An approximate method for solving MHD boundary layer flow over a stretching sheet with Joule heating and convective thermal condition

2021 ◽  
pp. 2250024
Author(s):  
M. M. Khader ◽  
M. M. Babatin
Keyword(s):  
Boundary Layer ◽  
Joule Heating ◽  
Stretching Sheet ◽  
Nonlinear Differential Equations ◽  
Convective Boundary Condition ◽  
Convective Boundary ◽  
Boundary Layer Equations ◽  
Small Parameters ◽  
Convective Thermal ◽  
Layer Flow

In this paper, He’s homotopy perturbation method (HPM) is used, which is an approximate analytical method for solving numerically the problem of Newtonian fluid flow past a porous exponentially stretching sheet with Joule heating and convective boundary condition. The major feature of HPM is that it does not need the small parameters in the equations and hence the determination of classical perturbation can be discarded. Due to the complete efficiency of the HPM, it becomes practically well suited for use in this field of study. Also, the obtained solutions for both the velocity and temperature field are graphically sketched. The results reveal that the proposed method is very effective, convenient, and quite accurate to systems of nonlinear differential equations. Results of this study shed light on the accuracy and efficiency of the HPM in solving these types of nonlinear boundary layer equations.

scholarly journals Effect of a Convective Boundary Condition on Boundary Layer Slip Flow and Heat Transfer Over a Stretching Sheet in View of the Exact Solution

2016 ◽  
Vol 46 (4) ◽  
pp. 85-95 ◽  
Author(s):  
Mona D. Aljoufi ◽  
Abdelhalim Ebaid
Keyword(s):  
Boundary Layer ◽  
Boundary Condition ◽  
Differential Equations ◽  
Exact Solutions ◽  
Shooting Method ◽  
Stretching Sheet ◽  
Nonlinear Differential Equations ◽  
Convective Boundary Condition ◽  
Current Paper ◽  
Convective Boundary

Abstract The exact solutions of a nonlinear differential equations system, describing the boundary layer flow over a stretching sheet with a convective boundary condition and a slip effect have been obtained in this paper. This problem has been numerically solved by using the shooting method in literature. The aim of the current paper is to check the accuracy of these published numerical results. This goal has been achieved via first obtaining the exact solutions of the governing nonlinear differential equations and then, by comparing them with the approximate numerical results reported in literature. The effects of the physical parameters on the flow field and the temperature distribution have been re-investigated through the new exact solutions. The main advantage of the current paper is the simple computational approach that has been introduced to analyze exactly the present physical problem. This simple analytical approach can be further applied to investigate similar problems. Although no remarkable differences have been detected between the current figures and those obtained in literature, the authors believe that if some numerical calculations were available for the fluid velocity and the temperature in literature then the convergence criteria and the accuracy of the shooting method used in Ref. [15] can be validated in view of the current exact expressions.

scholarly journals MHD Mixed Convective Boundary Layer Flow of a Nanofluid through a Porous Medium due to an Exponentially Stretching Sheet

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
M. Ferdows ◽  
Md. Shakhaoath Khan ◽  
Md. Mahmud Alam ◽  
Shuyu Sun
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Stretching Sheet ◽  
Numerical Solutions ◽  
Skin Friction Coefficient ◽  
Convective Boundary ◽  
Boundary Layer Equations ◽  
Exponentially Stretching Sheet ◽  
Layer Flow ◽  
Exponentially Stretching

Magnetohydrodynamic (MHD) boundary layer flow of a nanofluid over an exponentially stretching sheet was studied. The governing boundary layer equations are reduced into ordinary differential equations by a similarity transformation. The transformed equations are solved numerically using the Nactsheim-Swigert shooting technique together with Runge-Kutta six-order iteration schemes. The effects of the governing parameters on the flow field and heat transfer characteristics were obtained and discussed. The numerical solutions for the wall skin friction coefficient, the heat and mass transfer coefficient, and the velocity, temperature, and concentration profiles are computed, analyzed, and discussed graphically. Comparison with previously published work is performed and excellent agreement is observed.

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