might be used to reduce the absolute thermal resistance.
409:
in industrial processes to optimizing the performance of
6636:. John Wiley & Sons; 7th Edition, Interna edition.
5506:
Using the following boundary conditions, the constants
4350:
2654:
We use the general principle that the temperature drop
1817:{\displaystyle \mathbf {q} =-k{\boldsymbol {\nabla }}T}
565:
6561:. Springer Science & Business Media. p. 247.
5902:
and substituting into the general solution, we obtain
2789:
Substituting our own symbols into this formula gives:
6706:
6344:
6238:
6093:
5913:
5879:
5850:
5770:
5693:
5630:
5573:
5541:
5512:
5434:
5407:
5363:
5341:
5293:
5256:
5136:
5109:
5087:
4989:
4915:
4893:
4858:
4732:
4624:
4523:
4414:
4294:
4265:
4243:
4200:
4163:
4138:
4109:
4008:
3977:
3955:
3933:
3908:
3879:
3802:
3579:
3566:(a typical value for a heatsink for a TO-220 package)
3503:
3431:
3356:
3341:{\displaystyle T_{\rm {amb}}=21\ ^{\circ }{\text{C}}}
3298:
3235:
3185:
2993:
2798:
2742:
2710:
2683:
2660:
2568:
2526:
2466:
2424:
2381:
2329:
2292:
2153:
2114:
2075:
2038:
2007:
1976:
1941:
1910:
1834:
1791:
1761:
1733:
1694:
1649:
1613:
1572:
1543:
1519:
1490:
1461:
1419:
1388:
1364:
1340:
1310:
1283:
1259:
1237:
1196:
1170:
1144:
1120:
1089:
1056:
1032:
1010:
978:
954:
930:
906:
875:
851:
827:
803:
271:
147:
2562:
Maximum temperature drop from junction to ambient =
2184:
is the absolute thermal resistance of the heat sink.
4487:{\displaystyle R_{\rm {tot}}=R_{A}+R_{B}+R_{C}+...}
3947:
is the thermal conductivity (W/(K·m)) of the sample
2030:
is the temperature where the heat sink is attached.
260:
247:
237:
225:
220:
136:
123:
113:
101:
96:
6507:. Springer Science & Business Media. pp.
6372:
6330:
6218:
6063:
5894:
5865:
5833:
5756:
5673:
5616:
5556:
5527:
5486:
5415:
5378:
5349:
5327:
5279:
5230:
5117:
5095:
5061:
4953:
4901:
4879:
4810:
4701:
4593:
4486:
4300:
4274:
4249:
4223:
4176:
4147:
4122:
4089:
3983:
3961:
3939:
3917:
3892:
3859:
3754:
3558:
3483:
3411:
3348:(a typical specification for commercial equipment)
3340:
3282:
3215:
3168:
2972:
2777:
2725:
2696:
2669:
2642:
2546:
2509:
2445:
2402:
2355:
2315:
2176:
2137:
2098:
2059:
2022:
1991:
1956:
1925:
1870:
1816:
1773:
1745:
1712:
1676:
1631:
1595:
1549:
1525:
1496:
1467:
1433:
1394:
1370:
1346:
1322:
1289:
1265:
1243:
1204:
1178:
1152:
1126:
1095:
1071:
1038:
1016:
984:
960:
936:
912:
881:
857:
833:
809:
329:
205:
2284:absolute thermal resistance from junction to case
6748:Heat Transfer: Thermal Management of Electronics
6534:Heat Transfer: Thermal Management of Electronics
3969:is the thermal resistivity (K·m/W) of the sample
2778:{\displaystyle \Delta T={\dot {Q}}R_{\theta }\,}
6701:Directed Energy, Inc./IXYSRF (March 31, 2003)
6583:"Experiment vs. Simulation, Part 3: JESD51-14"
5834:{\displaystyle {T_{s,2}=C_{1}\ln r_{2}+C_{2}}}
5757:{\displaystyle {T_{s,1}=C_{1}\ln r_{1}+C_{2}}}
4505:Parallel thermal resistance in composite walls
3781:Derived from Fourier's law for heat conduction
6499:Ho-Ming Tong; Yi-Shao Lai; C.P. Wong (2013).
1884:Explanation from an electronics point of view
713:difference across a structure when a unit of
8:
6703:R Theta And Power Dissipation Technical Note
6656:: CS1 maint: multiple names: authors list (
4224:{\displaystyle {\frac {\Delta T}{\Delta x}}}
2453:above ambient: this is all we need to know.
6792:Thermal Management for Electronic Packaging
6557:Clemens J.M. Lasance; András Poppe (2013).
4321:Problems with electrical resistance analogy
2677:across a given absolute thermal resistance
2241:. Unsourced material may be challenged and
2272:
671:Heating, ventilation, and air conditioning
482:of an object because these properties are
6769:. Springer Science & Business Media.
6731:. Springer Science & Business Media.
6475:
6445:
6443:
6363:
6350:
6345:
6343:
6301:
6292:
6286:
6270:
6251:
6244:
6239:
6237:
6203:
6194:
6188:
6158:
6139:
6117:
6108:
6097:
6096:
6094:
6092:
6048:
6029:
6020:
5998:
5989:
5983:
5969:
5956:
5937:
5930:
5914:
5912:
5885:
5880:
5878:
5856:
5851:
5849:
5824:
5811:
5795:
5776:
5771:
5769:
5747:
5734:
5718:
5699:
5694:
5692:
5658:
5642:
5631:
5629:
5601:
5585:
5574:
5572:
5547:
5542:
5540:
5518:
5513:
5511:
5477:
5455:
5435:
5433:
5408:
5406:
5369:
5364:
5362:
5342:
5340:
5310:
5294:
5292:
5257:
5255:
5207:
5160:
5142:
5137:
5135:
5110:
5108:
5088:
5086:
5027:
5001:
4991:
4990:
4988:
4945:
4939:
4926:
4917:
4916:
4914:
4894:
4892:
4864:
4859:
4857:
4792:
4779:
4766:
4746:
4745:
4738:
4733:
4731:
4689:
4676:
4664:
4654:
4647:
4631:
4630:
4625:
4623:
4582:
4573:
4562:
4553:
4535:
4534:
4525:
4524:
4522:
4466:
4453:
4440:
4420:
4419:
4413:
4293:
4264:
4242:
4201:
4199:
4168:
4162:
4137:
4114:
4108:
4072:
4049:
4040:
4022:
4013:
4007:
3999:through the sample, the relationship is:
3976:
3954:
3932:
3907:
3884:
3878:
3839:
3816:
3807:
3801:
3747:
3730:
3725:
3720:
3714:
3699:
3694:
3689:
3683:
3668:
3663:
3658:
3652:
3644:
3635:
3629:
3611:
3605:
3597:
3595:
3581:
3580:
3578:
3555:
3550:
3545:
3540:
3534:
3513:
3512:
3508:
3502:
3480:
3475:
3470:
3465:
3459:
3441:
3440:
3436:
3430:
3408:
3403:
3398:
3393:
3387:
3366:
3365:
3361:
3355:
3333:
3327:
3304:
3303:
3297:
3275:
3269:
3245:
3244:
3240:
3234:
3200:
3199:
3188:
3187:
3184:
3152:
3151:
3147:
3132:
3131:
3127:
3109:
3108:
3104:
3099:
3085:
3084:
3061:
3060:
3036:
3035:
3031:
3026:
3024:
3008:
3007:
2996:
2995:
2992:
2969:
2955:
2954:
2950:
2935:
2934:
2930:
2912:
2911:
2907:
2887:
2886:
2875:
2874:
2857:
2856:
2833:
2832:
2808:
2807:
2803:
2797:
2774:
2768:
2753:
2752:
2741:
2712:
2711:
2709:
2688:
2682:
2659:
2627:
2626:
2603:
2602:
2578:
2577:
2573:
2567:
2536:
2535:
2531:
2525:
2499:
2498:
2494:
2476:
2475:
2471:
2465:
2433:
2432:
2423:
2390:
2389:
2380:
2339:
2338:
2334:
2328:
2302:
2301:
2297:
2291:
2261:Learn how and when to remove this message
2163:
2162:
2158:
2152:
2124:
2123:
2119:
2113:
2085:
2084:
2080:
2074:
2044:
2043:
2037:
2013:
2012:
2006:
1982:
1981:
1975:
1947:
1946:
1940:
1912:
1911:
1909:
1860:
1846:
1835:
1833:
1806:
1792:
1790:
1760:
1732:
1693:
1660:
1659:
1648:
1612:
1585:
1571:
1542:
1518:
1489:
1460:
1423:
1418:
1387:
1363:
1339:
1309:
1282:
1258:
1236:
1197:
1195:
1171:
1169:
1145:
1143:
1119:
1088:
1058:
1057:
1055:
1031:
1009:
977:
953:
929:
905:
874:
850:
826:
802:
321:
320:
314:
308:
307:
297:
291:
290:
280:
274:
273:
270:
194:
188:
187:
177:
171:
170:
163:
162:
156:
150:
149:
146:
82:Learn how and when to remove this message
769:
431:(W/K). It is essential in the design of
45:This article includes a list of general
6684:Thermal Resistance, Theory and Practice
6559:Thermal Management for LED Applications
6411:
5487:{\displaystyle {T(r)=C_{1}\ln r+C_{2}}}
5386:is a constant in the radial direction.
