In this study the momentum and energy equations are solved to analyze the flow between two parallel plates by employing second-order velocity slip and temperature jump conditions. The flow is considered to be laminar, incompressible, hydrodynamically/thermally fully developed, and steady state. In addition to the isoflux condition, viscous dissipation is included in the analysis. Closed form expressions for the temperature field and Nusselt number are obtained as a function of the Knudsen number and Brinkman number. The Nusselt number obtained by employing the second-order model is found to be lower compared to the continuum value and agrees well with the other theoretical models.
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.
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