This paper presents mathematical modelling and numerical analysis to evaluate entropy generation analysis (EGA) by considering pressure drop and second law efficiency based on thermodynamics for forced convection heat transfer in rectangular duct of a solar air heater with wire as artificial roughness in the form of arc shape geometry on the absorber plate. The investigation includes evaluations of entropy generation, entropy generation number, Bejan number and irreversibilities of roughened as well as smooth absorber plate solar air heaters to compare the relative performances. Furthermore, effects of various roughness parameters and operating parameters on entropy generation have also been investigated. Entropy generation and irreversibilities (exergy destroyed) has its minimum value at relative roughness height of 0.0422 and relative angle of attack of 0.33, which leads to the maximum exergetic efficiency. Entropy generation and exergy based analyses can be adopted for the evaluation of the overall performance of solar air heaters.

In thermos fluid dynamics, free convection flows external to different geometries, such as cylinders, ellipses, spheres, curved walls, wavy plates, cones, etc., play major role in various industrial and process engineering systems. The thermal buoyancy force associated with natural convection flows can play a critical role in determining skin friction and heat transfer rates at the boundary. In thermal engineering, natural convection flows from cylindrical bodies has gained exceptional interest. In this article, we mathematically evaluate an entropy analysis of magnetohydrodynamic third-grade convection flows from permeable cylinder considering velocity and thermal slip effects. The resulting non-linear coupled partial differential conservation equations with associated boundary conditions are solved with an efficient unconditionally stable implicit finite difference Keller-Box technique. The impacts of momentum and heat transport coefficients, entropy generation and Bejan number are computed for several values of non-dimensional parameters arising in the flow equations. Streamlines are plotted to analyze the heat transport process in a two-dimensional domain. Furthermore, the deviations of the flow variables are compared with those computed for a Newtonian fluid and this has important implications in industrial thermal material processing operations, aviation technology, different enterprises, energy systems and thermal enhancement of industrial flow processes.