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In this paper a new approach is taken to find the exact solutions for generalized unsteady magnetohydrodynamic transport of a rate-type fluid near an unbounded upright plate and is analyzed for ramped wall temperature and velocity with constant concentration. The vertical plate is suspended in a porous medium and encounters radiation effects. Solutions based on special functions are obtained using an integral transform for an unsteady MHD Maxwell fluid in the presence of ramped velocity, temperature and constant concentration. The relations for Nusselt number and skin-friction coefficient are efficiently computed to precisely estimate the rate of heat transfer at the boundary and the shear stress. Results are also discussed in detail and demonstrated graphically using software to comprehensively analyze the dynamics of the proposed problem, and the physical impact of several system parameters, such as magnetic field M, Prandtl number Pr, the relaxation time λ, dimensionless time τ, Schmidt number Sc, Mass and Thermal Grashof numbers Gm and Gr, respectively, is studied. Furthermore, solutions for some recently published work are compared with the current study that endorses the authenticity of our derived results and proves that those investigations are limiting or special cases of the current problem. [ABSTRACT FROM AUTHOR]

A number of mathematical methods have been developed to determine the complex rheological behavior of fluid's models. Such mathematical models are investigated using statistical, empirical, analytical, and iterative (numerical) methods. Due to this fact, this manuscript proposes an analytical analysis and comparison between Sumudu and Laplace transforms for the prediction of unsteady convective flow of magnetized second grade fluid. The mathematical model, say, unsteady convective flow of magnetized second grade fluid, is based on nonfractional approach consisting of ramped conditions. In order to investigate the heat transfer and velocity field profile, we invoked Sumudu and Laplace transforms for finding the hidden aspects of unsteady convective flow of magnetized second grade fluid. For the sake of the comparative analysis, the graphical illustration is depicted that reflects effective results for the first time in the open literature. In short, the obtained profiles of temperature and velocity fields with Laplace and Sumudu transforms are in good agreement on the basis of numerical simulations. [ABSTRACT FROM AUTHOR]

The impact of Newtonian heating on a time-dependent fractional magnetohydrodynamic (MHD) Maxwell fluid over an unbounded upright plate is investigated. The equations for heat, mass and momentum are established in terms of Caputo (C), Caputo–Fabrizio (CF) and Atangana–Baleanu (ABC) fractional derivatives. The solutions are evaluated by employing Laplace transforms. The change in the momentum profile due to variability in the values of parameters is graphically illustrated for all three C, CF and ABC models. The ABC model has proficiently revealed a memory effect. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Our aim in this article is to solve the composite fractional relaxation differential equation by using different definitions of the non-integer order derivative operator D t α , more specifically we employ the definitions of Caputo, Caputo–Fabrizio and Atangana–Baleanu of non-integer order derivative operators. We apply the Laplace transform method to solve the problem and express our solutions in terms of Lorenzo and Hartley's generalised G function. Furthermore, the effects of the parameters involved in the model are graphically highlighted. [ABSTRACT FROM AUTHOR]