Mixed convection of couple stress fluid in a vertical channel in the presence of heat generation or heat absorption

Abstract

The fully developed mixed convection of couple stress fluid in a vertical channel in the presence of heat generation or absorption is analyzed. The two boundaries of the channel are considered as isothermalisothermal, isoflux-isothermal and isothermal-isoflux for the left and right walls and kept either at equal or at different temperatures. The governing momentum and energy equations are coupled and non linear due to the viscous effects. The velocity field and the temperature field is obtained by perturbation series method which employs a perturbation parameter proportional to the Brinkman number. In addition, closed form expressions for reversal flow conditions at both the left-right channel walls are derived. The results are represented graphically for different values of perturbation parameter and couple stress parameter on velocity and temperature distributions. We observe that for purely viscous fluid the flow reversal was at the hot wall whereas for couple stress fluid there is a flow reversal both at left and right walls. The effect of the perturbation parameter on the flow for couple stress fluid is dominating compare to viscous fluid both on velocity and temperature. The profiles of temperature are significant for couple stress fluid for different values of perturbation parameter whereas the profiles were not sensible for same values for viscous fluid.

Key words: Mixed convection, viscous dissipation, buoyancy force, perturbation series