2004
DOI: 10.1016/j.ijheatmasstransfer.2004.06.027
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The extended Graetz problem with piecewise constant wall temperature for pipe and channel flows

Abstract: Axial heat conduction effects within the fluid can be important for duct flows if the Prandtl number is relatively low (liquid metals). In addition, axial heat conduction effects within the flow might also be important, if the heating zone is relatively short in length. The present paper shows an entirely analytical solution to the extended Graetz problem with piecewise constant wall temperature boundary conditions. The solution is based on a selfadjoint formalism resulting from a decomposition of the convecti… Show more

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Cited by 46 publications
(21 citation statements)
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“…It is known that heat conduction in the fluid occurs at low Pe-numbers [21] and plays a significant role especially for T w = const. [22].…”
Section: Pressure Drop Measurementmentioning
confidence: 99%
“…It is known that heat conduction in the fluid occurs at low Pe-numbers [21] and plays a significant role especially for T w = const. [22].…”
Section: Pressure Drop Measurementmentioning
confidence: 99%
“…Several researchers included thermal participation of the channel walls which is strongest near the entrance region [5,6] and can influence the overall performance of heat exchangers involving microchannel flow passages [7]. A heated region confined to a small region along the wall was studied by Weigand [8,9], who found that a small heated region extends the impact of axial conduction to higher Peclet numbers. There have been several thermal-entrance studies of microchannels with other velocity distributions, including Hartmann flow [10,11], porous-saturated flow [12], and slip flow [13].…”
Section: Introductionmentioning
confidence: 99%
“…Their investigation showed that the normally used assumption that the eddy diffusivity in axial and normal direction is the same is correct for the range of parameters under investigation. The effect of a piecewise changing wall heat flux or wall temperature has been analytically studied by Weigand et al [10] and Weigand and Lauffer [11]. Despite the large amount of work, which has been done on the extended Graetz problem for laminar and turbulent duct flows, very little investigations are known which study analytically the effect of conduction in the wall on the heat transfer in a duct.…”
Section: Introductionmentioning
confidence: 99%