Influence of magnetic field on double convection problem of fractional viscous fluid over an exponentially moving vertical plate: New trends of Caputo time-fractional derivative model

Abstract

In this article, the influence of a magnetic field is studied on a generalized viscous fluid model with double convection, due to simultaneous effects of heat and mass transfer induced by temperature and concentration gradients. The fluid is considered over an exponentially accelerated vertical plate with time-dependent boundary conditions. Additional effects of heat generation and chemical reaction are also considered. A generalized viscous fluid model consists of three partial differential equations of momentum, heat, and mass transfer with corresponding initial and boundary condition. The idea of non-integer order Caputo time-fractional derivatives is used, and exact solutions for velocity, temperature, and concentration in terms of Wright function and function of Lorenzo–Hartley are developed for ordinary cases. Graphical analysis of flow and fractional parameters is made by using computational software MathCad, and discussed. The results obtained are also in good agreement with the published results from the literature. As a result, it is found that temperature and fluid velocity can be enhanced for smaller values of fractional parameters.

First Solution of Fractional Bioconvection with Power Law Kernel for a Vertical Surface

“…By introducing Equations ( 39) and ( 40) into Equations ( 34) and (36), respectively, we have. In [72,73] the authors used the same kind of fractional modeling for some heat transfer models.…”

Numerical Investigation of the Time‐Fractional Whitham–Broer–Kaup Equation Involving without Singular Kernel Operators

“…e widely held dynamical schemes can be denoted by an appropriate set of FPDEs. Moreover, it is well identified that FPDEs solve mathematical models, such as Poincare conjecture and Calabi conjecture models [1][2][3][4][5][6][7][8][9][10][11][12].…”

Impact of radiation absorption on Caputo fractional fluid flow over an exponentially accelerated plate

“…The authors pointed out that the solution for velocity profile with fractional derivatives is faster than that of a classical one. The same conditions were then used by Shah et al [19] to study the effects of the double convection problem. Imran et al [20] continued Shah et al's [18] study by incorporating boundary conditions of Newtonian heating and arbitrary velocity.…”