Exact solution for heat transport of Newtonian fluid with quadratic order thermal slip in a porous medium

N. Vishnu GANESH,Qasem AL-MDALLAL,R. KALAIVANANC

doi:10.31197/atnaa.749630

Abstract

In this communication, an analytical solution for the thermal transfer of Newtonian fluid flow with quadratic order thermal and velocity slips is presented for the first time. The flow of a Newtonian fluid over a stretching sheet which is embedded in a porous medium is considered. Karniadakis and Beskok’s quadratic order slip boundary conditions are taking into account. A closed form of analytical solution of momentum equation is used to derive the analytical solution of heat transfer equation in terms of confluent hyper-geometric function with quadratic order thermal slip boundary condition. Accuracy of present results is assured with the numerical solution obtained by Iterative Power Series method with shooting technique. The impacts of porous medium parameter, tangential momentum accommodation coefficient, energy accommodation coefficient on velocity and temperature profiles, skin friction coefficient and reduced Nusselt number are discussed. The Nusselt number increases with the higher estimations of tangential momentum and energy accommodation coefficients.

Highlights

The investigation of uid ow in the presence of slip boundary conditions has received considerable interest due its accuracy of predicting the realistic behaviour in many engineering processes
An analytical solution for the thermal transfer of Newtonian uid ow with quadratic order thermal and velocity slips is presented for the rst time
A closed form of analytical solution of momentum equation is used to derive the analytical solution of heat transfer equation in terms of conuent hyper-geometric function with quadratic order thermal slip boundary condition

Summary

Introduction

The investigation of uid ow in the presence of slip boundary conditions has received considerable interest due its accuracy of predicting the realistic behaviour in many engineering processes. The use of no-slip condition in the above cases does not predict the actual physical situation. The consideration of velocity slip and temperature jump in this type of ow regime is very important to determine the velocity and temperature, respectively. Much attention has been given to this type of uid ow problem with various physical eects via both analytical and numerical techniques [4,5,6,7,8,9,10,11,12]

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