Flow and heat transfer of couple stress fluid in a vertical channel in the presence of heat source/sink

Abstract

Purpose The purpose of this paper is to consider the problem of fully developed laminar mixed convection flow of a couple stress fluid in a vertical channel with the third-kind boundary conditions in the presence or absence of heat source/sink effect. Design/methodology/approach Through proper choice of dimensionless variables, the governing equations are developed. These governing equations are solved analytically by the differential transform method and numerically by the Runge–Kutta shooting method. Analytical solutions for the velocity and temperature profiles for heat generation and absorption of the problem are reported. Findings The mass flow rate and Nusselt numbers at both the left and right channel walls on mixed convection parameter, Brinkman number, couple stress parameter and heat generation/absorption parameter for equal and unequal Biot numbers are presented. Favorable comparisons of special cases with previously published work are obtained. It is found that velocity, temperature, mass flow rate and Nusselt number decrease with couple stress parameter and increase with mixed convection parameter and Brinkman number. Originality/value The work done in this paper is not done earlier to the authors’ knowledge. This is the first paper in which the sixth-order differential equation is solved using the semi-numerical method, which is a differential method.

Spectral approach to study the entropy generation of radiative mixed convective couple stress fluid flow over a permeable stretching cylinder

“…where (33) diag½ and I are the diagonal and identity matrices of order ðN þ 1Þ Â ðN þ 1Þ. Now the entire systems can be framed as…”

“…31 Ojjela 32 studied the unsteady chemically reactive flow between parallel surfaces. Umavathi et al 33 analysed the flow considering heat source or sink. Fluid blessed with couple stress runs over oscillatory stretched surface was examined by Khan et al 34 Alizadeh et al 35 investigated the entropy analysis on the mixed convective radiative stagnant point flow over a cylindrical texture inside a porous medium.…”

MHD and Slip Effect on Two-immiscible Third Grade Fluid on Thin Film Flow over a Vertical Moving Belt

“…Loharsbi and Sahai [32] studied the two-phase magnetohydrodynamic (MHD) flow and heat transfer in a parallel plate channel with one of the fluids being electrically conducting. Later on, Malashetty et al [38,39] and Umavathi et al [40,41] studied the two-fluid flow and heat transfer with various geometries. Recently, Prathap-Kumar et al [42] studied the mixed convective flow of immiscible viscous fluids in a vertical channel.…”

Numerical Study of Mixed Convective Flow of a Couple Stress Fluid in a Vertical Channel with First Order Chemical Reaction and Heat Generation/Absorption

“…The blood flow through artery with mild stenosis with the effects of couple stress has been presented by Sinha and Singh [3]. Umavathi [4] has considered free flow of couple stress fluid which is also electrically conducting in a vertical channel. Umavathi et al [5] have investigated the heat transfer of two fluids such as viscous and couple stress fluids in a vertical channel.…”