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Heat Transfer Research
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Heat Transfer Research

DOI: 10.1615/HeatTransRes.2018025031
pages 839-849

MHD THIN FILM OLDROYD-B FLUID WITH HEAT AND VISCOUS DISSIPATION OVER OSCILLATING VERTICAL BELTS

Mehreen Fiza
Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Pakistan
Saeed Islam
Department of Mathematics, Abdul Wali Khan University Mardan, 23200 Pakistan
Hakeem Ullah
Department of Mathematics, Abdul Wali Khan University Mardan, 23200 Pakistan
Z. Ali
Department of Mathematics, Abdul Wali Khan University Mardan, 23200 Pakistan

ABSTRACT

In this paper, we investigated magnetohydrodynamic (MHD) thin film flow of an Oldroyd-B fluid in the presence of heat transfer with effect of viscous dissipation over an oscillating vertical belt. The fluid is assumed to be unsteady, and the basic governing equations are modeled in the form of nonlinear coupled partial differential equations with pertinent initial and boundary conditions. For the analytical solutions of the problem we use the optimal homotopy asymptotic method (OHAM). For comprehension, the physical presentation of such modeled parameters as the Prandtl number Pr, Brinkman number Br, time retardation parameter a, time relaxation parameter β, gravitational parameter St, and magnetic parameter M are plotted graphically and discussed. An increase in M increases the velocity and temperature distribution, the boundary-layer thickness decreases by increasing the Prandtl number, and the velocity decreases by increasing the gravitational parameter.

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