3780:
3495:heat-transfer pad for a TO-220 package)
3226:Let us substitute some sample numbers:
759:Electrical engineers are familiar with
6649:
3216:{\displaystyle {\dot {Q}}_{\rm {max}}}
2410:above the ambient temperature. Note: T
1933:is the power dissipated by the device.
322:
309:
292:
275:
217:
189:
172:
164:
151:
93:
29:Materials' resistance to heat transfer
2375:) that is guaranteed to be less than
2316:{\displaystyle R_{\theta {\rm {JC}}}}
2177:{\displaystyle R_{\theta {\rm {HA}}}}
2138:{\displaystyle R_{\theta {\rm {CH}}}}
2099:{\displaystyle R_{\theta {\rm {JC}}}}
488:electrical conductance and resistance
365:and the opposition they offer to the
7:
6634:Principles of Heat and Mass Transfer
5904:
5425:
5127:
4980:
4723:
4615:
4514:
2547:{\displaystyle R_{\theta {\rm {B}}}}
2239:adding citations to reliable sources
1677:{\displaystyle \Delta T={\dot {Q}}R}
2446:{\displaystyle \Delta T_{\rm {HS}}}
2403:{\displaystyle \Delta T_{\rm {HS}}}
709:Absolute thermal resistance is the
6673:The Journal of Physical Chemistry,
6261:
6258:
6255:
6252:
5674:{\displaystyle {T(r_{2})=T_{s,2}}}
5617:{\displaystyle {T(r_{1})=T_{s,1}}}
4756:
4753:
4750:
4747:
4638:
4635:
4632:
4542:
4539:
4536:
4427:
4424:
4421:
4389:) has been published as JESD51-8.
4266:
4212:
4204:
4139:
4075:
4060:
4052:
4025:
3909:
3842:
3819:
3517:
3514:
3442:
3370:
3367:
3311:
3308:
3305:
3290:(typical for a silicon transistor)
3252:
3249:
3246:
3207:
3204:
3201:
3156:
3153:
3133:
3113:
3110:
3089:
3086:
3077:
3068:
3065:
3062:
3043:
3040:
3037:
3015:
3012:
3009:
2959:
2956:
2936:
2916:
2913:
2894:
2891:
2888:
2861:
2858:
2849:
2840:
2837:
2834:
2815:
2812:
2809:
2743:
2661:
2631:
2628:
2619:
2610:
2607:
2604:
2585:
2582:
2579:
2537:
2500:
2480:
2477:
2437:
2434:
2425:
2394:
2391:
2382:
2346:
2343:
2340:
2306:
2303:
2167:
2164:
2128:
2125:
2089:
2086:
2051:
2048:
2045:
2014:
1983:
1948:
1695:
1650:
1614:
1573:
51:it lacks sufficient corresponding
25:
6798:Update on JEDEC Thermal Standards
4831:Resistance in series and parallel
4613:Simplifying the equation, we get
377:, and maximize the efficiency of
18:Thermal resistance in electronics
6668:10. K Einalipour, S. Sadeghzadeh
6373:{\displaystyle {r_{2}>r_{1}}}
4337:
2356:{\displaystyle T_{J{\rm {max}}}}
2211:
1861:
1847:
1836:
1807:
1793:
1198:
1172:
1146:
717:energy flows through it in unit
542:
36:
6536:. CRC Press. pp. 111–113.
5335:is not dependent of the radius
4954:{\displaystyle {|k_{f}-k_{g}|}}
4282:is the temperature difference (
2367:, or by conduction through the
2067:is the ambient air temperature.
1999:is the temperature at its case.
490:in the domain of electronics.
484:extensive rather than intensive
6307:
6279:
6209:
6181:
6170:
6132:
6004:
5976:
5924:
5918:
5684:The general solution gives us
5648:
5635:
5591:
5578:
5445:
5439:
5321:
5301:
5204:
5189:
4946:
4918:
4798:
4772:
3640:
3619:
3095:
3053:
2966:
2900:
2867:
2825:
2637:
2595:
557:format but may read better as
1:
4512:The total thermal resistance
4231:is the temperature gradient (
2060:{\displaystyle T_{\rm {amb}}}
437:thermally efficient materials
6727:Terry M. Tritt, ed. (2004).
6503:Advanced Flip Chip Packaging
4397:Resistance in composite wall
1596:{\displaystyle \Delta X=F/k}
1561:lumped element linear model
1205:{\displaystyle \mathbf {j} }
1179:{\displaystyle \mathbf {q} }
1153:{\displaystyle \mathbf {v} }
755:Onsager reciprocal relations
507:kelvins per watt (mâ‹…K/W) in
6765:Xingcun Colin Tong (2011).
6606:10.1109/STHERM.2011.5767204
5401:. With the assumption that
5328:{\displaystyle {kr(dT/dr)}}
5280:{\displaystyle {A=2\pi rL}}
4497:Parallel thermal resistance
4123:{\displaystyle R_{\theta }}
3893:{\displaystyle R_{\theta }}
2697:{\displaystyle R_{\theta }}
2023:{\displaystyle T_{\rm {H}}}
1992:{\displaystyle T_{\rm {C}}}
1957:{\displaystyle T_{\rm {J}}}
1889:Equivalent thermal circuits
1713:{\displaystyle \Delta V=IR}
1632:{\displaystyle \Delta P=QR}
721:. It is the reciprocal of
705:Absolute thermal resistance
6841:
6450:Lasance, C. J. M. (2008).
2726:{\displaystyle {\dot {Q}}}
1926:{\displaystyle {\dot {Q}}}
1072:{\displaystyle {\dot {Q}}}
748:
745:Analogies and nomenclature
643:magnetic resonance imaging
462:in various applications.
6477:10.1080/01457630701673188
6456:Heat Transfer Engineering
6428:"The Design of Heatsinks"
4880:{\displaystyle {R_{tot}}}
4177:{\displaystyle \phi _{q}}
2414:appears to be undefined.
1724:distributed linear model
1606:Hagen–Poiseuille equation
6804:Soil Thermal Resistivity
6688:Infineon Technologies AG
6677:10.1021/acs.jpcc.0c02051
4387:surface-mount technology
4275:{\displaystyle \Delta T}
4148:{\displaystyle \Delta x}
3918:{\displaystyle \Delta x}
3491:(a typical value for an
2670:{\displaystyle \Delta T}
737:= 1 K = 1 °C.
6746:Younes Shabany (2011).
6532:Younes Shabany (2011).
5895:{\displaystyle {C_{2}}}
5866:{\displaystyle {C_{1}}}
5557:{\displaystyle {C_{2}}}
5528:{\displaystyle {C_{1}}}
5379:{\displaystyle {q_{r}}}
3179:The designer now knows
2704:with a given heat flow
2556:thermal transfer grease
1642:Newton's law of cooling
1550:{\displaystyle \sigma }
1536:electrical conductivity
1127:{\displaystyle \sigma }
566:converting this section
66:more precise citations.
