scholarly journals Lie group analysis of heat flux effect on MHD second slip flow for a slightly rarefied gas past a stretching sheet with heat generation

2019 ◽  
Vol 1 (22) ◽  
pp. 45-59
Author(s):  
Ahmed M. Megahed ◽  
Reda G. Abdel-Rahman
Keyword(s):  
Heat Flux ◽  
Heat Generation ◽  
Lie Group ◽  
Stretching Sheet ◽  
Rarefied Gas ◽  
Slip Flow ◽  
Group Analysis ◽  
Dimensionless Temperature ◽  
Lie Group Analysis ◽  
Slightly Rarefied Gas

The present paper discusses steady MHD second order slip flow and heat transfer for a slightly rarefied gas due to an impermeable stretching sheet with heat flux and internal heat generation. By using the Lie group analysis, new similarity transformations are obtained. Employing these transformations, allows the partial differential equations governing the problem to transform into a system of ordinary differential equations which are later treated numerically using shooting method. Effects of the governing parameters on the dimensionless velocity and dimensionless temperature profiles are outlined graphically. Furthermore, results for the local skin-friction coefficient and the local Nusselt number are presented for some different values of the governing parameters in a tabular form. Also, results show that there is a strong dependency of the dimensionless temperature on the heat flux.

Lie group analysis and numerical solutions for magneto-convective slip flow of nanofluid over a moving plate with Newtonian heating boundary condition

2015 ◽  
Vol 93 (12) ◽  
pp. 1501-1509 ◽  
Author(s):  
M.J. Uddin ◽  
O. Anwar Bég ◽  
N. Amran ◽  
A.I.MD. Ismail
Keyword(s):  
Boundary Condition ◽  
Lie Group ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Slip Flow ◽  
Group Analysis ◽  
Lie Group Analysis ◽  
Nanoparticle Volume Fraction ◽  
Newtonian Heating ◽  
Moving Plate

Magnetohydrodynamic laminar boundary layer slip flow of a nanofluid over a moving plate with Newtonian heating boundary condition in the presence of heat generation–absorption effects is studied using Lie group analysis and a numerical method. The model used for the nanofluid includes the effects of Brownian motion and thermophoresis. The governing transport equations are non-dimensionalized and transformed into a set of similarity equations using similarity transformations generated by Lie group transformations. The transformed equations are then solved using the Runge–Kutta–Fehlberg fourth- and fifth-order numerical method in Maple 17, which is also used to generate relevant graphs and tables. The flow, heat, and nanoparticle volume fraction characteristics are shown to depend on a number of thermophysical parameters, namely, Brownian motion, thermophoresis, Lewis number, Prandtl number, linear momentum slip, magnetic field, suction–injection, Newtonian heating, and heat generation–absorption. The effects of these parameters on the dimensionless stream function, velocity, temperature, nanoparticle volume fraction, wall heat, and mass transfer rates are investigated. Comparisons of the present numerical solutions with published works show very good correlation. The study finds applications in nano-technological magnetic materials processing.

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