ESCI SJR: 0.22 SNIP: 0.446 CiteScore™: 0.5

ISSN 打印: 2152-5102
ISSN 在线: 2152-5110

# 国际流体力学研究期刊

DOI: 10.1615/InterJFluidMechRes.v33.i2.30
pages 153-167

## Magnetohydrodynamic Free Convection of a Large Prandtl Number Liquid Over a Nonisothermal Two-Dimensional Body

Mohamed F. El-Amin
Mathematics Department, Aswan Faculty of Science, South Valley University, Aswan, 81258; King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Kingdom of Saudi Arabia
M. A. EL-Hakiem
Mathematics Department, Aswan Faculty of Science, South Valley University, Aswan, Egypt
Rama Subba Reddy Gorla
Department of Mechanical Engineering, Cleveland State University, Cleveland, OH, 44115 USA; Department of Mechanical Engineering, University of Akron, Akron, Ohio 44325, USA; Department of Mechanical & Civil Engineering, Purdue University Northwest, Westville, IN 46391, USA

### ABSTRACT

A boundary layer analysis is presented to investigate the free convection over a nonisothermal two-dimensional body under the action of a transverse nonuniform magnetic field. Two simplifications are used in this work: the first one is used due to the fact that many of the industrial liquids have large Prandtl number and, therefore, the terms that are divided by Pr in the nondimensional governing equations could be neglected; the second simplification is used to treat the shear stress for power law non-Newtonian fluids τ = K(∂u/∂y)n as a shear stress model. Solutions are obtained with variations in surface temperature or with variations in heat flux. The effects of the magnetic parameter M, the body shape parameter m, and the surface thermal variation parameter ρ as well as the heat flux parameter s are examined. Velocity profiles as well as temperature distributions are shown graphically for two cases: variable wall temperature condition (VWT) and variable wall flux condition (VWF). The numerical values of the wall shear stress and the heat transfer rate are entered in tables for the two cases.

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