In this paper, we turn our attention to the mathematical model to simulate steady, hydromagnetic, and radiating nanofluid flow past an exponentially stretching sheet. A numerical modeling technique, simplified finite difference method (SFDM), has been applied to the flow model that is based on partial differential equations (PDEs) which is converted to nonlinear ordinary differential equations (ODEs) by using similarity variables. For the resultant algebraic system, the SFDM uses the tridiagonal matrix algorithm (TDMA) in computing the solution. The effectiveness of numerical scheme is verified by comparing it with solution from the literature. However, where reference solution is not available, one can compare its numerical results with the results of MATLAB built-in package bvp4c. The velocity, temperature, and concentration profiles are graphed for a variety of parameters, i.e., Prandtl number, Grashof number, thermal radiation parameter, Darcy number, Eckert number, Lewis number, and Brownian and thermophoresis parameters. The significant effects of the associated emerging thermophysical parameters, i.e., skin friction coefficient, local Nusselt number, and local Sherwood numbers are analyzed and discussed in detail. Numerical results are compared from the available literature and found a close agreement with each other. It is found that the Eckert number upsurges the velocity curve. However, the dimensionless temperature declines with the Grashof number. It is also shown that the SFDM gives good results when compared with the results obtained from bvp4c and results from the literature.
This paper discusses unsteady/steady radiating magnetohydrodynamic (MHD) nanofluid flow over a slippery stretching sheet. Introducing similarity variables reduces partial differential equations (PDEs) into a new set of partial differential equations (PDEs) where a solution is a function of two independent variables. For the time integration, we perform first order explicit Euler method and spatial derivatives are approximated by the finite differences. The steady flow solution is computed by MATLAB built-in solver bvp4c. The flow regime is controlled by a number of thermophysical parameters such as thermal Grashof number (Gr), Lewis number (Le), Eckert number (Ec), Brownian motion (Nb) and thermophoresis (Nt) and heat source or sink (S), Prandtl number (Pr), magnetic field parameter (M), and Darcy number (Da). The findings are analyzed by validation through graphs and tables for velocity, temperature and concentration profiles and the skin friction coefficient, the local Nusselt and the local Sherwood numbers, respectively. The results converge in accordance with the grid convergence test. For an unsteady flow, the temperature of the nanofluid is higher near the surface without thermophoresis parameter Nt and reduced significantly when Nt is present. Moreover, concentration boundary layer thickness decreases with an increase of Darcy number Da.
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