This study reports the thermal analysis and species transport to manifest non-Newtonian materials flowing over linear stretch sheets. The heat transfer phenomenon is presented by the Cattaneo–Christov definition of heat flux. Mass transportation is modeled using traditional Fick’s second law. In addition, the contribution of Joule heating and radiation to thermal transmission is also considered. Thermo-diffusion and diffusion-thermo are significant contributions involved in thermal transmission and species. The physical depiction of the scenario under consideration is modeled through the boundary layer approach. Similar analysis has been made to convert the PDE model system into the respective ODE. Then, the transformed physical expressions are calculated for momentum, thermal, and species transport within the boundary layer. The reported study is a novel contribution due to the combined comportment of thermal relaxation time, radiation, Joule heating, and thermo-diffusion, which are not yet explored. Several engineering systems are based on their applications and utilization.

This paper studies heat transfer in a two-dimensional magnetohydrodynamic viscous incompressible flow in convergent/divergent channels. The temperature profile was obtained numerically for both cases of convergent/divergent channels. It was found that the temperature profile increases with an increase in Reynold number, Prandtl number, Nusselt number and angle of the wall but decreases with an increase in Hartmann number. A relatively new numerical method called the spectral homotopy analysis method (SHAM) was used to solve the governing non-linear differential equations. The SHAM 3rd order results matched with the DTM and shooting, showing that SHAM is feasible as a technique to be used.

The variable-order (VO) fractional calculus can be seen as a natural extension of the constant-order, which can be utilized in physical and biological applications. In this study, we derive a new numerical approximation for the VO fractional Riemann–Liouville integral formula and developed an implicit difference scheme (IDS) for the variable-order fractional sub-diffusion equation (VO-FSDE). The derived approximation used in the VO time fractional derivative with the central difference approximation for the space derivative. Investigated the unconditional stability by the van Neumann method, consistency, and convergence analysis of the proposed scheme. Finally, a numerical example is presented to verify the theoretical analysis and effectiveness of the proposed scheme.

Stretched flows have numerous applications in different industrial, biomedical and engineering processes. Current research is conducted to examine the flow phenomenon of Prandtl fluid model over a moveable surface. The phenomenon of mass and thermal transportation is based on generalized theory of Cattaneo–Christov which considers the involvement of relaxation times. In addition to these, variable characteristics of thermal conductivity and diffusion coefficient are considered as a function of temperature. The physical problem in Cartesian coordinate system is modeled via boundary layer theory which yields a coupled system of partial differential equations. Group scaling transportation is applied to model these PDEs system. The converted equations have been approximated via optimal homotopic scheme. The efficiency and validity of used approach has been shown by computing the error analysis and establishing a comparative study. It is noted that the enhancement in magnetic parameter plays a controlling role for velocity field and it augment the concentration and temperature fields. Furthermore, increase in thermal relaxation parameter and Prandtl number maintains the fluid temperature.