MHD slip flow of chemically reacting UCM fluid through a dilating channel with heat source/sink

K Pravin Kashyap,Samir Kumar Das,Odelu Ojjela

doi:10.1515/nleng-2018-0036

K Pravin Kashyap, Samir Kumar Das + Show 1 more

Open Access

https://doi.org/10.1515/nleng-2018-0036

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Abstract

Abstract The present article explores the effects of uniform heat source and first order destructive chemical reaction on an upper convected Maxwell fluid through an expanding or contracting channel with the porous slip condition at the upper plate. It is assumed that the fluid is sucked or injected through the upper plate. The temperature and concentration at the plates is maintained constant. Using suitable similarity transformations, nonlinear coupled ODEs are developed from the governing PDEs. The subsequent ODEs are converted into a first order system and integrated via shooting method. The effect of various prominent parameters on heat, flow and mass transfer characteristics are studied in detail through graphs and tables. The present results suggest that the presence of chemical reaction and heat source yields in the reduction of concentration and of the enhancement of temperature the fluid. It is also observed that the wall expansion shows an increasing effect on the radial velocity component, but the slip parameter exhibits an opposing effect. The viscous case has been studied as a special case where the present results are found to be close to the earlier ones. The flow of such nonlinear viscoelastic fluids has important applications in separation processes like petroleum and medical industries.

Highlights

The expanding and contracting boundaries have applications in many practical situations such as of ltration, the regression of grains in the course of combustion of solid propellant, binary gas di usion, arti cial dialysis, the ow of blood, circulation of blood and air during the respiration process, separation processes of other membranes
As convective heat transport in porous channels due to Ohmic heating and buoyancy forces have a major part in applications of heat exchangers and nuclear reactors, we have considered the effect of mixed convection in the present model
The unsteady slip ow of mixed convective chemically reacting upper convected Maxwell uid through an expanding or contracting channel with uniform heat source is investigated with numerical computations using a shooting approach

Summary

Introduction

The expanding and contracting boundaries have applications in many practical situations such as of ltration, the regression of grains in the course of combustion of solid propellant, binary gas di usion, arti cial dialysis, the ow of blood, circulation of blood and air during the respiration process, separation processes of other membranes. Hayat et al [41] studied the magnetic eld e ects on a chemically reacting third grade uid above a stretching sheet using HAM and analysed the velocity, skin friction, concentration and local Sherwood number proles with respect to various parameters. Choi et al [50] have analyzed the 2-D ow of upper convected Maxwell uid in a porous surface channel using both 4th order Runge Kutta integration scheme and power series Their observation suggested that at a constant Reynolds number the longitudinal velocity at the center line decreases for the higher Deborah number and it has a attening e ect on axial velocity for high Reynolds numbers for a xed Deborah number. This numerical problem is solved by using a suitable initial guess vector for ‘as’ and iterate the vector ‘y’ to get the values at the upper boundary by using R-K 4th order algorithm such that the algebraic problem is satis ed

Results

Conclusions

A Appendix