Abstract
A Couette-Poiseuille flow between parallel plates saturated with porous medium is studied with emphasis on viscous dissipation effect on the temperature field; assuming a fully developed flow, with both plates subjected to unequal and uniform heat flux. Temperature field and Nusselt number are derived as a function of Brinkman number and porous medium shape factor. By specifying the ratio of wall to mean velocity as one, the resulting velocity and temperature fields attribute to a significant increase in Nusselt number for the moving wall as the permeability of porous medium increases. Increased permeability signifies competing effect between enhanced convection in the proximity of the moving wall and higher local viscous dissipation. When the former effect dominates, heat transfer coefficient increases. Effects of Reynolds number on the temperature field is elucidated, including a comparison between a microchannel and conventional duct to evaluate the characteristic length scale effect. As Reynolds number goes up in a microchannel, heat generation in the form of viscous dissipation intensifies and overrides the convection effect, causing an increase in the highest temperature along the duct on the contrary to the findings in conventional duct.
Highlights
The fluid flow and heat transfer in a Couette-Poiseuille flow in a channel play a vital role in a wide variety of materials processing applications which includes sheet metal forming, extrusion, wire and fiber glass drawing, continuous casting, and more, whereby in all of these applications, heat is continuously transferred to fluid from moving plane [1]
In order to facilitate the discussion of Couette-Poiseuille flow in a saturated porous medium, the velocity field in the channel for different porous medium shape factors S is depicted in Figure 2 for
It is noteworthy to point out that overall viscous dissipation corresponding to S = 1 drops to a minimum and picks up tremendously towards the fixed wall, revealing a much lower viscous dissipation at the velocity field in the channel for different porous medium shape factors S is depicted in Figure 2 for U ⁄U = 1, that results in profile with a maximum velocity
Summary
The fluid flow and heat transfer in a Couette-Poiseuille flow in a channel play a vital role in a wide variety of materials processing applications which includes sheet metal forming, extrusion, wire and fiber glass drawing, continuous casting, and more, whereby in all of these applications, heat is continuously transferred to fluid from moving plane [1]. Laminar heat transfer problems in Poiseuille flow for Newtonian fluids in parallel plates have been solved [2] while Aydin and Avci [3] subsequently studied Poiseuille flow in laminar heat convection for two different thermal boundary conditions—constant heat flux and constant wall temperature respectively—accounting for the effect of viscous dissipation and highlighted the importance of viscous dissipation. Investigated the effect of viscous dissipation on the heat transfer rate for Couette-Poiseuille flow in a saturated porous medium between two plane parallel plates. The study concurred on the significance of viscous dissipation on Couette-Poiseuille flow but did not further any explorations on the thermal boundary condition implementation at the fixed boundary further explorations onofthe condition implementation at the fixed boundary nor nor theany length scale effect thethermal parallelboundary plate channel on dimensional temperature field. The would compare the significance of viscous viscous dissipation to porous the temperature fieldstudy in microchannel and conventional size channel for dissipation different Re.to the temperature field in microchannel and conventional size channel for different Re
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