A theoretical study of the effect of variable viscosity and variable thermal conductivity on the classical plane Couette-Poiseuille flow is presented in this brief communication. The investigation concerns engine oil, air, and water taking into account the variation of these quantities with temperature. The results are obtained with the numerical simulation of the governing equations and cover large temperature differences. Velocity and temperature profiles are presented as well as the volume flow rate and the heat flux between the plates. It is found that temperature profiles are close to the straight line for oil and water and depart significantly from the straight line for air due to nonlinear thermal conductivity. Dynamic viscosity plays an important role on the results which depart significantly from those of a fluid with constant properties.

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