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.

The main goal of the research is to investigate the effects of temperature and concentration slip on the MHD Casson-Williamson nanofluid flow through a porous sheet, with a focus on viscous dissipation. This research has a novel approach, as it seeks to incorporate various factors that have not been previously studied in this context. Moreover, an inclined magnetic field from the outside is applied to the stretched surface. Besides this, it is considered that the viscosity of nanofluids depends on temperature while all other physical characteristics are taken to be constant. It is hypothesized that the expanding surface that stretched exponentially is what caused the flow motions of the nanofluid. There are several engineering applications for this type of study, which is based on MHD non-Newtonian nanofluid flow across a stretched surface with heat generation and viscous dissipation. They include solar energy storage, energy distribution, chemical reactors, and the manufacturing of polymers. To examine the heat transmission and mass transfer rates, tools like thermophoresis and Brownian motion were implemented. The flow problem is formally represented as a set of nonlinear PDEs that are then, through the use of dimensionless variables, converted into a set of ODEs. To numerically obtain the solution to the problem, the shifted Chebyshev polynomials of the third-kind approximation along with the spectral collocation technique are utilized. This process transforms the existing model into an algebraic equation system that was created as a restricted optimization problem, which is then optimized to obtain the solution and the unknown coefficients. For a variety of pertinent parameter values, the graphic and tabular representations of the concentration, temperature, velocities, rate of heat mass transfer, and shear stresses of nano-fluids at the surface of the sheet are shown. Finally, there is a remarkable amount of agreement between the earlier investigation and the comparison research that was conducted. The results indicate that an increase in the magnetic parameter, Casson parameter, viscosity parameter, and suction parameter causes a reduction in both the velocity and boundary layer thickness. In addition, as the viscosity parameter, Casson parameter, and magnetic parameter increase, both the concentration and temperature exhibit an increase in their values. MSC 2010: 41A30; 65N12; 65M60; 76F12.

The purpose of this research is to examine the effects of heat generation, viscous dissipation, and magnetic field on the characteristics of non-Newtonian Williamson nanofluid flow caused by an exponential stretching sheet implanted in a porous media. The process of heat transfer is examined while taking into account how the temperature affects the thermal conductivity as well as the viscosity of the Williamson nanofluids. Also, the analysis of their flow performances under the influence of slip velocity was the study’s main contribution. Using the spectral collocation technique (SCM), the equations that describe the current problem are transformed into a collection of ordinary differential equations and then solved. The spectral collocation method (SCM) proposed here basically depends on the properties of the Appell-type Changhee polynomials (ACPs). First, with the aid of ACPs, we develop an approximate derivative formula. 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, the 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 reveals a good degree of agreement.

The current research examines the rate of heat and mass transfer in MHD non-Newtonian Williamson nanofluid flow across an exponentially permeable stretched surface sensitive to heat generation/absorption and mass suction. The influences of Brownian motion and thermophoresis are included. In addition, the stretched surface is subjected to an angled outside magnetic field. This study incorporates the variable viscosity, viscous dissipation, and slip velocity. The fundamental rules of motion and heat transmission have been constructed mathematically to fit the current flow problem. By using appropriate self-similarity transformations, the supplied system of PDEs is transformed into a nonlinear system of ODEs. Here, we use the spectral collocation method with the help of Vieta-Lucas polynomials approximation. This procedure converts the present model to a system of algebraic equations which is developed as a constrained optimization problem, which is then optimized to get the solution and the unknown coefficients. Calculations are made for the skin friction, wall temperature gradient, and wall concentration gradient. By comparing our findings in some special cases to those in the literature, a review of the literature confirms the results described here.