The effect of heat generation on convective heat transfer for laminar flows in a multi-passage circular pipe maintained under constant wall temperature

Abstract

A LITERATURE survey [l-lo] indicates that heat transfer studies for laminar flows in multi-passage circular pipes based on temperature distributions including heat generation effects are not available. The existing conventional convective heat transfer problems in flows of multi-passage tubes are based on lumped parameter type analyses [l] which are not rigorous. However, recent interest in the heat generation effect on convective heat transfer properties [ll] has led to this note where the effect of an arbitrary heat generation density in the inner and outer flows on convective heat transfer properties of the multi-passage flow is studied. The thickness of the separating surface and the resistance of heat conductivity of the inner separating wall are neglected. It has been shown that the Nusselt numbers on the outer surface and at the inner separating surface of a multi-passage pipe flow can be defined in three different ways. Also shown was that the Nusselt numbers depend on two dimensionless parameters fl2J: the ratio of the thermal conducti~ties of the fluids in the inner and outer passages, kkr and the product of kk and the ratio of the Peclet numbers of the flows in the inner and outer passages, n = kkkPe, the heat exchanger number of the multi-passage flow. The effect of heat generation is reflected by the dimensionless heat generation numbers yi and y0 for the inner and outer flows, respectively, where y = (~H)/[k~(~e)], L. is the radius of the conduit, H the heat generation volume density, k the thermal conductivity, and Pe the Peclet number [ll, 131. The Nusselt numbers in this multi-passage flow are defined relative to the mixed, combined bulk temperature of the inner and outer region flows.