Magnetohydrodynamic Time-Dependent Bio-Nanofluid Flow in a Porous Medium with Variable Thermophysical Properties

M Irfan,A Aslam,M Asif Farooq,A Mushtaq,Z H Shamsi,Hafiz Muhammad Ali

doi:10.1155/2021/6666863

Abstract

In this work, a theoretical model with a numerical solution is brought forward for a bio-nanofluid with varying fluid features over a slippery sheet. The partial differential equations (PDEs) involving temperature-dependent quantities have been translated into ordinary differential equations (ODEs) by using similarity variables. Numerical verifications have been done in three different methods: finite difference method, shooting method, and bvp4c. To figure out the influence of parameters on the flows, the graphs are plotted for the velocity, temperature, concentration, and microorganism curves. The boundary layer thickness of the microorganism profile reduces with the Schmidt number and Peclet number. In addition to adding radiative heat flux, we added heat generation, rate of chemical reaction, and first-order slip. Adding these parameters brought new aspects to the underlying profiles. Moreover, the obtained data of the skin friction coefficient, the local Nusselt number, the local Sherwood number, and the local density of motile microorganisms are tabulated against various parameters for the physical parameters. From the results, it is apparent that the local Nusselt number decreases with the Brownian and thermophoretic parameters. The data obtained for physical parameters have a close agreement with the published data. Finally, the graphs for slip conditions are significantly different when the comparison is drawn with no-slip condition.

Highlights

A theoretical model with a numerical solution is brought forward for a bio-nanofluid with varying fluid features over a slippery sheet. e partial differential equations (PDEs) involving temperature-dependent quantities have been translated into ordinary differential equations (ODEs) by using similarity variables
To figure out the influence of parameters on the flows, the graphs are plotted for the velocity, temperature, concentration, and microorganism curves. e boundary layer thickness of the microorganism profile reduces with the Schmidt number and Peclet number
E data in Table 4 show computational results for the local Nusselt number, the local Sherwood number, and the local density number of motile microorganisms obtained with bvp4c. e local Nusselt number Nux is reduced against Brownian motion parameter Nb, thermophoretic parameter Nt, Eckert number Ec, heat source parameter s, and thermal conductive parameter h4

Summary

Flow Model

Consider the movement of a nanofluid containing gyrotactic microorganisms past a stretching sheet with variable physical properties. e magnetic field β2o is applied normal to the surface. Consider the movement of a nanofluid containing gyrotactic microorganisms past a stretching sheet with variable physical properties. E magnetic field β2o is applied normal to the surface. Due to low magnetic Reynolds number, the induced magnetic field is assumed negligible. E stretching velocity is Uw ax(1 − A1t)− 1. E governing model is [48]. The boundary condition corresponding to the considered model is taken as u􏽢1 Uw(x, t) + N1zzuy􏽢1, v 0, T􏽢 1. E physical quantities of the interest in this study are the local skin friction coefficient Cfx, the local Nusselt number Nux, the local Sherwood number Shx, and the local density number of motile microorganisms Nnx defined as. Re−x1/2Shx − φ′(0), Re−x1/2Nnx − χ′(0), where the local Reynolds number is defined as Rex (Uwx/])

Numerical Process

Results and Discussion

A: Unsteadiness parameter