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This paper presents a new design of open parallel microchannels embedded within a permeable continuous moving surface due to reduction of exergy losses in magnetohydrodynamic (MHD) flow at a prescribed surface temperature (PST). The entropy generation number is formulated by an integral of the local rate of entropy generation along the width of the surface based on an equal number of microchannels and no-slip gaps interspersed between those microchannels. The velocity, the temperature, the velocity gradient and the temperature gradient adjacent to the wall are substituted into this equation resulting from the momentum and energy equations obtained numerically by an explicit Runge-Kutta (4, 5) formula, the Dormand-Prince pair and shooting method. The entropy generation number, as well as the Bejan number, for various values of the involved parameters of the problem are also presented and discussed in detail.

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.

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