Jñānābha‎, Vol. 52 (2) (2022), (280-290)

UNSTEADY STAGNATION FLOW OF VISCOELASTIC FLUID THROUGH POROUS MEDIUM OVER STRETCHING/SHRINKING SURFACE USING UCM MODEL

By

Sushila Choudhary1, Anil Sharma2, Prasun Choudhary3 and Suresh Kumar4

1,2,3Department of Mathematics, University of Rajasthan, Jaipur-302004, Rajasthan, India

4S.B.K. Govt. College, Jaisalmer-345001, Rajasthan, India

Email: sumathru11@gmail.com, anilsharma9414@gmail.com, prasun.iimet@gmail.com

Corresponding author: smusumaths@gmail.com

(Received: December 18, 2021; In format: December 18, 2021; Revised: March 26, 2022; Accepted: November 30, 2022)

DOI: https://doi.org/10.58250/jnanabha.2022.52233

Abstract

In the present paper, Upper-Convected Maxwell model is used for formulation of the problem of two-dimensional unsteady stagnation point flow of viscoelastic fluid which passes through a porous medium over a stretching/shrinking surface. The effect of magnetic field on flow is also considered in the presence of time dependent heat source/sink. Using similarity parameters, we convert the governing non-linear system of partial differential equations into non dimensional system of ordinary differential equations. This system of equations is solved by using Runge-Kutta fourth order method with shooting technique. Effect of different physical parameters e.g. Maxwell parameter(β), permeability parameter(K), unsteadiness parameter(γ), velocity ratio parameter(λ) etc. on flow and heat transfer characteristics are analyzed and discussed graphically. It is observed that for some values of λ, dual solution also exists for both velocity and temperature, and existence and uniqueness of solution also depends upon unsteadiness parameter. For the validation of present study, the results are compared to previous investigations and found in good agreement.

2020 Mathematical Sciences Classification: 76A05, 76M55, 76S05, 76W05, 65L06.

Keywords and Phrases: Upper-Convected Maxwell fluid, Unsteady, MHD, Permeability parameter, Heat source/sink, Skin friction coefficient, Nusselt number.