Viscous dissipation effect on heat trans

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 an electromagnetic field with the boundary condition appropriate to the slip flow regime. For isoflux walls, closed-form expressions for the local and bulk temperature profiles and the Nusselt number are provided in terms of dimensionless slip length, Hartmann number, and Brinkman number, accounting for viscous dissipation. The analytical solutions derived reveal that the contribution of viscous dissipation to the Nusselt number can reach nearly 10% under certain circumstances, particularly in stronger electromagnetic fields. This necessitates consideration of viscous heating; otherwise, heat transfer rates may be inaccurately estimated, depending on whether the fluid is heated or cooled. Additionally, singularities in Nusselt number values shift closer together when viscous dissipation is included, and it is observed that an increase in the Hartmann number enhances convection, particularly reflected in smaller dimensionless slip length values.