Abstract
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.
Highlights
Heat transfer in parallel plates flow plays an essential role in processes such as in heat exchangers, extrusion, glass fiber drawing, and metal forming, where the heat is exchanged continuously with the surrounding fluid and plate surfaces [1]
In this study on heat induced by viscous dissipation caused by an oscillating microchannel fluid flow that is laminar, unsteady, constant properties, and Newtonian, the governing equations are solved numerically for the same unsteady hydrodynamic conditions, but three different cases of thermal boundary conditions
They are parallel plates with both sides subjected to constant surface temperature, both sides insulated and the third case with upper side subject to constant surface
Summary
Heat transfer in parallel plates flow plays an essential role in processes such as in heat exchangers, extrusion, glass fiber drawing, and metal forming, where the heat is exchanged continuously with the surrounding fluid and plate surfaces [1]. The insight of fluid rheology behaviour is vital and can affect the quality efficiency during the heat transfer process. The effect of viscous dissipation can contribute to a significant amount of heat generation under certain situations such as flow in microchannels and microtubes [3,4,5]. The viscous dissipation effect in the conservation of energy is in the form of a dimensionless term, known as the Brinkman number, Br, with a zero value of Br implying no viscous dissipation
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