The effect of viscous dissipation on forced convective heat transfer for a Couette-Poiseuille flow of a power-law fluid subjected to asymmetric thermal boundary conditions is investigated here. The Couette-Poiseuille flow studied is limited to one with a maximum velocity, where the location that corresponds to the maximum velocity has to be solved numerically. A new analytical expression is obtained for the Nusselt number, in terms of the heat flux ratio applied to the top and bottom parallel plates and in terms of the Brinkman number as defined for the power-law fluid. Present results, when reduced to a few special cases, are in excellent agreement with published results. An asymptotic Brinkman number is observed in the Nusselt number versus Brinkman number plot, which shows a sign change in Nu for the range of power-law indices tested.

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The heat induced by viscous dissipation in a microchannel fluid, due to a small oscillating motion of the lower plate, is investigated for the first time. The methodology is by applying the momentum and energy equations and solving them for three cases of standard thermal boundary conditions. The first two cases involve symmetric boundary conditions of constant surface temperature on both plates and both plates insulated, respectively. The third case has the asymmetric conditions that the lower plate is insulated while the upper plate is maintained at constant temperature. Results reveal that, although the fluid velocity is only depending on the oscillation rate of the plate, the temperature field for all three cases show that the induced heating is dependent on the oscillation rate of the plate, but strongly dependent on the parameters Brinkman number and Prandtl number. All three cases prove that the increasing oscillation rate or Brinkman number and decreasing Prandtl number, when it is less than unity, will significantly increase the temperature field. The present model is applied to the synovial fluid motion in artificial hip implant and results in heat induced by viscous dissipation for the second case shows remarkably close agreement with the experimental literature.

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