Exact solutions involving special functions for unsteady convective flow of magnetohydrodynamic second grade fluid with ramped conditions

Abstract

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.

Fractional Modeling of Viscous Fluid over a Moveable Inclined Plate Subject to Exponential Heating with Singular and Non-Singular Kernels

“…Moreover, there is a comparative study for fractional model of MHD Maxwell fluid to anticipate the heat effect by Riaz et al [24]. Some other fractional associated studies are discussed in detail; see for instance [25,26]; most of the studies are focused on flow problems with non-integer differential operators, heat transport MHD Jeffrey fluid movement and second grade fluid.…”

Unsteady rotating MHD flow of a second‐grade hybrid nanofluid in a porous medium: Laplace and Sumudu transforms

“…Theorem I. (Riaz et al 30 ) If R u ( ) denote the Sumudu transform of r t ( ), then the derivatives with integer order have the following Sumudu transform:…”

“…The following theorem is extremely useful for efficiently solving differential equations containing many integrals using the ST. □ Theorem II. (Riaz et al 30 ) Let A contains r t ( ). The F u ( ) n be the Sumudu transform of r t ( ) nth antiderivative, achieved by n times consecutively integrating the r t ( ) function,…”

Generalized Mittag-Leffler Kernel Form Solutions of Free Convection Heat and Mass Transfer Flow of Maxwell Fluid with Newtonian Heating: Prabhakar Fractional Derivative Approach

“…Researchers studied these three types of non-Newtonian models, and each model has different characteristics. Some common models that describe the computational and physical characteristics of non-Newtonian fluids are second grade and third grade models, the Jeffery model, Casson model, Maxwell model, and power law model [1][2][3][4][5][6]. Such fluid models are simple, but each model has certain limitations; for example, second grade fluid is a simple sub-class of a differential type of non-Newtonian fluid.…”