Abstract
This article presents the problem, in which we study the unsteady double convection flow of a magnetohydrodynamics (MHD) differential-type fluid flow in the presence of heat source, Newtonian heating, and Dufour effect over an infinite vertical plate with fractional mass diffusion and thermal transports. The constitutive equations for the mass flux and thermal flux are modeled for noninteger-order derivative Caputo–Fabrizio (CF) with nonsingular kernel, respectively. The Laplace transform and Laplace inversion numerical algorithms are used to derive the analytical and semianalytical solutions for the dimensionless concentration, temperature, and velocity fields. Expressions for the skin friction and rates of heat and mass transfer from the plate to fluid with noninteger and integer orders, respectively, are also determined. Furthermore, the influence of flow parameters and fractional parameters α and β on the concentration, temperature, and velocity fields are tabularly and graphically underlined and discussed. Furthermore, a comparison between second-grade and viscous fluids for noninteger and integer is also depicted. It is observed that integer-order fluids have greater velocities than noninteger-order fluids. This shows how the fractional parameters affect the fluid flow.
Highlights
Academic Editor: Marcus Aguiar is article presents the problem, in which we study the unsteady double convection flow of a magnetohydrodynamics (MHD) differential-type fluid flow in the presence of heat source, Newtonian heating, and Dufour effect over an infinite vertical plate with fractional mass diffusion and thermal transports. e constitutive equations for the mass flux and thermal flux are modeled for noninteger-order derivative Caputo–Fabrizio (CF) with nonsingular kernel, respectively. e Laplace transform and Laplace inversion numerical algorithms are used to derive the analytical and semianalytical solutions for the dimensionless concentration, temperature, and velocity fields
Free convection flows ensuing from the heat and mass transfer directed by the combined buoyancy effects because of temperature and concentration variations have been widely studied due to their applications in geotechnical engineering and chemical and bioengineering and in industrial activities [1]
The mass transfer due to the concentration disparity influences the rate of heat transfer. e driving force for the free convection is buoyancy, so its effects cannot be neglected whether the velocity of the fluid is small and change in temperature between the ambient fluid and surface is large enough [2,3,4]
Summary
0+, the heat transfer from the plate to the fluid is proportional to the local surface temperature. Locity, temperature, and concentration are functions of ξ1 and t 1 only. For such a flow, the constraint of incompressibility is identically satisfied. Boussinesq approximation, the convection flow is governed by the following set of partial differential equations [32, 33, 37]: z〔u1. To establish a model with time-fractional derivatives, we assume a thermal process with memory illustrated by the generalized fractional constitutive equation for thermal flux and mass diffusion, respectively [38, 39]: j(y, t).
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