Apparent entropy production difference with heat and fluid flow irreversibilities

An entropy-based procedure is presented to assess the solution accuracy in heat transfer problems with fluid flow using the second law of thermodynamics. The procedure is implemented by a control-volume-based finite-element formulation for discrete equations arising from the conservation laws and the second law. The study involves a comparison of the local entropy production rates computed from two forms of the discretized entropy equation. The computed local entropy production for two heat transfer problems, using the positive-definite and the transport forms of the entropy generation equation, agrees well with analytical solutions. It is demonstrated by the results of the numerical studies that there exists a relationship between a newly defined parameter, called the apparent error in entropy production, and the solution error in the computed value of the scalar in each control volume.