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Objective:   Many methods have been used to maximize the capacity of heat transport. A constant pressure gradient or the motion of the wall can be used to increase the heat transfer rate and minimize entropy. The main goal of our investigation is to develop a mathematical model of a non-Newtonian fluid bounded within a parallel geometry. Minimization of entropy generation within the system also forms part of our objective.Method:   Perturbation theory is applied to the nonlinear complex system of equations to obtain a series solution. The regular perturbation method is used to obtain analytical solutions to the resulting dimensionless nonlinear ordinary differential equations. A numerical scheme (the shooting method) is also used to validate the series solution obtained.Results:   The flow and temperature of the fluid are accelerated as functions of the non-Newtonian parameter (via the power-law index). The pressure gradient parameter escalates the heat and volume flux fields. The energy loss due to entropy increases via the viscous heating parameter. A diminishing characteristic is predicted for the wall shear stress that occurs at the bottom plate versus the time-constant parameter. The Reynolds number suppresses the volume flux field.

Scrutiny of entropy optimized tangent hyperbolic fluid (non-Newtonian) through perturbation and numerical methods between heated plates