The Space-Time Coupled Fractional Cattaneo-Friedrich Maxwell Model with Caputo Derivatives

In the current article, we have thoroughly investigated the collective impact of mixed convection with thermal radiation and chemical reaction on MHD flow of viscous and electrically conducting fluid (Cattaneo-Friedrich Maxwell-CFM model) over a permeable surface embedded in a porous medium. Here we have utilized the Caputo time-fractional derivatives and mechanical laws (generalized shear stress constitutive equation and generalized Fourier's and Fick's laws) are being used to fractionalize the presented model. The effects of radiative heat flux, Ohmic dissipation, and internal absorption are presented through generalized Fourier's law while Fick's law or mass transfer equation offers the effects of first order chemically reactive species. The finite element method and finite difference method are being utilized to numerically solve the nonlinear coupled differential equations. It is established, through compression of numerical and analytical solutions, that the presented model is convergent. Further, error analysis of the subject model is also carried out. Moreover, for better illustration of results, we have also offered a graphical and tabular presentation of impacts of the parameters of interest on velocity, temperature, concentration profile, local skin friction coefficient, and heat and mass transfer. It is evident from the obtained results that velocity near and away from the surface increases with the enhancement of fractional derivative parameter whereas an opposite trend is observed in the case of temperature. Furthermore, it is noticed that temperature shows a decreasing behavior for the value $$ and $$ , on the other hand entirely opposite trend is witnessed for $$ and $$ . From an engineering perspective, we have acquired comprehensive outcomes such that the heat transfer offers an increasing trend in the case of T and thermal fractional parameter $$ . Additionally, the chemical reaction parameter and Sc significantly contribute towards the mass transfer rate. Since, in literature, one cannot refer to such results with non-integer Caputo fractional derivatives thus the results obtained through the current assessment hold significance for future research avenues. Moreover, the numerical inferences of the subject study may contribute to an advanced thermal processing method in the food industry to swiftly increase the temperature for cooking or sterilization drives.