A numerical treatment for partial slip flow and heat transfer of non-Newtonian Reiner-Rivlin fluid due to rotating disk

Abstract

In this article, partial slip flow of Reiner-Rivlin fluid induced by a rough rotating disk is modeled. Heat transfer is also addressed by assuming more general temperature jump condition. The constitutive relations in Reiner-Rivlin fluid lead to a coupled and strongly non-linear differential system. A convenient numerical treatment is invoked to solve the resulting similarity equations for broad ranges of non-Newtonian fluid parameter and slip coefficients. Our main interest is to predict the behaviors of fluid elasticity and wall slip coefficients on the von-Kármán flow problem. Expressions of wall skin friction and surface heat transfer are calculated and deliberated for broad parameter values. Different from radial and axial velocities, tangential velocity appears to increase as Reiner-Rivlin fluid parameter (K) increases. Reduction in surface drag coefficient, which is vital in some applications, can be accomplished by increasing the parameter K. Volumetric flow rate is also inversely proportional to the parameter K. However, heat transfer rate diminishes when parameter K enlarges. We also conclude that larger torque would be required to keep steady rotation of the disk for higher values of wall slip coefficients.