Abstract

In this work, the heat transfer, subject to the effect of viscous dissipation, in a laminar fully-developed flow of a Herschel-Bulkley fluid between parallel plates was analyzed analytically. Both constant and asymmetric wall heat fluxes are considered. For a power-law index, n, higher than 0.5 the average calorific power generated by viscous effects only depends on the ratio between the fluid yield and wall stresses, c. In dimensional form, the temperature difference between the two walls and the temperature gradient at the duct symmetry plane, are independent of the rheological characteristics of the fluid, only depending on the fluid thermal conductivity, the distance between the walls and the difference between the wall heat fluxes. When the Brinkman number, Br*, is equal to 0.25 a singular point arises where the Nusselt numbers, Nu, remains constant and equal to 4 regardless of the values of n, c and wall heat fluxes. This behavior can be explained by the competing effects of n or c on the heat transfer. While decreasing n or increasing c increases the value of Nu for Br*<0.25 and decreases it for Br*>0.25, an increase in the Brinkman number always decreases the Nusselt number.

摘要

在这项工作中，分析了平行板之间的Herschel-Bulkley流体在层流完全展开的层流中受粘滞耗散影响的传热。恒定壁热通量和不对称壁热通量都考虑在内。对于幂律指数n大于0.5，由粘滞效应产生的平均发热量仅取决于流体屈服强度与壁应力之比c。以尺寸形式，两个壁之间的温差和管道对称平面处的温度梯度与流体的流变特性无关，仅取决于流体的导热系数，壁之间的距离以及壁之间的差异热通量。当布林克曼数Br *等于0.25时，无论n，c和壁热通量的值如何，努塞尔特数Nu都保持恒定且等于4时会出现一个奇异点。这种行为可以通过n或c对热传递的竞争效应来解释。减少n或增加c 当Br * <0.25时，增加Nu的值，而当Br *> 0.25时，减小Nu的值，Brinkman数的增加总是使Nusselt数减小。