This paper aims to study viscous heating, Joule heating and their simultaneous impacts on Al2O3-water nanofluid laminar flow and thermal characteristics in the presence of a magnetic field inside microchannels. The flow field and heat transfer are modeled two- and three-dimensionally by employing the finite volume method. To investigate the influence of viscosity variation with temperature on viscous heating, a temperature-dependent viscosity correlation specifically presented for Al2O3-water is employed. Predicted results indicate that viscosity changes due to temperature changes are negligible and although viscous heating can be reasonably ignored in the absence of the magnetic field, it must be taken into account when the magnetic field is applied. At the Hartmann number of 20, near microchannel walls, the velocity gradient rises up to 165% where the viscous dissipation significantly increases the temperature. In addition, when the magnetic field is applied, the 2D model underestimates the temperature compared to the 3D model where the effects of maximum velocity and velocity gradient on the energy equation and heat dissipation exist. The temperature profiles demonstrate that at the Hartmann number of 20, the effects of Joule heating or viscous heating increase the maximum dimensionless temperature by a factor of about 2.5 and by the rise of the Hartmann number, the dimensionless temperature increases and the effects of Joule and viscous heating become more significant. All in all, it is concluded that the heat generated by viscous and Joule heating can remarkably decrease the cooling performance of microchannels in the presence of magnetic fields.
