Analysis of slip flow heat transfer between two unsymmetrically heated parallel plates with viscous dissipation

This paper presents an analytical investigation to study the heat transfer and fluid flow characteristics in the slip flow region for hydrodynamically and thermally fully developed flow between parallel plates. Both upper and lower plates are subjected to asymmetric heat flux boundary conditions. The effect of first order velocity slip, temperature jump, asymmetric heat flux ratio and viscous dissipation on the heat transfer performance is analyzed. Closed form expressions are obtained for the temperature distribution and Nusselt number. Present predictions are verified for the cases that neglect the viscous heating and microscale effects. The effect of asymmetric heat flux ratio with and without viscous dissipation on Nusselt number for both macroscale and microscale is highlighted. The heat transfer characteristics are found to depend on various modeling parameters, namely, modified Brinkman number, Knudsen number and heat flux ratio.