Analytical Solution for Impact of Caputo-Fabrizio Fractional Derivative on MHD Casson Fluid with Thermal Radiation and Chemical Reaction Effects

Fractional derivatives have been proven to showcase a spectrum of solutions that is useful in the fields of engineering, medical, and manufacturing sciences. Studies on the application of fractional derivatives on fluid flow are relatively new, especially in analytical studies. Thus, geometrical representations for fractional derivatives in the mechanics of fluid flows are yet to be discovered. Nonetheless, theoretical studies will be useful in facilitating future experimental studies. Therefore, the aim of this study is to showcase an analytical solution on the impact of the Caputo-Fabrizio fractional derivative for a magnethohydrodynamic (MHD) Casson fluid flow with thermal radiation and chemical reaction. Analytical solutions are obtained via Laplace transform through compound functions. The obtained solutions are first verified, then analysed. It is observed from the study that variations in the fractional derivative parameter, α, exhibits a transitional behaviour of fluid between unsteady state and steady state. Numerical analyses on skin friction, Nusselt number, and Sherwood number were also analysed. Behaviour of these three properties were in agreement of that from past literature.

Thermal and chemically reactive features of Casson nanofluid flow with thermophoresis and Brownian effect over an exponentially stretching surface

Heat and mass transfer of the MHD flow of Casson nanofluid by an exponential stretching sheet discussed in this analysis. The MHD with joule heating effects for Casson nanofluid numerically investigated. To characterize the transport property of heat and mass, we considered the thermophoresis and Brownian effect along with thermal radiation and thermophoretic effects. Additionally, we consider the microorganism theory to analyze the suspended nanoparticles by bio-convection. The mathematical model developed on the base of boundary layer flow of casson nanofluid at exponentially stretching surface in term of partial differential equations. The partial differential equations are transformed into nonlinear ordinary differential equations by means of similarity variable transformations. The non-dimensionalized differential equations have numerically tackled by using the Bvp4c MATLAB technique. The graphical outcomes are obtained against the various parameters. Moreover, physical quantities are examined graphically and tabulating data. It is reviewed that resistance of fluid flow improves by the higher estimation of the Casson fluid parameter. Therefore, the axial and transverse velocities are reduced. Further, it is noticed from the tabulated data that more vital values of the Casson fluid parameter diminishes the skin friction and mass transfer rate but enhances the heat transfer rate.

Casson fluid flow with heat and mass transfer in a channel using the differential transform method

In the present investigation, we consider the heat and mass transfer characteristics of steady, incompressible and electrically conducting Casson fluid flow in a channel. The effect of chemical reactions have also been considered. The differential transform method (DTM) is applied to a system of non-linear ODEs, and the results are obtained in the form of DTM series. The principal gain of this approach is that it applies to the non-linear ODEs without requiring any discretization, linearization or perturbation. The velocity, mass and heat transfer profiles thus obtained are in good agreement with those provided by the quasi-linearization method (QLM). Graphical results for velocity, concentration and temperature fields are presented for a certain range of values of the governing parameters.