6825:Electronic engineering
6374:
6332:
6220:
6065:
5896:
5867:
5835:
5758:
5675:
5618:
5558:
5529:
5488:
5417:
5394:
5380:
5351:
5329:
5281:
5232:
5119:
5097:
5063:
4955:
4903:
4881:
4840:
4812:
4703:
4595:
4506:
4488:
4302:
4276:
4251:
4235:·m) across the sample,
4225:
4178:
4149:
4124:
4091:
3985:
3963:
3941:
3919:
3894:
3861:
3756:
3560:
3485:
3413:
3342:
3284:
3217:
3170:
2974:
2779:
2727:
2698:
2671:
2644:
2548:
2511:
2447:
2404:
2357:
2317:
2188:
2178:
2139:
2100:
2061:
2024:
1993:
1958:
1927:
1872:
1818:
1775:
1747:
1714:
1678:
1633:
1597:
1551:
1527:
1498:
1469:
1454:electrical resistivity
1435:
1396:
1381:electrical conductance
1372:
1348:
1324:
1291:
1267:
1245:
1206:
1180:
1154:
1128:
1097:
1073:
1040:
1018:
986:
962:
938:
914:
883:
859:
835:
811:
534:Practical applications
387:mechanical engineering
331:
207:
6375:
6333:
6221:
6066:
5897:
5868:
5836:
5759:
5676:
5619:
5559:
5530:
5489:
5418:
5392:
5381:
5352:
5330:
5282:
5233:
5120:
5098:
5064:
4971:temperature gradients
4956:
4904:
4882:
4838:
4813:
4704:
4596:
4504:
4489:
4402:Resistances in series
4330:Measurement standards
4316:) through the sample.
4303:
4277:
4252:
4226:
4179:
4150:
4125:
4092:
3986:
3964:
3942:
3920:
3895:
3862:
3757:
3561:
3486:
3414:
3343:
3285:
3218:
3171:
2975:
2780:
2728:
2699:
2672:
2645:
2549:
2512:
2448:
2405:
2369:printed circuit board
2358:
2318:
2179:
2140:
2101:
2062:
2025:
1994:
1959:
1928:
1896:
1873:
1819:
1776:
1748:
1715:
1679:
1634:
1598:
1552:
1528:
1499:
1470:
1468:{\displaystyle \rho }
1436:
1397:
1373:
1349:
1325:
1292:
1276:electrical resistance
1268:
1246:
1207:
1181:
1155:
1129:
1098:
1074:
1041:
1019:
987:
963:
939:
915:
884:
860:
836:
812:
665:Environmental science
355:, thermal conductance
332:
243:kelvin per watt (K/W)
208:
119:watt per kelvin (W/K)
6720:thermal conductivity
6395:Thermal design power
6342:
6236:
6091:
5911:
5877:
5848:
5768:
5691:
5628:
5571:
5539:
5510:
5432:
5405:
5361:
5339:
5291:
5254:
5134:
5107:
5085:
4987:
4913:
4891:
4856:
4730:
4622:
4521:
4412:
4292:
4286:) across the sample,
4263:
4241:
4198:
4188:through the sample (
4161:
4136:
4107:
4006:
3975:
3953:
3931:
3906:
3877:
3800:
3577:
3570:The result is then:
3501:
3429:
3354:
3296:
3233:
3183:
2991:
2796:
2740:
2708:
2681:
2658:
2566:
2524:
2464:
2422:
2379:
2327:
2290:
2235:improve this section
2151:
2112:
2073:
2036:
2005:
1974:
1966:junction temperature
1939:
1908:
1832:
1789:
1759:
1731:
1692:
1647:
1611:
1570:
1541:
1517:
1512:thermal conductivity
1488:
1459:
1417:
1386:
1362:
1338:
1308:
1281:
1257:
1235:
1194:
1168:
1142:
1118:
1087:
1054:
1030:
1008:
976:
952:
928:
904:
873:
849:
825:
801:
524:British thermal unit
371:temperature gradient
269:
145:
6806:for power companies
6790:Guoping Xu (2006),
6468:2008HTrEn..29..149L
6400:Safe operating area
6390:Thermal engineering
5416:{\displaystyle {k}}
5399:boundary conditions
5350:{\displaystyle {r}}
5118:{\displaystyle {k}}
5096:{\displaystyle {k}}
4902:{\displaystyle {q}}
2203:Example calculation
1774:{\displaystyle ...}
1746:{\displaystyle ...}
1449:thermal resistivity
1434:{\displaystyle 1/k}
1357:thermal conductance
1323:{\displaystyle ...}
1253:thermal resistance
785:electrical analogy
776:structural analogy
723:thermal conductance
600:Electronics cooling
594:Building insulation
456:building insulation
417:Thermal conductance
399:temperature control
348:thermal engineering
97:Thermal conductance
6802:The importance of
6794:, Sun Microsystems
6434:2016-09-05 at the
6370:
6328:
6216:
6061:
5892:
5863:
5831:
5754:
5671:
5614:
5554:
5525:
5484:
5413:
5395:
5376:
5347:
5325:
5277:
5228:
5115:
5093:
5059:
4951:
4899:
4877:
4841:
4808:
4699:
4591:
4507:
4484:
4376:natural convection
4349:. You can help by
4298:
4272:
4247:
4221:
4174:
4145:
4120:
4087:
3981:
3959:
3937:
3915:
3890:
3857:
3752:
3556:
3481:
3409:
3338:
3280:
3213:
3166:
2984:and, rearranging,
2970:
2775:
2723:
2694:
2667:
2640:
2544:
2507:
2443:
2400:
2353:
2313:
2189:
2174:
2135:
2096:
2057:
2020:
1989:
1954:
1923:
1868:
1814:
1771:
1743:
1710:
1674:
1629:
1593:
1547:
1523:
1507:fluid conductivity
1494:
1465:
1431:
1392:
1368:
1344:
1320:
1287:
1263:
1241:
1202:
1176:
1150:
1124:
1093:
1069:
1049:heat transfer rate
1036:
1014:
982:
958:
934:
910:
879:
855:
831:
807:
779:hydraulic analogy
568:, if appropriate.
