Classical and minimum entropy generation analyses for steady state conduction with temperature dependent thermal conductivity and asymmetric thermal boundary conditions: Regular and functionally graded materials

Minimum entropy generation (MEG) temperature profiles are derived for steady conduction in a plane wall, a hollow cylinder and a hollow sphere and compared with the classical results. Cases of constant thermal conductivity, temperature dependent and location dependent thermal conductivities for each geometry are analyzed. Results are presented for the classical and the minimum entropy temperature profiles illustrating the effect of thermal asymmetry and variable thermal conductivity in each geometry. These results show that the difference between the classical and the MEG temperature profiles is largest when there is a strong thermal asymmetry. For all three geometries, the effect of temperature dependent thermal conductivity on the classical temperatures is moderate but its effect on the MEG temperatures is only small. Both the classical and minimum entropy generation rates, for each geometry, are found to be strong functions of thermal asymmetry and thermal conductivity variation parameter. Comparison of results for a hollow cylinder and a hollow sphere reveals that rate of entropy generation in a hollow sphere is much higher than in a hollow cylinder for the same thermal asymmetry and radius ratio.