FUW TRENDS IN SCIENCE & TECHNOLOGY JOURNAL
(A Peer Review Journal)
e–ISSN: 2408–5162; p–ISSN: 2048–5170
keywords: Poiseuille flow, MHD, viscous dissipation, Joule dissipation, Nusselt numbers
This study investigates analytically the effects of pressure forces, radial magnetic field, viscous and Joule dissipations on the Nusselt number for a steady, fully developed MHD pressure driven flow through an asymmetrically heated annulus of two infinitely concentric cylinders. The surfaces of both cylinders are kept at unequal temperatures. The governing momentum and energy equations are transformed by defining relevant dimensionless variables and solved analytically using the method of undetermined coefficient. The effects of various controlling parameters on the flow are graphically presented. Significant result from the present work is that, increase in Hartmann number has a marked effect on the temperature distribution for cases of Brinkman number (Br≠0) which is a case of heat generation due to viscous and Joule dissipation, while in the absence of dissipation, the Hartmann number has an insignificant effect on the temperature profile. In addition, the Nusselt number at the inner surface of the outer cylinder displays an unbounded swing which is significantly influenced by the degree of asymmetric heating.
Brinkman HC 1951. Heat effects in capillary flow I. Appl. Sci. Res., A2: 120-124. Cheng CH, Kou HS & Huang WH 1990. Flow reversal and heat transfer of fully developed mixed convection in vertical channels. J. Thermo. Heat Trans., 4: 375-383. Hamadah TT & Wirtz RA 1991. Analysis of laminar fully developed nixed convection in a vertical channel with opposing buoyancy. ASME J. Heat Transfer, 113: 507-510. Aung W & Worku G 1986. Developing flow and flow reversal in a vertical channel with asymmetric wall temperatures. ASME J. Heat Transfer, 108: 299-304. Ramjee R & Satyamurty VV 2010. Limiting Nusselt numbers for viscous dissipation flow between parallel plates kept at unequal wall temperatures. Int. Commun. Heat Mass Trans., 37: 1251-1254. Jambal O, Shigechi T, Davaa G & Momoki S 2005. Effects of viscous dissipation and fluid axial heat conduction on heat transfer for non-Newtonian fluids in ducts with uniform wall temperature Part II. Int. Commun. Heat & Mass Trans., 32: 1174-1183. Lahjomri J, Oubarra A & Alemany A 2002. Heat transfer by laminar Hartmann flow in thermal entrance region with a step change in wall temperatures: the Graetz problem extended. Int. J. Heat Mass Transfer, 45: 1127-1148. Aydin O & Avci M 2006. Viscous dissipation effects on heat transfer in a Poiseuille flow. Appl. Energy, 83: 495-512. Kumar MMJ & Satyamurty VV 2011. Limiting Nusselt numbers for laminar forced convection in asymmetrically heated annuli with viscous dissipation. Int. Commun. Heat & Mass Trans., 38: 923-7. Mondal PK & Mukherjee S 2012. Viscous dissipation effects on the limiting value of Nusselt number for a shear driven flow through an asymmetrically heated annulus. J. Mech. Engr. Sci., 226(12): 2941-2949. Globe S 1959. Laminar MHD Flow in an Annular Channel. Phys Fluids, pp. 404-412. Singh SK, Jha BK & Singh AK 1997. Natural convection in vertical concentric annuli under a radial magnetic field. Int. J. Heat & Mass Trans., 32: 399-408. Antimirov MY & Kolyshkin AA 1984. Unsteady MHD flow in an annular channel with radial magnetic field. Magnetohyrodynamics, 20: 285-92. Emad MA & Mohamed AE 2005. Viscous dissipation and Joule heating effects on MHD-free convection from a vertical plate with power-law variation in surface temperature in presence of Hall and ion-slip currents. Appl. Maths. Modelling, 29:579-595. Mozayyeni HR & Rahimi AB 2012. Mixed convection in cylindrical annulus with rotating outer cylinder and constant magnetic field with an effect in the radial direction. Scientia Iranica, 19: 91-105. Nazibuddin A & Manas D 2015. Heat transfer in an unsteady MHD flow through an inifinte annulus with radiation. Boundary Value Problem, 11:DOI10.1186/s13661-041-0279-z. Chamkha AJ 2000. Unsteady laminar hydrodynamic fluid particle flow and heat transfer in channels and circular pipes. Int. J. Heat Fluid Flow, 21: 740-46.