444:thermal resistance
411:electronic devices
407:thermal management
403:thermal insulation
359:thermal resistance
327:
251:SI base units
221:Thermal resistance
203:
127:SI base units
6776:978-1-4419-7759-5
6757:978-1-4398-1468-0
6738:978-0-306-48327-1
6615:978-1-61284-740-5
6568:978-1-4614-5091-7
6543:978-1-4398-1468-0
6518:978-1-4419-5768-9
6325:
6213:
6105:
6081:
6080:
6035:
6008:
5504:
5503:
5248:
5247:
5225:
5178:
5079:
5078:
5045:
5014:
4999:
4828:
4827:
4805:
4719:
4718:
4696:
4611:
4610:
4588:
4568:
4548:
4380:forced convection
4367:
4366:
4310:rate of heat flow
4301:{\displaystyle q}
4250:{\displaystyle A}
4219:
4085:
4067:
4047:
3984:{\displaystyle A}
3962:{\displaystyle r}
3940:{\displaystyle k}
3855:
3834:
3778:
3777:
3750:
3746:
3736:
3733:
3723:
3713:
3702:
3692:
3682:
3671:
3661:
3651:
3638:
3628:
3614:
3604:
3589:
3553:
3543:
3533:
3478:
3468:
3458:
3406:
3396:
3386:
3336:
3326:
3278:
3268:
3196:
3164:
3004:
2883:
2761:
2720:
2271:
2270:
2263:
1920:
1881:
1880:
1668:
1526:{\displaystyle k}
1497:{\displaystyle k}
1444:fluid resistivity
1395:{\displaystyle G}
1371:{\displaystyle G}
1347:{\displaystyle G}
1333:fluid conductance
1290:{\displaystyle R}
1266:{\displaystyle R}
1244:{\displaystyle R}
1096:{\displaystyle I}
1066:
1039:{\displaystyle Q}
1017:{\displaystyle F}
985:{\displaystyle V}
961:{\displaystyle T}
937:{\displaystyle P}
913:{\displaystyle X}
882:{\displaystyle q}
858:{\displaystyle Q}
834:{\displaystyle V}
810:{\displaystyle J}
751:analogical models
692:Geothermal energy
659:Materials science
606:Automotive design
587:
586:
526:(ft⋅°F⋅h/Btu) in
516:degree Fahrenheit
494:Thermal insulance
395:energy management
383:materials science
340:
339:
216:
215:
92:
91:
84:
16:(Redirected from
6832:
6780:
6761:
6742:
6662:
6661:
6655:
6647:
6629:
6620:
6619:
6593:
6587:
6586:
6579:
6573:
6572:
6554:
6548:
6547:
6529:
6523:
6522:
6506:
6496:
6490:
6489:
6479:
6447:
6438:
6425:
6419:
6416:
6379:
6377:
6376:
6371:
6369:
6368:
6367:
6355:
6354:
6337:
6335:
6334:
6329:
6327:
6326:
6324:
6310:
6306:
6305:
6296:
6291:
6290:
6271:
6266:
6265:
6264:
6225:
6223:
6222:
6217:
6215:
6214:
6212:
6208:
6207:
6198:
6193:
6192:
6173:
6169:
6168:
6150:
6149:
6118:
6113:
6112:
6107:
6106:
6098:
6070:
6068:
6067:
6062:
6060:
6059:
6058:
6040:
6036:
6034:
6033:
6021:
6009:
6007:
6003:
6002:
5993:
5988:
5987:
5968:
5967:
5966:
5948:
5947:
5931:
5905:
5901:
5899:
5898:
5893:
5891:
5890:
5889:
5872:
5870:
5869:
5864:
5862:
5861:
5860:
5840:
5838:
5837:
5832:
5830:
5829:
5828:
5816:
5815:
5800:
5799:
5787:
5786:
5763:
5761:
5760:
5755:
5753:
5752:
5751:
5739:
5738:
5723:
5722:
5710:
5709:
5680:
5678:
5677:
5672:
5670:
5669:
5668:
5647:
5646:
5623:
5621:
5620:
5615:
5613:
5612:
5611:
5590:
5589:
5564:can be computed
5563:
5561:
5560:
5555:
5553:
5552:
5551:
5534:
5532:
5531:
5526:
5524:
5523:
5522:
5493:
5491:
5490:
5485:
5483:
5482:
5481:
5460:
5459:
5426:
5422:
5420:
5419:
5414:
5412:
5385:
5383:
5382:
5377:
5375:
5374:
5373:
5356:
5354:
5353:
5348:
5346:
5334:
5332:
5331:
5326:
5324:
5314:
5286:
5284:
5283:
5278:
5276:
5237:
5235:
5234:
5229:
5227:
5226:
5224:
5216:
5208:
5179:
5177:
5169:
5161:
5147:
5146:
5128:
5124:
5122:
5121:
5116:
5114:
5102:
5100:
5099:
5094:
5092:
5068:
5066:
5065:
5060:
5058:
5051:
5047:
5046:
5044:
5036:
5028:
5015:
5013:
5002:
5000:
4992:
4981:
4960:
4958:
4957:
4952:
4950:
4949:
4944:
4943:
4931:
4930:
4921:
4908:
4906:
4905:
4900:
4898:
4886:
4884:
4883:
4878:
4876:
4875:
4874:
4817:
4815:
4814:
4809:
4807:
4806:
4804:
4797:
4796:
4784:
4783:
4767:
4762:
4761:
4760:
4759:
4724:
4708:
4706:
4705:
4700:
4698:
4697:
4695:
4694:
4693:
4681:
4680:
4670:
4669:
4668:
4659:
4658:
4648:
4643:
4642:
4641:
4616:
4600:
4598:
4597:
4592:
4590:
4589:
4587:
4586:
4574:
4569:
4567:
4566:
4554:
4549:
4547:
4546:
4545:
4526:
4515:
4493:
4491:
4490:
4485:
4471:
4470:
4458:
4457:
4445:
4444:
4432:
4431:
4430:
4362:
4359:
4341:
4334:
4307:
4305:
4304:
4299:
4281:
4279:
4278:
4273:
4256:
4254:
4253:
4248:
4230:
4228:
4227:
4222:
4220:
4218:
4210:
4202:
4183:
4181:
4180:
4175:
4173:
4172:
4154:
4152:
4151:
4146:
4129:
4127:
4126:
4121:
4119:
4118:
4096:
4094:
4093:
4088:
4086:
4081:
4073:
4068:
4066:
4058:
4050:
4048:
4046:
4045:
4044:
4031:
4023:
4018:
4017:
3990:
3988:
3987:
3982:
3968:
3966:
3965:
3960:
3946:
3944:
3943:
3938:
3924:
3922:
3921:
3916:
3899:
3897:
3896:
3891:
3889:
3888:
3866:
3864:
3863:
3858:
3856:
3851:
3840:
3835:
3833:
3825:
3817:
3812:
3811:
3761:
3759:
3758:
3753:
3751:
3748:
3744:
3737:
3735:
3734:
3731:
3729:
3724:
3721:
3719:
3718:
3711:
3703:
3700:
3698:
3693:
3690:
3688:
3687:
3680:
3672:
3669:
3667:
3662:
3659:
3657:
3656:
3649:
3643:
3639:
3636:
3634:
3633:
3626:
3615:
3612:
3610:
3609:
3602:
3596:
3591:
3590:
3582:
3565:
3563:
3562:
3557:
3554:
3551:
3549:
3544:
3541:
3539:
3538:
3531:
3523:
3522:
3521:
3520:
3490:
3488:
3487:
3482:
3479:
3476:
3474:
3469:
3466:
3464:
3463:
3456:
3448:
3447:
3446:
3445:
3418:
3416:
3415:
3410:
3407:
3404:
3402:
3397:
3394:
3392:
3391:
3384:
3376:
3375:
3374:
3373:
3347:
3345:
3344:
3339:
3337:
3334:
3332:
3331:
3324:
3316:
3315:
3314:
3289:
3287:
3286:
3281:
3279:
3276:
3274:
3273:
3266:
3258:
3257:
3256:
3255:
3222:
3220:
3219:
3214:
3212:
3211:
3210:
3198:
3197:
3189:
3175:
3173:
3172:
3167:
3165:
3163:
3162:
3161:
3160:
3159:
3139:
3138:
3137:
3136:
3119:
3118:
3117:
3116:
3098:
3094:
3093:
3092:
3073:
3072:
3071:
3049:
3048:
3047:
3046:
3025:
3020:
3019:
3018:
3006:
3005:
2997:
2979:
2977:
2976:
2971:
2965:
2964:
2963:
2962:
2942:
2941:
2940:
2939:
2922:
2921:
2920:
2919:
2899:
2898:
2897:
2885:
2884:
2876:
2866:
2865:
2864:
2845:
2844:
2843:
2821:
