Effects of Viscous Dissipation and Rarefaction on Parallel Plates with Constant Heat Flux Boundary Conditions

Abstract

The effect of viscous dissipation and rarefaction on heat transfer characteristics of hydrodynamically and thermally fully developed flow between parallel plates with constant heat flux conditions is analyzed. Three different types of heat flux boundary conditions, i.e., both plates kept at different constant heat fluxes, both plates kept at equal constant heat fluxes, and one plate insulated, are applied. In all cases, closed form expressions are obtained for the temperature distribution and Nusselt number. Viscous dissipation, rarefaction, and heat flux ratio are found to influence the heat transfer substantially. The present predictions are verified for the cases which neglect the microscale and viscous heating effect. The obtained results are in good agreement with other analytical results.

Comprehensive Analysis of Convective Heat Transfer in Parallel Plate Microchannel with Viscous Dissipation and Constant Heat Flux Boundary Conditions

“…On the contrary, for the case of Br = 0, Kn = 0, the present solution predicts Nu = 2.69, which is exactly same as reported by various researchers [9,17,[36][37][38]. ð Þ $10 À5 À 10 À4 m, O q ð Þ $ 1 À 10 3 W/m 2 : Considering these values, one can evaluate the order of magnitude for Brinkman number as: O Br j j ð Þ$10 1 À 10 À3 [23].…”

“…In addition, for the case of Br = 0, Kn = 0, present solution (Nu = 4.12) reduces the Nusselt number, which is exactly same as reported by various researchers [9,16,[36][37][38].…”

“…Present prediction is validated for the cases that neglect both viscous heating and microscale effects (Kn = 0). For these cases, the Nusselt number is found to be exactly same as reported by earlier researchers [9,16,[36][37][38]. The results obtained from the present analysis are elaborated below.…”

“…While, the fully developed Nusselt number does not vary significantly with the change in the thermophysical properties in the analysis [34,35]. Efforts have been made to study the effect of second order boundary conditions and asymmetric heat flux boundary conditions on the heat transfer characteristics of various geometries such as: parallel plate microchannels and micropipe [36][37][38]. It is observed that the asymmetric heat flux condition significantly alters the temperature profile and singularities in Nusselt number are obtained for various values of Knudsen number [18][19][20].…”

“…It is reported that velocity slip and temperature jump affect the heat transfer performance in opposite ways [15]. Also, the studies report the deviation in heat transfer performance by considering the first and second order slip models [36][37][38]. The effect of asymmetric heat flux ratio on the heat transfer ratio and the heat transfer performance has also been reported [9,[18][19][20].…”