A new modeling for 3D Carreau fluid flow considering nonlinear thermal radiation

Abstract

A mathematical analysis for 3D forced convective flow of Carreau fluid over a bidirectional stretched surface is presented. The Carreau liquid model is the generalization of linear materials which reveal the aspects of shear thinning (n<1) and shear thickening (n>1) liquids. Additionally, heat transfer phenomenon is inspected in this research work by utilizing the non-linear thermal radiation and convective surface boundary conditions. The boundary layer equations of 3D Carreau fluid are established by means of usual boundary layer approximations. The governing set of PDEs is rendered into coupled non-linear ODEs via appropriate transformations. Numerical solutions are computed for the resulting non-linear ODEs by employing an effective numerical scheme namely bvp4c function in Matlab. Features of numerous sundry thermophysical parameters on the liquid velocity, temperature, skin friction and Nusselt number are explored and discussed in detail. The present study reveals that the liquid velocity declines for shear thinning liquids (n<1) for the larger values of ratio of stretching rates parameter α and for shear thickening liquids (n>1) conflicting behavior is detected. It is also pragmatic that thermal radiation parameter Rd is an augmenting function of temperature distribution on both situations. To comprehend the legitimacy of numerical results a comparison between bvp4c results with the analytical results obtained by the homotopy analysis method (HAM) is also made in this exploration and alleged an admirable agreement. Furthermore, authentication of numerical outcomes is achieved via benchmarking with previously reported limiting cases and we generally found a splendid correlation with these results.