Abstract
This research note’s objective is to elaborate on the study of the unsteady MHD natural convective flow of the Jeffery fluid with the fractional derivative model. The fluid flow phenomenon happens between two vertical parallel plates immersed in a porous medium. The one plate is moving with the time-dependent velocity U_{0} f(t), while the other is fixed. The mathematical model is presented with the system of the partial differential equation along with physical conditions. Appropriate dimensionless variables are employed in the system of equations, and then this dimensionless model is transformed into the Caputo fractional-order model and solved analytically by the Laplace transform. The exact expressions for velocity and temperature, which satisfy the imposed initial and boundary conditions, are obtained. Memory effects in the fluid are observed which the classical model fails to elaborate. Interesting results are revealed from the investigation of emerging parameters as Grashof number, Prandtl number, relaxation time parameter, Jeffery fluid parameter, Hartmann number, porosity, and fractional parameter. The results are elucidated with the detailed discussion and the assistance of the graphs. For the sake of validation of results, the corresponding solutions for viscous fluids are also obtained and compared with the solutions already existing in the literature.
Highlights
The interest developing in the studies of non-Newtonian fluid in the last few years is owing to its practical implementation in industry and technology
Jeffery fluid is noted as an important model of non-Newtonian fluid because of its simplicity
3.1 Exact solution of temperature we find the exact solution of temperature by using the Laplace transformation
Summary
The interest developing in the studies of non-Newtonian fluid in the last few years is owing to its practical implementation in industry and technology. The examination of MHD impacts on the transfer of heat of an Oldroyd-B fluid via nonlocal kernels was carried by Riaz [23] They explored the semi-analytical solutions, and the results were demonstrated by graphs. Nazish et al [27] performed the analysis of natural convective fluid flow on the inclined magnetic field They used the fractional Caputo, Caputo–Fabrizio, and Atangana–Baleanu operators to highlight the influence of transference of heat and mass on fluid flow. The study of impacts of MHD on Jeffery fluid via fractional derivative was carried out by various researchers in [41,42,43,44,45]. The objective of this manuscript is to study the heat transfer analysis of the MHD fractional Jeffery fluid in a channel with generalized boundary conditions.
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