Lie group analysis and numerical solution of magnetohydrodynamic free convective slip flow of micropolar fluid over a moving plate with heat transfer

Abstract

a b s t r a c tIn this paper, we investigate magnetohydrodynamic free convective flow of micropolar fluid over a moving flat plate using the Lie group transformations and numerical methods. Instead of using conventional no-slip boundary conditions, we used both the velocity and thermal slip boundary conditions to achieve physically realistic and practically useful results. The governing boundary layer equations are non-dimensionalized and transformed into a set of coupled ordinary differential equations (ODEs) using similarity transformations generated by the Lie group, before being solved numerically using Matlab stiff ODE solver ode15s and Matlab trust-region-reflective algorithm lsqnonlin. The effects of governing parameters on the dimensionless velocity, angular velocity, temperature, skin friction and heat transfer rate are investigated. Our analysis revealed that the dimensionless velocity and angular velocity decrease whilst the dimensionless temperature increases with the velocity slip parameter. Thermal slip reduces the dimensionless velocity and temperature but raises the dimensionless angular velocity. Magnetic field suppresses the velocity but elevates the temperature and angular velocity. Results reported in this paper are in good agreement with the ones reported by the previous authors.

Application of differential transformation method in micropolar fluid flow and heat transfer through permeable walls

“…Recently effect of using micropolar fluid, nanofluid, etc. on flow and heat transfer has been studied by several authors [12][13][14][15][16][17][18][19][20][21][22][23].…”

Numerical solutions for gyrotactic bioconvection in nanofluid-saturated porous media with Stefan blowing and multiple slip effects

“…Uddin et al (2014) investigated the steady 2D magnetohydrodynamic laminar free convective boundary layer slip flow of a nanofluid from a stretching/shrinking sheet in a quiescent fluid, showing that the velocity increases whereas the temperature and concentration decreases with the velocity slip. Uddin et al (2015a) studied the magnetohydrodynamic free convective slip flow of a micropolar fluid over a moving plate. The same authors also investigated the hydromagnetic thermo-solutal nanofluid slip flow in a Darcian porous medium with zero mass flux boundary condition.…”

Scaling Group Transformation for Mixed Convection in a Power-Law Fluid Saturated Porous Medium With Effects of Soret, Radiation and Variable Properties

“…The main advantages of these Lie group transformations is to obtain similarity transformations for the system of nonlinear partial differential equations. Moreover, the Lie Group technique has been applied by many researchers (see Oberlack (1999), (Kandasamy et al, 2010), (Afify et al, 2014), (Ferdows et al, 2013) and (Uddin et al, 2015)). Recently, ElAziz and Afify (2016) reported Lie group analysis for a power-law fluid over a stretching sheet with effect of magnetohydrodynamic and variable properties.…”