2820:
2819:
2818:
2784:
2782:
2781:
2776:
2773:
2772:
2763:
2762:
2754:
2732:
2730:
2729:
2724:
2722:
2721:
2713:
2703:
2701:
2700:
2695:
2693:
2692:
2676:
2674:
2673:
2668:
2649:
2647:
2646:
2641:
2636:
2635:
2634:
2615:
2614:
2613:
2591:
2590:
2589:
2588:
2553:
2551:
2550:
2545:
2543:
2542:
2541:
2540:
2516:
2514:
2513:
2508:
2506:
2505:
2504:
2503:
2486:
2485:
2484:
2483:
2452:
2450:
2449:
2444:
2442:
2441:
2440:
2409:
2407:
2406:
2401:
2399:
2398:
2397:
2362:
2360:
2359:
2354:
2352:
2351:
2350:
2349:
2322:
2320:
2319:
2314:
2312:
2311:
2310:
2309:
2273:
2266:
2259:
2255:
2252:
2246:
2215:
2207:
2183:
2181:
2180:
2175:
2173:
2172:
2171:
2170:
2144:
2142:
2141:
2136:
2134:
2133:
2132:
2131:
2105:
2103:
2102:
2097:
2095:
2094:
2093:
2092:
2066:
2064:
2063:
2058:
2056:
2055:
2054:
2029:
2027:
2026:
2021:
2019:
2018:
2017:
1998:
1996:
1995:
1990:
1988:
1987:
1986:
1963:
1961:
1960:
1955:
1953:
1952:
1951:
1932:
1930:
1929:
1924:
1922:
1921:
1913:
1877:
1875:
1874:
1869:
1864:
1850:
1839:
1823:
1821:
1820:
1815:
1810:
1796:
1780:
1778:
1777:
1772:
1752:
1750:
1749:
1744:
1719:
1717:
1716:
1711:
1683:
1681:
1680:
1675:
1670:
1669:
1661:
1638:
1636:
1635:
1630:
1602:
1600:
1599:
1594:
1589:
1556:
1554:
1553:
1548:
1532:
1530:
1529:
1524:
1503:
1501:
1500:
1495:
1474:
1472:
1471:
1466:
1440:
1438:
1437:
1432:
1427:
1401:
1399:
1398:
1393:
1377:
1375:
1374:
1369:
1353:
1351:
1350:
1345:
1329:
1327:
1326:
1321:
1296:
1294:
1293:
1288:
1272:
1270:
1269:
1264:
1250:
1248:
1247:
1242:
1230:fluid resistance
1211:
1209:
1208:
1203:
1201:
1185:
1183:
1182:
1177:
1175:
1159:
1157:
1156:
1151:
1149:
1133:
1131:
1130:
1125:
1102:
1100:
1099:
1094:
1078:
1076:
1075:
1070:
1068:
1067:
1059:
1045:
1043:
1042:
1037:
1023:
1021:
1020:
1015:
991:
989:
988:
983:
967:
965:
964:
959:
943:
941:
940:
935:
919:
917:
916:
911:
888:
886:
885:
880:
864:
862:
861:
856:
840:
838:
837:
832:
816:
814:
813:
808:
770:
582:
579:
573:
564:You can help by
546:
545:
538:
336:
334:
333:
328:
326:
325:
319:
318:
313:
312:
305:
304:
296:
295:
288:
287:
279:
278:
252:
233:
218:
212:
210:
209:
204:
202:
201:
193:
192:
185:
184:
176:
175:
168:
167:
161:
160:
155:
154:
128:
109:
94:
87:
80:
76:
73:
67:
62:this article by
53:inline citations
40:
39:
32:
21:
6840:
6839:
6835:
6834:
6833:
6831:
6830:
6829:
6820:Heat conduction
6810:
6809:
6787:
6777:
6764:
6758:
6745:
6739:
6726:
6716:
6714:Further reading
6666:
6665:
6648:
6644:
6631:
6630:
6623:
6616:
6600:. p. 222.
6595:
6594:
6590:
6581:
6580:
6576:
6569:
6556:
6555:
6551:
6544:
6531:
6530:
6526:
6519:
6498:
6497:
6493:
6449:
6448:
6441:
6436:Wayback Machine
6426:
6422:
6417:
6413:
6408:
6386:
6359:
6346:
6340:
6339:
6311:
6297:
6282:
6272:
6240:
6234:
6233:
6199:
6184:
6174:
6154:
6135:
6119:
6095:
6089:
6088:
6044:
6025:
6016:
5994:
5979:
5952:
5933:
5932:
5909:
5908:
5881:
5875:
5874:
5852:
5846:
5845:
5820:
5807:
5791:
5772:
5766:
5765:
5743:
5730:
5714:
5695:
5689:
5688:
5654:
5638:
5626:
5625:
5597:
5581:
5569:
5568:
5543:
5537:
5536:
5514:
5508:
5507:
5473:
5451:
5430:
5429:
5403:
5402:
5365:
5359:
5358:
5337:
5336:
5289:
5288:
5252:
5251:
5217:
5209:
5170:
5162:
5138:
5132:
5131:
5105:
5104:
5083:
5082:
5037:
5029:
5020:
5016:
5006:
4985:
4984:
4967:
4935:
4922:
4911:
4910:
4889:
4888:
4860:
4854:
4853:
4833:
4788:
4775:
4771:
4734:
4728:
4727:
4685:
4672:
4671:
4660:
4650:
4649:
4626:
4620:
4619:
4578:
4558:
4530:
4519:
4518:
4499:
4462:
4449:
4436:
4415:
4410:
4409:
4404:
4399:
4363:
4357:
4354:
4347:needs expansion
4332:
4323:
4290:
4289:
4261:
4260:
4239:
4238:
4211:
4203:
4196:
4195:
4164:
4159:
4158:
4134:
4133:
4110:
4105:
4104:
4074:
4059:
4051:
4036:
4032:
4024:
4009:
4004:
4003:
3973:
3972:
3951:
3950:
3929:
3928:
3904:
3903:
3880:
3875:
3874:
3841:
3826:
3818:
3803:
3798:
3797:
3791:heat conduction
3783:
3710:
3679:
3648:
3625:
3601:
3575:
3574:
3530:
3504:
3499:
3498:
3455:
3432:
3427:
3426:
3419:(for a typical
3383:
3357:
3352:
3351:
3323:
3299:
3294:
3293:
3265:
3236:
3231:
3230:
3186:
3181:
3180:
3143:
3123:
3100:
3080:
3056:
3027:
2994:
2989:
2988:
2946:
2926:
2903:
2873:
2852:
2828:
2799:
2794:
2793:
2764:
2738:
2737:
2733:through it is:
2706:
2705:
2684:
2679:
2678:
2656:
2655:
2622:
2598:
2569:
2564:
2563:
2527:
2522:
2521:
2490:
2467:
2462:
2461:
2428:
2420:
2419:
2413:
2385:
2377:
2376:
2330:
2325:
2324:
2293:
2288:
2287:
2267:
2256:
2250:
2247:
2232:
2216:
2205:
2187:
2154:
2149:
2148:
2115:
2110:
2109:
2076:
2071:
2070:
2039:
2034:
2033:
2008:
2003:
2002:
1977:
1972:
1971:
1942:
1937:
1936:
1906:
1905:
1891:
1886:
1830:
1829:
1787:
1786:
1757:
1756:
1729:
1728:
1690:
1689:
1645:
1644:
1609:
1608:
1568:
1567:
1539:
1538:
1515:
1514:
1486:
1485:
1457:
1456:
1415:
1414:
1384:
1383:
1360:
1359:
1336:
1335:
1306:
1305:
1279:
1278:
1255:
1254:
1233:
1232:
1192:
1191:
1189:current density
1166:
1165:
1140:
1139:
1116:
1115:
1085:
1084:
1052:
1051:
1028:
1027:
1006:
1005:
974:
973:
950:
949:
926:
925:
902:
901:
871:
870:
847:
846:
823:
822:
799:
798:
757:
749:Main articles:
747:
731:degrees Celsius
707:
698:Thermal imaging
649:Food processing
639:Medical devices
618:Heat exchangers
583:
577:
574:
563:
547:
543:
536:
433:heat exchangers
379:thermal systems
306:
289:
272:
267:
266:
250:
231:
228:
186:
169:
148:
143:
142:
126:
107:
104:
88:
77:
71:
68:
58:Please help to
57:
41:
37:
30:
23:
22:
15:
12:
11:
5:
6838:
6836:
6828:
6827:
6822:
6812:
6811:
6808:
6807:
6800:
6795:
6786:
6785:External links
6783:
6782:
6781:
6775:
6762:
6756:
6743:
6737:
6715:
6712:
6711:
6710:
6699:
6664:
6663:
6643:978-0470646151
6642:
6621:
6614:
6588:
6574:
6567:
6549:
6542:
6524:
6517:
6491:
6462:(2): 149–168.
