A fractional and analytic investigation of thermo-diffusion process on free convection flow: an application to surface modification technology

It is worth noted that soft and hard inchromizing entirely depends upon high temperature on materials. Due to this fact, thermal diffusion process can enhance the life expectancy of tools based on surface modification technology. The main objective of this investigation is to explore the thermo-diffusion effects on unsteady-free convection flow in the presence of magnetic field. For developing the governing equations of thermal diffusion process in terms of fractional differentiation, a modern approach of Atangana–Baleanu differential operator is invoked for knowing the memory effects on thermal diffusion process. The temperature, velocity, and concentration are obtained through analytical calculation via Laplace and Fourier sine transform methods. A parametric study is focused for hidden phenomenon of thermo-diffusion process which exhibits typical and rheological properties such as optimal temperature ranges, temperature resistance, increase or decrease of temperature, and few others. Finally, the characteristics of thermal diffusion process are presented graphically based on some physical parameters such as heat transfer (Grashof number), heat capacity (Prandtl number), enthalpy (Dufour number), momentum and mass diffusivity (Schmidt number), magnetization (magnetic field), and few other embedded parameters.