Numerical solution for flow of a Eyring–Powell fluid in a pipe with prescribed surface temperature

Abstract

In the current study, the flow and heat transfer of MHD Eyring–Powell fluid in a circular infinite pipe is discussed. The rheology of fluid is described by constitutive equation of Eyring–Powell fluid. The solution is constructed for both constant and variable viscosity cases. For variable viscosity case, the viscosity function is defined by Reynolds and Vogel’s models. The solution of each case is calculated numerically with the help of eminent iterative numerical technique. The effects of thermo-fluidic parameters on flow and heat transfer phenomenon are highlighted through graphs. The velocity and temperature profiles diminish against magnetic parameter $$(M_{e} )$$ and material parameter (M) in all cases, whereas both velocity and temperature profiles rise via magnitude of the pressure gradient and material parameter Y. The validity of our numerical results due to shooting method is presented by comparing them with the numerical results produced by pseudo-spectral collocation method. Relative absolute errors are plotted, and achieved accuracies are of the order four and five in w and $$\theta$$, respectively. The outcomes of current investigation may be useful in thin film, catalytic reactors, polymer solutions and paper production, etc.