Mixed convection with variable viscosity in an inclined channel with prescribed wall temperatures

The fully developed laminar mixed convection of a Newtonian fluid with temperature-dependent viscosity in an inclined plane channel with prescribed wall temperatures is studied analytically. First, an analytical solution which holds for any dependence of viscosity on temperature is found. Then, a model to describe this dependence is presented and applied to the general solution, and some examples are discussed. The results show that the changes of viscosity with temperature may yield relevant effects on the dimensionless velocity distribution and on the friction factors even in the case of forced convection. On the contrary, the effect of a variable viscosity on the dimensionless pressure drop is important only when it is coupled with that of buoyancy forces. In fact, in some cases, the difference between the pressure and the hydrostatic pressure increases along the flow direction.