Application of differential transform method to unsteady free convective heat transfer of a couple stress fluid over a stretching sheet

In the present article, the transient rheological boundary layer flow over a stretching sheet with heat transfer is investigated, a topic of relevance to non-Newtonian thermal materials processing. Stokes couple stress model is deployed to simulate non-Newtonian characteristics. Similarity transformations are utilized to convert the governing partial differential equations into nonlinear ordinary differential equations with appropriate wall and free stream boundary conditions. The non-dimensional boundary value problem emerging is shown to be controlled by a number of key thermophysical and rheological parameters, namely the rheological couple stress parameter, unsteadiness parameter, Prandtl number (Pr), buoyancy parameter. The semi-analytical Differential Transform Method (DTM) is used to solve the reduced nonlinear coupled ordinary differential boundary value problem. A numerical solution is also obtained via the MATLAB built in solver ‘bvp4c’ to validate the results. Further validation with published results from the literature is included. Fluid velocity is enhanced with increasing couple stress parameter whereas it is decreased with unsteadiness parameter. Temperature is elevated with couple stress parameter whereas it is initially reduced with unsteadiness parameter. The flow is accelerated with increasing positive buoyancy parameter (for heating of the fluid) whereas it is decelerated with increasing negative buoyancy parameter (cooling of the fluid). Temperature and thermal boundary layer thickness are boosted with increasing positive values of buoyancy parameter. Increasing Prandtl number decelerates the flow, reduces temperatures, increases momentum boundary layer thickness and decreases thermal boundary layer thickness. Excellent accuracy is achieved with the DTM approach.