Radiation effects on transient magnetohydrodynamic natural convection flow with heat generation

• Published in: International journal of thermal sciences 2012-08, Vol.58, p.79-91
• Main Authors: Mahfooz, S.M., Hossain, M.A., Gorla, Rama Subba Reddy
• Format: Article
• Language: English
• Subjects: Boundaries; Computational fluid dynamics; Convection; Convection and heat transfer; Exact sciences and technology; Fluid dynamics; Fluid flow; Fundamental areas of phenomenology (including applications); Heat generation; Heat source; Heat transfer; Laminar boundary layers; Laminar flows; Magnetohydrodynamics and electrohydrodynamics; Mathematical analysis; Mathematical models; Natural convection; Optically dense fluid; Physics; Radiation; Transient; Turbulent flows, convection, and heat transfer
• ISSN: 1290-0729; 1778-4166
• DOI: 10.1016/j.ijthermalsci.2012.03.002

In the present investigation, we have considered the radiation effects on a transient two-dimensional natural convection laminar boundary-layer flow of viscous incompressible electrically conducting and optically dense fluid along a vertical flat surface with heat generation. Using a method of transformed coordinates, the boundary-layer equations are transformed into a new form. The transformed equations can then be solved straight forwardly by any numerical methods designed for regular and stationary geometries. In this paper, an implicit finite difference scheme is used. The governing equations have been reduced in the form that are valid for small and large time regimes, by using stream-function formulation. The results obtained for the above mentioned three time regimes are compared and found in excellent agreement. Moreover, the solutions are also obtained in terms of transient local shear stress, transient local rate of heat transfer, transient velocity and temperature distribution for a wide range of parameters Plank constant Rd, surface temperature variation parameter θw, Hartman number M and heat generation parameter λ for the liquid metals having Prandtl number Pr=0.005, 0.05 and 0.1. ► We have investigated the transient natural convection boundary-layer flow. ► Transverse magnetic field and internal heat generation are included. ► Heat transfer decreases with increasing radiation parameter and wall temperature. ► Transient shear stress decreases and heat transfer increases with magnetic field. ► Increase in the internal heat generation leads to reduce the heat transfer rate.