Entropy Generation Analysis of Transient Heat Conduction in a Solid Slab with Fixed Temperature Boundary Conditions

Analysis of entropy generation rate for transient heat conduction, taking place in homogeneous solid slab with fixed temperature boundary conditions, is presented. The initial condition is defined as a constant temperature. The exact solution is solved and used to analyze the local and total entropy generation rates. Two cases, heating and cooling processes, are considered in this study. It is found that the local entropy generation rate dramatically changes at small time and slowly approaches the local entropy generation rate of steady state case. The location of minimum local entropy generation rate can be found in the slab for both heating and cooling cases. For the total entropy generation rate, it shows very high value at small time. This is due to high temperature gradient. It, then, sharply reduces and converges to the total entropy generation rate of steady state case. However, the minimum total entropy generation rate is found for heating case, while it cannot be detected for cooling case. The minimum total entropy generation rate, found in heating case, is observed that it is lower than that of steady state case. The boundary conditions clearly express the effect on the local and total entropy generation rates for transient heat conduction. However, the effect of initial condition on the entropy generation rates can be neglected, especially at large time. Key-Words: Entropy Generation Rate, Second Law Analysis, Transient Heat Conduction, Steady State Heat Conduction, Boundary Condition of the First Type, Exact Solution