Vol.24, No.2, 2024, pp. 247–253
 https://doi.org/10.69644/ivk-2024-02-0247

ON THE ONSET OF STATIONARY CONVECTION ON JEFFREY NANOFLUID LAYER SATURATED WITH A POROUS MEDIUM: BRINKMAN MODEL

Pushap Lata Sharma1, Praveen Lata1, Deepak Bains1, Ajit Kumar1, Gian C. Rana2*

1) Department of Mathematics & Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, INDIA

2) Department of Mathematics, NSCBM Government PG College, Hamirpur 177005, Himachal Pradesh, INDIA

D. Bains  0000-0001-8078-923X; G.C Rana  0000-0003-2724-8308 *email: drgcrana15@gmail.com

 

Abstract

In this paper, we investigate the onset of convection in a Jeffrey nanofluid layer saturated with the porous medium using Darcy-Brinkmann model. Normal mode analysis and Galerkin type weighted residual method (GWRM) are used to analyse conservation equations. Effects of Brownian motion and thermophoresis are taken into account in the Jeffrey nanofluid model. The Buongiorno model deployed for nanoparticles incorporates the influences of thermophoresis and Brownian motion. Three cases of free-free, rigid-rigid and rigid-free boundaries are considered. For stationary convection, the effects of Darcy number, Jeffrey parameter, Lewis number, nanoparticle Rayleigh number, porosity and modified diffusivity ratio for all the above mentioned boundary conditions are investigated analytically and graphically. The numerical computed values of stationary thermal Rayleigh number are presented graphically for three distinct combinations of boundary conditions. The study is of great significance in many different areas such as automotive, pharmaceutical, geophysics, soil sciences, food processing, oceanography, limnology, etc., and excellent coincidence is found regarding the present paper and earlier published work.

Keywords: thermal instability, nanoparticles, nanofluids, Brownian motion

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