Effect of Temperature-Dependent Variable Viscosity on Magnetohydrodynamic Natural Convection Flow along a Vertical Wavy Surface

Abstract

The effect of temperature dependent variable viscosity on magnetohydrodynamic (MHD) natural convection flow of viscous incompressible fluid along a uniformly heated vertical wavy surface has been investigated. The governing boundary layer equations are first transformed into a nondimensional form using suitable set of dimensionless variables. The resulting nonlinear system of partial differential equations are mapped into the domain of a vertical flat plate and then solved numerically employing the implicit finite difference method, known as Keller-box scheme. The numerical results of the surface shear stress in terms of skin friction coefficient and the rate of heat transfer in terms of local Nusselt number, the stream lines and the isotherms are shown graphically for a selection of parameters set consisting of viscosity parameter (ε), magnetic parameter (M), and Prandtl number (Pr). Numerical results of the local skin friction coefficient and the rate of heat transfer for different values are also presented in tabular form.

Effects of Stress Work on MHD Natural Convection Flow along a Vertical Wavy Surface with Joule Heating

“…Comparison of the values of skin friction coefficient C fx , and the heat transfer coefficient Nu x with Parveen and Alim (2011b) and present work for the variation of Prandtl number Pr while Ec = stress work and the joule heating parameter J are ignored to make the numerical data comparable withParveen and Alim (2011b) for different values of Prandtl number Pr. It is obvious from the comparison table that the present results agreed well with the results ofParveen and Alim (2011b).Numerical values of local shearing stress and the rate of heat transfer are calculated from equations (22) and (23) in terms of the skin-friction coefficients C fx and Nusselt number Nu x respectively for a wide range of the axial distance variable x starting from the leading edge for different values of the parameters Pr, Ec, M, Ge, J and .The velocity and temperature of the flow field is found to change more or less with the variation of the flow parameters. The effect of the flow parameters on the velocity and temperature fields, the skin friction coefficients, the rate of heat transfer, streamlines and the isotherms are analyzed with the help of graphs.The effects for different values of magnetic parameter M on the velocity and temperature have been presented graphically in figures 2(a) and 2(b).…”

Mixed Convection of Non-Newtonian Erying Powell Fluid with Temperature-Dependent Viscosity over a Vertically Stretched Surface

“…In [24], a mathematical analysis of a continuous, incompressible flow of a temperature-dependent on nanofluid from a vertical stretching surface under the external magnetic field and gravitational body force effects has been carried out using the Reynolds exponential viscosity model. The examination of convective flow and heat transport of fluids with temperature-dependent properties is of a great significance for the functional value of modern fluid systems, as mentioned in [25] and [26]. Another analysis of the flow problem associated with this particular effect on temperature-dependent viscosity moving over a vertical plate has drawn some researchers' attention [27][28][29].…”

Unsteady Natural Convection with Temperature-Dependent Viscosity in a Square Cavity Filled with a Porous Medium

“…The study of convective flow and heat transfer of fluids with temperature-dependent properties is of considerable interest in the modern fluid systems of practical importance (see Alim et al 2014;Bondareva et al 2013;Hirayama and Takaki 1993;Hyun and Lee 1988;Jiji 2006;Juarez et al 2011;Martynenko and Khramtsov 2005;Parveen and Alim 2011;Sivasankaran and Ho 2008;Umavathi and Ojjela 2015). It is well known that in the case of the moderate temperature differences, an influence of the temperature-dependent fluid properties in cavities on the fluid structure and heat transfer becomes more essential.…”

“…It has been found that for the higher values of the viscosity variation parameter, one can find an intensification of the friction force at the wall and attenuation of the heat transfer rate. Parveen and Alim (2011) have analyzed an influence of the temperature-dependent viscosity on MHD natural convection along the hot vertical wavy wall. The authors have found that the local skin friction parameter and local heat transfer rate decrease with the increasing dimensionless magnetic parameter.…”