6439:
6420:
6410:
6409:
6407:
6404:
6403:
6402:
6397:
6392:
6385:
6382:
6381:
6380:
6366:
6362:
6358:
6353:
6349:
6323:
6320:
6317:
6314:
6309:
6304:
6300:
6295:
6289:
6285:
6281:
6278:
6275:
6269:
6263:
6260:
6257:
6254:
6250:
6247:
6243:
6227:
6226:
6211:
6206:
6202:
6197:
6191:
6187:
6183:
6180:
6177:
6172:
6167:
6164:
6161:
6157:
6153:
6148:
6145:
6142:
6138:
6134:
6131:
6128:
6125:
6122:
6116:
6111:
6104:
6101:
6079:
6078:
6073:
6071:
6057:
6054:
6051:
6047:
6043:
6039:
6032:
6028:
6024:
6019:
6015:
6012:
6006:
6001:
5997:
5992:
5986:
5982:
5978:
5975:
5972:
5965:
5962:
5959:
5955:
5951:
5946:
5943:
5940:
5936:
5929:
5926:
5923:
5920:
5917:
5888:
5884:
5859:
5855:
5842:
5841:
5827:
5823:
5819:
5814:
5810:
5806:
5803:
5798:
5794:
5790:
5785:
5782:
5779:
5775:
5750:
5746:
5742:
5737:
5733:
5729:
5726:
5721:
5717:
5713:
5708:
5705:
5702:
5698:
5682:
5681:
5667:
5664:
5661:
5657:
5653:
5650:
5645:
5641:
5637:
5634:
5610:
5607:
5604:
5600:
5596:
5593:
5588:
5584:
5580:
5577:
5550:
5546:
5521:
5517:
5502:
5501:
5496:
5494:
5480:
5476:
5472:
5469:
5466:
5463:
5458:
5454:
5450:
5447:
5444:
5441:
5438:
5411:
5372:
5368:
5345:
5323:
5320:
5317:
5313:
5309:
5306:
5303:
5300:
5297:
5275:
5272:
5269:
5266:
5263:
5260:
5246:
5245:
5240:
5238:
5223:
5220:
5215:
5212:
5206:
5203:
5200:
5197:
5194:
5191:
5188:
5185:
5182:
5176:
5173:
5168:
5165:
5159:
5156:
5153:
5150:
5145:
5141:
5113:
5091:
5077:
5076:
5071:
5069:
5057:
5054:
5050:
5043:
5040:
5035:
5032:
5026:
5023:
5019:
5012:
5009:
5005:
4998:
4995:
4966:
4965:Radial systems
4963:
4948:
4942:
4938:
4934:
4929:
4925:
4920:
4897:
4873:
4870:
4867:
4863:
4832:
4829:
4826:
4825:
4820:
4818:
4803:
4800:
4795:
4791:
4787:
4782:
4778:
4774:
4770:
4765:
4758:
4755:
4752:
4749:
4744:
4741:
4737:
4717:
4716:
4711:
4709:
4692:
4688:
4684:
4679:
4675:
4667:
4663:
4657:
4653:
4646:
4640:
4637:
4634:
4629:
4609:
4608:
4603:
4601:
4585:
4581:
4577:
4572:
4565:
4561:
4557:
4552:
4544:
4541:
4538:
4533:
4529:
4498:
4495:
4483:
4480:
4477:
4474:
4469:
4465:
4461:
4456:
4452:
4448:
4443:
4439:
4435:
4429:
4426:
4423:
4418:
4403:
4400:
4398:
4395:
4365:
4364:
4344:
4342:
4331:
4328:
4322:
4319:
4318:
4317:
4297:
4287:
4271:
4268:
4258:
4246:
4236:
4217:
4214:
4209:
4206:
4193:
4171:
4167:
4156:
4144:
4141:
4131:
4117:
4113:
4098:
4097:
4084:
4080:
4077:
4071:
4065:
4062:
4057:
4054:
4043:
4039:
4035:
4030:
4027:
4021:
4016:
4012:
3993:
3992:
3980:
3970:
3958:
3948:
3936:
3926:
3914:
3911:
3901:
3887:
3883:
3868:
3867:
3854:
3850:
3847:
3844:
3838:
3832:
3829:
3824:
3821:
3815:
3810:
3806:
3782:
3779:
3776:
3775:
3763:
3762:
3743:
3740:
3728:
3717:
3709:
3706:
3697:
3686:
3678:
3675:
3666:
3655:
3647:
3642:
3632:
3624:
3621:
3618:
3608:
3600:
3594:
3588:
3585:
3568:
3567:
3548:
3537:
3529:
3526:
3519:
3516:
3511:
3507:
3496:
3473:
3462:
3454:
3451:
3444:
3439:
3435:
3424:
3401:
3390:
3382:
3379:
3372:
3369:
3364:
3360:
3349:
3330:
3322:
3319:
3313:
3310:
3307:
3302:
3291:
3272:
3264:
3261:
3254:
3251:
3248:
3243:
3239:
3209:
3206:
3203:
3195:
3192:
3177:
3176:
3158:
3155:
3150:
3146:
3142:
3135:
3130:
3126:
3122:
3115:
3112:
3107:
3103:
3097:
3091:
3088:
3083:
3079:
3076:
3070:
3067:
3064:
3059:
3055:
3052:
3045:
3042:
3039:
3034:
3030:
3023:
3017:
3014:
3011:
3003:
3000:
2982:
2981:
2968:
2961:
2958:
2953:
2949:
2945:
2938:
2933:
2929:
2925:
2918:
2915:
2910:
2906:
2902:
2896:
2893:
2890:
2882:
2879:
2872:
2869:
2863:
2860:
2855:
2851:
2848:
2842:
2839:
2836:
2831:
2827:
2824:
2817:
2814:
2811:
2806:
2802:
2787:
2786:
2771:
2767:
2760:
2757:
2751:
2748:
2745:
2719:
2716:
2691:
2687:
2666:
2663:
2652:
2651:
2639:
2633:
2630:
2625:
2621:
2618:
2612:
2609:
2606:
2601:
2597:
2594:
2587:
2584:
2581:
2576:
2572:
2539:
2534:
2530:
2518:
2517:
2502:
2497:
2493:
2489:
2482:
2479:
2474:
2470:
2439:
2436:
2431:
2427:
2411:
2396:
2393:
2388:
2384:
2348:
2345:
2342:
2337:
2333:
2308:
2305:
2300:
2296:
2278:
2277:
2269:
2268:
2219:
2217:
2210:
2204:
2201:
2186:
2185:
2169:
2166:
2161:
2157:
2146:
2130:
2127:
2122:
2118:
2107:
2091:
2088:
2083:
2079:
2068:
2053:
2050:
2047:
2042:
2031:
2016:
2011:
2000:
1985:
1980:
1969:
1968:in the device.
1950:
1945:
1934:
1919:
1916:
1902:
1890:
1887:
1885:
1882:
1879:
1878:
1867:
1863:
1859:
1856:
1853:
1849:
1845:
1842:
1838:
1824:
1813:
1809:
1805:
1802:
1799:
1795:
1781:
1770:
1767:
1764:
1753:
1742:
1739:
1736:
1725:
1721:
1720:
1709:
1706:
1703:
1700:
1697:
1684:
1673:
1667:
1664:
1658:
1655:
1652:
1639:
1628:
1625:
1622:
1619:
1616:
1603:
1592:
1588:
1584:
1581:
1578:
1575:
1562:
1558:
1557:
1546:
1533:
1522:
1509:
1504:
1493:
1480:
1476:
1475:
1464:
1451:
1446:
1441:
1430:
1426:
1422:
1409:
1403:
1402:
1391:
1378:
1367:
1354:
1343:
1330:
1319:
1316:
1313:
1302:
1298:
1297:
1286:
1273:
1262:
1251:
1240:
1227:
1217:
1213:
1212:
1200:
1186:
1174:
1160:
1148:
1134:
1123:
1110:
1104:
1103:
1092:
1079:
1065:
1062:
1046:
1035:
1024:
1013:
999:
993:
992:
981:
968:
957:
944:
933:
920:
909:
896:
890:
889:
878:
865:
854:
841:
830:
817:
806:
793:
787:
786:
783:
780:
777:
774:
746:
743:
706:
703:
702:
701:
695:
689:
683:
677:
674:
668:
662:
656:
653:pasteurization
646:
636:
633:
627:
621:
615:
609:
603:
597:
585:
584:
550:
548:
541:
535:
532:
528:imperial units
352:thermodynamics
338:
337:
324:
317:
311:
303:
300:
294:
286:
283:
277:
264:
258:
257:
254:
245:
244:
241:
235:
234:
229:
227:Common symbols
226:
223:
222:
214:
213:
200:
197:
191:
183:
180:
174:
166:
159:
153:
140:
134:
133:
130:
121:
120:
117:
111:
110:
105:
103:Common symbols
102:
99:
98:
90:
89:
44:
42:
35:
28:
24:
14:
13:
10:
9:
6:
4:
3:
2:
6837:
6826:
6823:
6821:
6818:
6817:
6815:
6805:
6801:
6799:
6796:
6793:
6789:
6788:
6784:
6778:
6772:
6768:
6763:
6759:
6753:
6750:. CRC Press.
