The effects of uniform injection and suction on heat transfer with viscous dissipation through a permeable surface in zero pressure gradient

Abstract

In the present study; the effects of injection/suction velocity and viscous dissipation on the temperature dis-tribution through a permeable surface with constant temperature was investigated theoretically. The hydro-dynamic and thermal wall functions which include the influence of viscous dissipation and injection/suction velocity were obtained for the boundary layer flow with zero pressure gradient in streamwise. The effect of viscous dissipation was considered with a dimensionless parameter of Br-m = u(tau)(3)rho/q(w) which is a modified Brinkman number. It was noted that the temperature distribution in both the laminar and turbulent boundary layers was substantially influenced by the viscous dissipation. Moreover, viscous dissipation induced internal heat generation causes to a jump in the fluid temperature at the wall T-w,T-f for high Br-m values. In addition, it was seen that viscous dissipation effect on temperature distribution can be noticeably controlled by using injection and suction through permeable surface. Viscous dissipation effect weakens with injection (suction) for low (high) Br-m case. Finally, the critical modified Brinkman number Br-m,Br- (crit) where the heat transfer direction begins to change with strengthening viscous dissipation induced internal heat generation in the flow field has been obtained. It has been found that Br-m,Br- (crit) increases with increasing suction velocity while it decreases with in-creasing injection velocity. It has further observed that Br-m,Br- (crit )decreases (increases) with increasing Pr for suction (injection) although it takes the same values for different Pr values in case of no-injection and suction.