Non-Newtonian nanofluid flow across an exponentially stretching sheet with viscous dissipation: numerical study using an SCM based on Appell–Changhee polynomials

The objective of this article is to investigate how the properties of a non-Newtonian Williamson nanofluid flow, which occurs due to an exponential stretching sheet placed in a porous medium, are influenced by heat generation, viscous dissipation, and magnetic field. This study focuses on analyzing the heat transfer process by considering the impact of temperature on the thermal conductivity and viscosity of Williamson nanofluids. Additionally, the research significantly contributes by investigating the flow characteristics of these nanofluids when influenced by slip velocity. Using the spectral collocation method (SCM), the equations that describe the current problem are transformed into a collection of ordinary differential equations and then solved. The SCM proposed here basically depends on the properties of the Appell-type Changhee polynomials (ACPs). First, with the aid of ACPs, we give an approximate formula of the derivatives for the approximated functions. Through this procedure, the provided model is transformed into a nonlinear set of algebraic equations. Physical factors of interest, such as skin friction, the Nusselt number, and the Sherwood number, are explained using tabular expressions. Data are displayed as graphs for the nanofluid’s velocity, temperature, and concentration. The primary findings showed that increasing the Williamson, magnetic, thermal conductivity, and Brownian parameters significantly improves the thermal field. Finally, testing the suggested method with specific cases from some past literature-based publications reveal a good degree of agreement.