Abstract
This paper presents an analysis of the energy exchange resulting from a 2D steady magnetohydrodynamics (MHD) flow past a permeable surface with partial slip in the presence of the viscous dissipation effect under convective heating boundary conditions. A magnetic field can effectively control the motion of an electrically conducting fluid in micro scale systems, which can be applied for fluid transportation. Local similarity solutions for the transformed governing equations are obtained, and the reduced ordinary differential equations solved numerically via an explicit Runge-Kutta (4, 5) formula, the Dormand-Prince pair and shooting method, which is valid for fixed positions along the surface. The effects of various physical parameters, such as the magnetic parameter, the slip coefficient, the suction/injection parameter, the Biot number, the Prandtl number and the Eckert number, on the flow and heat transfer characteristics are presented graphically and discussed. The results indicate that the heat transfer rate increases with the increase in Biot number, slip coefficient, suction and magnetic parameter, whereas it decreases with the increase in Eckert number and injection.
Highlights
The problem of slip MHD flow with viscous dissipation past a permeable surface has many important technological and industrial applications, especially in Microelectromechanical Systems (MEMS), such as micro MHD pumps [1], micromixing of physiological samples [2,3], biological transportation and drug delivery [4,5]
Since most biological transportation applications based on magnetic fields are in the micro/nano systems [6,7,8], it is vital to consider the effect of velocity slip at the boundaries [9,10]
We considered slip MHD flow and heat transfer past a permeable horizontal surface at a convective surface boundary condition in the presence of viscous dissipation effects
Summary
The problem of slip MHD flow with viscous dissipation past a permeable surface has many important technological and industrial applications, especially in Microelectromechanical Systems (MEMS), such as micro MHD pumps [1], micromixing of physiological samples [2,3], biological transportation and drug delivery [4,5]. Martin and Boyd [17] have analyzed the slip flow and heat transfer past a flat surface at constant wall temperature Their results demonstrate that the boundary layer equations can be used to study flow at MEMS scale and provide useful information to study the effects of rarefaction on the shear stress and structure of the flow. Unlike the common thermal boundary conditions, such as constant temperature or constant heat flux, Aziz [30] demonstrated that a similarity solution is possible if the convective heat transfer associated with the hot fluid on the lower surface of the plate is proportional to x−0.5 These results were later improved by Ishak [31] with the addition of the permeability effect along the surface. Even though problem plays a prominent role in the fluid flow and heat transfer control of micro scale systems, no attempt so far has been made to analyze MHD flow and heat transfer past a permeable surface with partial slip and viscous dissipation
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