Effect of variable thermal conductivity on entropy generation in a plate with internal energy generation

The current numerical investigation aims at analyzing the effect of variable thermal conductivity on local and global entropy generation rates in an energy generating plate dissipating heat by conjugate conduction-forced convection heat transfer. In order to fulfill this objective, the physical model of the plate dissipating heat into surrounding coolant is transformed into a mathematical model governing the temperature field in the plate as well as flow and thermal fields in the fluid. The resulting mathematical model, being a set of coupled and non linear partial differential equations, is solved by adopting stream function-vorticity formulation and by employing Alternating direction implicit scheme. Keeping Prandtl number of the fluid, temperature of the free stream coolant and maximum permissible plate temperature as fixed, numerical predictions are obtained for wide range of values of aspect ratio, conduction-convection parameter, energy generation parameter and flow Reynolds number. It is concluded that unrealistic constant thermal conductivity assumption leads to underestimation of entropy generation rates. It is also found that an increase in energy generation parameter results in significant increase in underestimation of global entropy generation rate