Viscous dissipation effect on heat transfer characteristics of mixed electromagnetic/pressure driven liquid flows inside micropumps

This paper presents the effect of viscous dissipation on heat transfer characteristics of mixed electromagnetic/pressure driven liquid slip flows inside parallel plate microchannels. Flow is governed by the Navier-Stokes equations subject to the imposition of electromagnetic field with the boundary condition appropriate to the slip flow regime. For isoflux walls, some closed form expressions for the local and bulk temperature profiles and the Nusselt number in terms of dimensionless slip length, Hartmann number and Brinkman number are given, while the viscous dissipation is also taken into account. Then the analytical solutions derived in this analysis are elaborated. It turns out that since the contribution of the viscous dissipation on the Nusselt number under the given circumstances, especially a stronger electromagnetic field, may reach to nearly 10%, therefore, the viscous heating should be taken into consideration. Otherwise, the heat transfer rate may be overestimated or underestimated depending on whether the fluid is being heated or cooled. Also, there are singularities in Nusselt number values, which move close together by including the viscous dissipation. Further, an increase in the Hartmann number increases the convection, which is especially reflected in smaller values of dimensionless slip length.