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

Abstract

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 θ < 2 and φ < 2, on the other hand entirely opposite trend is witnessed for θ ≥ 3 and φ ≥ 3. From an engineering perspective, we have acquired comprehensive outcomes such that the heat transfer offers an increasing trend in the case of T R and thermal fractional parameter β 1 . 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.

Caputo–Fabrizio fractional model of MHD second grade fluid with Newtonian heating and heat generation

“…The authors studied the unequal diffusivities of chemical species in a Forchhiemer medium by using Scott Blair model of viscoelastic fluid with unsteady convection in 28 . The author studied the effects of mixed convection with thermal radiation and chemical by using the space-time coupled Cattaneo-Friedrich Maxwell Model with Caputo fractional derivatives in a porous medium 29 . The authors used the fractional calculus to analyzed the thermo-diffusion phenomenon numerically in a Darcy medium 30 .…”

Numerical analysis of nonlinear time‐fractional fluid models for simulating heat transport processes in porous medium

“…This study will address the DOFDEs for the kinetic description of hybrid nanofluid and relaxation phenomena [20]. Numerous researchers have investigated the numerical solutions of time simple-order fractional equations utilizing multiple mathematical methods, [21][22][23][24]. On the other hand, the time distributed-order fractional equation offers a more flexible depiction of the actual impact of the medium and its interplay with the liquid [25].…”

Modeling and computation of nanofluid for thermo-dynamical analysis between vertical plates

“…8 An excellent piece of work based on the space-time Maxwell fractional model through CTFD was proposed in reference. 9 Hussain et al investigated HNF on a stretched surface along with shape factors in reference. 10 Abu-Hamdeh et al 11 examined the Powell-Eyring nanofluid and Jumped thermal conditions based on solar energy.…”