6749:
6744:
6740:
6734:
6730:
6725:
6724:
6723:
6721:
6713:
6708:
6704:
6700:
6697:
6693:
6689:
6685:
6681:
6680:
6679:
6678:
6674:
6671:
6659:
6653:
6645:
6639:
6635:
6628:
6626:
6622:
6617:
6611:
6607:
6603:
6599:
6592:
6589:
6585:. 2013-02-22.
6584:
6578:
6575:
6570:
6564:
6560:
6553:
6550:
6545:
6539:
6535:
6528:
6525:
6520:
6514:
6510:
6505:
6504:
6495:
6492:
6487:
6483:
6478:
6473:
6469:
6465:
6461:
6457:
6453:
6446:
6444:
6440:
6437:
6433:
6429:
6424:
6421:
6415:
6412:
6405:
6401:
6398:
6396:
6393:
6391:
6388:
6387:
6383:
6364:
6360:
6356:
6351:
6347:
6321:
6318:
6315:
6312:
6302:
6298:
6293:
6287:
6283:
6276:
6273:
6267:
6248:
6245:
6241:
6232:
6231:
6230:
6204:
6200:
6195:
6189:
6185:
6178:
6175:
6165:
6162:
6159:
6155:
6151:
6146:
6143:
6140:
6136:
6129:
6126:
6123:
6120:
6114:
6109:
6102:
6099:
6087:
6086:
6085:
6077:
6074:
6072:
6055:
6052:
6049:
6045:
6041:
6037:
6030:
6026:
6022:
6017:
6013:
6010:
5999:
5995:
5990:
5984:
5980:
5973:
5970:
5963:
5960:
5957:
5953:
5949:
5944:
5941:
5938:
5934:
5927:
5921:
5915:
5907:
5906:
5903:
5886:
5882:
5857:
5853:
5825:
5821:
5817:
5812:
5808:
5804:
5801:
5796:
5792:
5788:
5783:
5780:
5777:
5773:
5764:and
5748:
5744:
5740:
5735:
5731:
5727:
5724:
5719:
5715:
5711:
5706:
5703:
5700:
5696:
5687:
5686:
5685:
5665:
5662:
5659:
5655:
5651:
5643:
5639:
5632:
5624:and
5608:
5605:
5602:
5598:
5594:
5586:
5582:
5575:
5567:
5566:
5565:
5548:
5544:
5519:
5515:
5500:
5497:
5495:
5478:
5474:
5470:
5467:
5464:
5461:
5456:
5452:
5448:
5442:
5436:
5428:
5427:
5424:
5409:
5400:
5391:
5387:
5370:
5366:
5343:
5318:
5315:
5311:
5307:
5304:
5298:
5295:
5273:
5270:
5267:
5264:
5261:
5258:
5244:
5241:
5239:
5221:
5218:
5213:
5210:
5201:
5198:
5195:
5192:
5186:
5183:
5180:
5174:
5171:
5166:
5163:
5157:
5154:
5151:
5148:
5143:
5139:
5130:
5129:
5126:
5111:
5089:
5075:
5072:
5070:
5055:
5052:
5048:
5041:
5038:
5033:
5030:
5024:
5021:
5017:
5010:
5007:
5003:
4996:
4993:
4983:
4982:
4979:
4977:
4976:Fourier's law
4972:
4964:
4962:
4940:
4936:
4932:
4927:
4923:
4895:
4871:
4868:
4865:
4861:
4851:
4847:
4837:
4830:
4824:
4821:
4819:
4801:
4793:
4789:
4785:
4780:
4776:
4768:
4763:
4742:
4739:
4735:
4726:
4725:
4722:
4715:
4712:
4710:
4690:
4686:
4682:
4677:
4673:
4665:
4661:
4655:
4651:
4644:
4627:
4618:
4617:
4614:
4607:
4604:
4602:
4583:
4579:
4575:
4570:
4563:
4559:
4555:
4550:
4531:
4527:
4517:
4516:
4513:
4510:
4503:
4496:
4494:
4481:
4478:
4475:
4472:
4467:
4463:
4459:
4454:
4450:
4446:
4441:
4437:
4433:
4416:
4407:
4401:
4396:
4394:
4390:
4388:
4383:
4381:
4377:
4373:
4361:
4352:
4348:
4345:This section
4343:
4340:
4336:
4335:
4329:
4327:
4320:
4315:
4311:
4295:
4288:
4285:
4269:
4259:
4244:
4237:
4234:
4215:
4207:
4194:
4191:
4187:
4169:
4165:
4157:
4142:
4132:
4115:
4111:
4103:
4102:
4101:
4082:
4078:
4069:
4063:
4055:
4041:
4037:
4033:
4028:
4019:
4014:
4010:
4002:
4001:
4000:
3998:
3978:
3971:
3956:
3949:
3934:
3927:
3912:
3902:
3885:
3881:
3873:
3872:
3871:
3852:
3848:
3845:
3836:
3830:
3827:
3822:
3813:
3808:
3804:
3796:
3795:
3794:
3792:
3788:
3787:Fourier's Law
3774:
3770:
3768:
3741:
3738:
3726:
3715:
3707:
3704:
3695:
3684:
3676:
3673:
3664:
3653:
3645:
3630:
3622:
3616:
3606:
3598:
3592:
3586:
3583:
3573:
3572:
3571:
3546:
3535:
3527:
3524:
3509:
3505:
3497:
3494:
3471:
3460:
3452:
3449:
3437:
3433:
3425:
3422:
3399:
3388:
3380:
3377:
3362:
3358:
3350:
3328:
3320:
3317:
3300:
3292:
3270:
3262:
3259:
3241:
3237:
3229:
3228:
3227:
3224:
3193:
3190:
3148:
3144:
3140:
3128:
3124:
3120:
3105:
3101:
3081:
3074:
3057:
3050:
3032:
3028:
3021:
3001:
2998:
2987:
2986:
2985:
2951:
2947:
2943:
2931:
2927:
2923:
2908:
2904:
2880:
2877:
2870:
2853:
2846:
2829:
2822:
2804:
2800:
2792:
2791:
2790:
2769:
2765:
2758:
2755:
2749:
2746:
2736:
2735:
2734:
2717:
2714:
2689:
2685:
2664:
2623:
2616:
2599:
2592:
2574:
2570:
2561:
2560:
2559:
2557:
2532:
2528:
2495:
2491:
2487:
2472:
2468:
2459:
2458:
2457:
2454:
2429:
2415:
2386:
2374:
2370:
2366:
2335:
2331:
2298:
2294:
2285:
2280:
2279:
2275:
2274:
2265:
2262:
2254:
2244:
2240:
2236:
2230:
2229:
2225:
2220:This section
2218:
2214:
2209:
2208:
2202:
2200:
2198:
2193:
2159:
2155:
2147:
2120:
2116:
2108:
2081:
2077:
2069:
2040:
2032:
2009:
2001:
1978:
1970:
1967:
1943:
1935:
1917:
1914:
1904:
1903:
1900:
1895:
1888:
1883:
1865:
1857:
1854:
1851:
1843:
1840:
1828:
1825:
1811:
1803:
1800:
1797:
1785:
1784:Fourier's law
1782:
1768:
1765:
1762:
1754:
1740:
1737:
1734:
1726:
1723:
1722:
1707:
1704:
1701:
1698:
1688:
1685:
1671:
1665:
1662:
1656:
1653:
1643:
1640:
1626:
1623:
1620:
1617:
1607:
1604:
1590:
1586:
1582:
1579:
1576:
1566:
1563:
1560:
1559:
1544:
1537:
1534:
1520:
1513:
1510:
1508:
1505:
1491:
1484:
1481:
1479:conductivity
1478:
1477:
1462:
1455:
1452:
1450:
1447:
1445:
1442:
1428:
1424:
1420:
1413:
1410:
1408:
1405:
1404:
1389:
1382:
1379:
1365:
1358:
1355:
1341:
1334:
1331:
1317:
1314:
1311:
1303:
1300:
1299:
1284:
1277:
1274:
1260:
1252:
1238:
1231:
1228:
1225:
1221:
1218:
1215:
1214:
1190:
1187:
1164:
1161:
1138:
1135:
1121:
1114:
1111:
1109:
1106:
1105:
1090:
1083:
1080:
1063:
1060:
1050:
1047:
1033:
1025:
1011:
1004:
1000:
998:
995:
994:
979:
972:
969:
955:
948:
945:
931:
924:
921:
907:
900:
897:
895:
892:
891:
876:
869:
866:
852:
845:
842:
828:
821:
818:
804:
797:
794:
792:
789:
788:
784:
781:
778:
775:
772:
771:
768:
766:
762:
756:
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742:
738:
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732:
728:
724:
720:
716:
712:
704:
699:
696:
693:
690:
687:
686:Manufacturing
684:
681:
678:
675:
672:
669:
666:
663:
660:
657:
654:
650:
647:
644:
640:
637:
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631:
628:
625:
622:
619:
616:
613:
610:
607:
604:
601:
598:
595:
592:
591:
590:
581:
572:is available.
