MHD natural convection with Joule and viscous heating effects in iso-flux porous medium-filled enclosures.pdfVIP

Appl. Math. Mech. -Engl. Ed. 31(9), 1105–1112 (2010) Applied Mathematics DOI 10.1007/s10483-010-1346-6 and Mechanics c Shanghai University and Springer-Verlag Berlin Heidelberg 2010 (English Edition) MHD natural convection with Joule and viscous heating effects in iso-flux porous medium-filled enclosures∗ Y. M. AL-BADAWI, H. M. DUWAIRI (Mechanical Engineering Department, Faculty of Engineering and Technology, The University of Jordan, Amman 11942, Jordan) (Communicated by Zhe-wei ZHOU) Abstract In this study, the magnetohydrodynamics (MHD) natural convection heat transfer with Joule and viscous heating effects inside an iso-flux porous medium-filled inclined rectangular enclosure is studied numerically. An iso-heat flux is applied for heating and cooling the two opposing walls of the enclosure while the other walls are adi- abatic. The Forchheimer extension of Darcy-Oberbeck-Boussinesq and energy equations is transformed into a dimensionless form using a set of suitable variables instead of a fi- nite difference scheme. The governing parameters are the magnetic influence number, the modified Rayleigh number, the inclination angle, and the aspect ratio of the enclosure. The results show that viscous and Joule heating effects decrease heat transfer rates. Key words magnetohydrodynamics (MHD), natural convection, porous media Chinese Library Classification O345, O11 2000 Mathematics Subject Classification 74K10, 74D05 Nomenclature u, the velocity in the x direction, ms−1;