Z. Naturforsch. 69a, 705 – 713
(2014)
doi:10.5560/ZNA.2014-0059
On the Numerical Solution of the Nonlinear Radiation Heat Transfer Problem in a Three-Dimensional Flow
Ammar
Mushtaq1,
Meraj
Mustafa2,
Tasawar
Hayat3,4, and
Ahmed
Alsaedi4
1 Research Centre for Modeling and Simulation (RCMS), National University of Sciences and Technology (NUST), Islamabad 44000, Pakistan
2 School of Natural Sciences (SNS), National University of Sciences and Technology (NUST), Islamabad 44000, Pakistan
3 Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan
4 Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80257, Jeddah 21589, Saudi Arabia
Received March 28, 2014 / revised July 28, 2014 / published online October 8, 2014
The steady laminar three-dimensional magnetohydrodynamic (MHD) boundary layer flow and heat transfer over a stretching sheet is investigated. The sheet is linearly stretched in two lateral directions. Heat transfer analysis is performed by utilizing a nonlinear radiative heat flux in Rosseland approximation for thermal radiation. Two different wall conditions, namely (i) constant wall temperature and (ii) prescribed surface temperature are considered. The developed nonlinear boundary value problems (BVPs) are solved numerically through fifth-order Runge–Kutta method using a shooting technique. To ascertain the accuracy of results the solutions are also computed by using built in function bvp4c of MATLAB. The behaviours of interesting parameters are carefully analyzed through graphs for velocity and temperature distributions. The dimensionless expressions of wall shear stress and heat transfer rate at the sheet
are evaluated and discussed. It is seen that a point of inflection of the temperature function exists for sufficiently large values of wall to ambient temperature ratio. The solutions are in excellent agreement with the previous studies in a limiting sense. To our knowledge, the novel idea of nonlinear thermal radiation in three-dimensional flow is just introduced here.
Key words: Three-Dimensional Flow; Nonlinear Thermal Radiation; Bi-Directional Stretching Sheet; Shooting Method; Rosseland Approximation.