571:
567:
561:
560:
556:
551:This section
549:
540:
539:
533:
531:
529:
525:
521:
517:
514:
510:
506:
502:
500:
495:
491:
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481:
477:
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457:
453:
449:
445:
440:
438:
434:
430:
426:
422:
418:
414:
412:
408:
404:
400:
396:
392:
388:
384:
380:
376:
375:thermal shock
372:
368:
364:
360:
356:
353:
349:
345:
344:heat transfer
315:
301:
298:
284:
281:
265:
263:
259:
255:
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246:
242:
240:
236:
230:
224:
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95:
86:
83:
75:
65:
61:
55:
54:
48:
43:
34:
33:
27:
19:
6766:
6747:
6728:
6717:
6672:
6669:
6667:
6633:
6597:
6591:
6577:
6558:
6552:
6533:
6527:
6502:
6494:
6459:
6455:
6423:
6414:
6228:
6082:
6075:
5844:Solving for
5843:
5683:
5505:
5498:
5423:is constant
5396:
5249:
5242:
5080:
5073:
4968:
4842:
4822:
4720:
4713:
4612:
4605:
4511:
4508:
4408:
4405:
4391:
4384:
4368:
4358:January 2015
4355:
4351:adding to it
4346:
4324:
4099:
3994:
3869:
3784:
3771:
3764:
3569:
3225:
3178:
2983:
2788:
2653:
2519:
2455:
2416:
2283:
2281:
2257:
2251:January 2015
2248:
2233:Please help
2221:
2194:
2192:capacitors.
2190:
1301:conductance
1108:flux density
899:displacement
758:
739:
734:
708:
680:Solar energy
588:
578:October 2023
575:
570:Editing help
552:
505:square metre
498:
493:
492:
472:conductivity
464:
447:
443:
442:Conversely,
441:
420:
416:
415:
367:heat current
358:
354:
341:
239:SI unit
115:SI unit
78:
72:January 2015
69:
50:
26:
3767:reliability
1565:Hooke's law
1412:flexibility
1407:resistivity
1220:flexibility
1216:resistance
947:temperature
765:Hooke's law
711:temperature
513:square foot
468:resistivity
452:temperature
391:electronics
64:introducing
6814:Categories
6675:2020. DOI:
6406:References
6338:such that
4846:isothermal
1226:defined)
1026:flow rate
630:Cryogenics
460:heat sinks
373:, prevent
47:references
6652:cite book
6486:121803741
6316:π
6277:
6179:
6152:−
6124:π
6103:˙
6014:
5974:
5950:−
5805:
5728:
5465:
5268:π
5196:π
5184:−
5152:−
4933:−
4850:adiabatic
4267:Δ
4213:Δ
4205:Δ
4186:heat flux
4166:ϕ
4140:Δ
4116:θ
4076:Δ
4061:Δ
4053:Δ
4038:ϕ
4026:Δ
4015:θ
3997:heat flux
3910:Δ
3886:θ
3843:Δ
3820:Δ
3809:θ
3716:∘
3685:∘
3654:∘
3631:∘
3617:−
3607:∘
3587:˙
3536:∘
3510:θ
3493:elastomer
3461:∘
3438:θ
3389:∘
3363:θ
3329:∘
3271:∘
3194:˙
3149:θ
3129:θ
3106:θ
3078:Δ
3051:−
3002:˙
2952:θ
2932:θ
2909:θ
2881:˙
2850:Δ
2823:−
2770:θ
2759:˙
2744:Δ
2718:˙
2690:θ
2662:Δ
2620:Δ
2593:−
2533:θ
2496:θ
2473:θ
2426:Δ
2383:Δ
2373:heat sink
2365:heat sink
2299:θ
2286:(symbol:
2222:does not
2197:heat sink
2160:θ
2121:θ
2082:θ
1918:˙
1899:heat sink
1862:∇
1858:σ
1855:−
1844:σ
1827:Ohm's law
1808:∇
1801:−
1696:Δ
1687:Ohm's law
1666:˙
1651:Δ
1615:Δ
1574:Δ
1545:σ
1483:stiffness
1463:ρ
1163:heat flux
1122:σ
1064:˙
971:potential
894:potential
761:Ohm's law
624:Aerospace
323:Θ
299:−
282:−
262:Dimension
196:−
190:Θ
179:−
138:Dimension
6432:Archived
6384:See also
3423:package)
2276:Example
1224:rheology
1137:velocity
1001:load or
923:pressure
791:quantity
782:thermal
612:Cookware
509:SI units
256:kgâ‹…mâ‹…sâ‹…K
132:kgâ‹…mâ‹…sâ‹…K
6707:Ixys RF
6696:Germany
6464:Bibcode
4308:is the
4184:is the
4100:where:
3870:where:
2243:removed
2228:sources
1964:is the
1082:current
796:impulse
60:improve
6773:
6754:
6735:
6692:Munich
6640:
6612:
6565:
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6515:
6511:–461.
6484:
5250:Where
5081:Where
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3681:
3650:
3627:
3603:
3532:
3457:
3421:TO-220
3385:
3325:
3267:
2520:where
1113:stress
868:charge
820:volume
725:. The
553:is in
501:-value
429:kelvin
405:, and
393:, and
350:, and
49:, but
6482:S2CID
4372:JEDEC
3785:From
1003:force
773:type
559:prose
520:hours
480:shape
425:watts
6771:ISBN
6752:ISBN
6733:ISBN
6658:link
6638:ISBN
6610:ISBN
6563:ISBN
6538:ISBN
6513:ISBN
6357:>
5873:and
5535:and
4192:·m),
3789:for
3742:18.6
2226:any
2224:cite
1755:...
1727:...
1304:...
997:flux
844:heat
753:and
719:time
715:heat
555:list
522:per
478:and
476:size
427:per
363:heat
357:and
6602:doi
6509:460
6472:doi
6076:(7)
5499:(6)
5243:(5)
5074:(4)
4823:(3)
4714:(2)
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4353:.
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6442:^
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5725:ln
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4961:.
4382:.
3769:.
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727:SI
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