Influence in a Darcy's medium with heat production and radiation on MHD convection flow via modern fractional approach

Khan, İlyas; Saeed, Syed Tauseef; Riaz, Muhammad Bilal; Abro, Kashif Ali; Husnine, Syed Muhammad; Nisar, Kottakkaran Sooppy

doi:10.1016/j.jmrt.2020.06.059

Cited by 14 publications

(7 citation statements)

References 25 publications

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“…Wherefore, it is unable to predict the earlier state of the process called memory effect which is absent in classical models, but fractional calculus famous for having memory effects. It is found in the literature, several fractional differential operators exists, for instance, Caputo with kernel (singular and local), Atangana-Baleanu with kernel (non-singular and non-local), Caputo-Fabrizio with kernel (non-singular and local), and few others are discussed [31,32,38,39]. For local and non-local kernel, convective flow with ramped conditions on temperature are studied by Riaz et al [40].…”

Section: Introductionmentioning

confidence: 99%

Thermophysical Investigation of Oldroyd-B Fluid with Functional Effects of Permeability: Memory Effect Study Using Non-Singular Kernel Derivative Approach

et al. 2021

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It is well established fact that the functional effects, such as relaxation and retardation of materials, can be measured for magnetized permeability based on relative increase or decrease during magnetization. In this context, a mathematical model is formulated based on slippage and non-slippage assumptions for Oldroyd-B fluid with magnetized permeability. An innovative definition of Caputo-Fabrizio time fractional derivative is implemented to hypothesize the constitutive energy and momentum equations. The exact solutions of presented problem, are determined by using mathematical techniques, namely Laplace transform with slipping boundary conditions have been invoked to tackle governing equations of velocity and temperature. The Nusselt number and limiting solutions have also been persuaded to estimate the heat emission rate through physical interpretation. In order to provide the validation of the problem, the absence of retardation time parameter led the investigated solutions with good agreement in literature. Additionally, comprehensively scrutinize the dynamics of the considered problem with parametric analysis is accomplished, the graphical illustration is depicted for slipping and non-slipping solutions for temperature and velocity. A comparative studies between fractional and non-fractional models describes that the fractional model elucidate the memory effects more efficiently.

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Section: Introductionmentioning

confidence: 99%

Thermophysical Investigation of Oldroyd-B Fluid with Functional Effects of Permeability: Memory Effect Study Using Non-Singular Kernel Derivative Approach

et al. 2021

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“…Some more investigations regarding MHD boundary layer flow have been done, like, Nisar et al 23 studied numerically the impact of micropolar fluid and porosity on MHD channel flow. Khan et al 24 presented a study based on MHD convection flow through a model fractional approach.…”

Section: Introductionmentioning

confidence: 99%

Numerical investigation of MHD flow of Williamson nanofluid with variable viscosity pasting a wedge within porous media: A non‐Darcy model approach

et al. 2022

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The present analysis is done for the investigation of the effect of various physical parameters on magnetohydrodynamic Williamson nanofluid boundary layer flow past a wedge through porous media taking a non-Darcy-Falkner-Skan model with consideration of varying wall temperature, variable viscosity, the effect of Brownian motion, and thermophoresis in the presence of heat source. The corresponding governing equations under the appropriate boundary conditions are first converted into ordinary differential equations (ODEs) in view of similarity transformations.Application of shooting method has been made to deal with these ODEs, and the effects of various parameters on nondimensional velocity, temperature, and concentration are investigated through graphs. Also, the effects of various parameters on surface skin friction, heat, and mass transfer rates are analyzed and are shown in Table 3. It has been noticed that heat and mass transfer rates are enhanced with variable viscosity coefficient and reduced with Brownian motion and thermophoresis parameters. As a significant outcome, the skin friction is found to be increased with increasing values of the Williamson parameter

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“…They used the homotopy analysis method to calculate the governing equation and Mathematica software (Wolfram Mathematica, New Jersey, NJ, United State) to provide a graphical illustration of the velocity gradient, temperature, and concentration gradient of the Casson model. Although research on the Casson model is ongoing, we include some related studies based on heat transfer [25][26][27][28][29], fractional models of fluids with magnetic field [30][31][32][33][34][35][36][37][38][39][40], and some others [41][42][43][44][45][46][47][48][49][50][51][52][53][54] herein. Motivated by the above discussion, we analyzed an analytic solution of incompressible and magnetic Casson fluid subjected to temperature and concentration dependence within a porous-surfaced plate.…”

Section: Introductionmentioning

confidence: 99%

Exact Symmetric Solutions of MHD Casson Fluid Using Chemically Reactive Flow with Generalized Boundary Conditions

et al. 2021

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Dynamic analysis of magnetic fluids with the combined effect of heat sink and chemical reactions based on their physical properties demonstrates strong shock resistance capabilities, low-frequency response, low energy consumption, and high sensitivity. Therefore, the applied magnetic field always takes diamagnetic, ferromagnetic, and paramagnetic forms. The influence of radiation is considered in the temperature profile. This manuscript investigates an analytic solution of incompressible and magnetic Casson fluid in Darcy’s medium subjected to temperature and concentration dependence within a porous-surfaced plate with generalized boundary conditions. The substantial mathematical technique of the Laplace transform with inversion is invoked in the governing equations of the magnetic Casson fluid. The analytic results are transformed into a special function for the plate with a constant velocity, a plate with linear velocity, a plate with exponential velocity, and a plate with sinusoidal velocity. Graphical illustrations of the investigated analytic solutions at four different times are presented. Our results suggest that the velocity profile decreases by increasing the value of the magnetic field, which reflects the control of resistive force. The Nusselt number remains constant at a fixed Rd and is reduced by raising the Rd value.

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Influence in a Darcy's medium with heat production and radiation on MHD convection flow via modern fractional approach

Cited by 14 publications

References 25 publications

Thermophysical Investigation of Oldroyd-B Fluid with Functional Effects of Permeability: Memory Effect Study Using Non-Singular Kernel Derivative Approach

Thermophysical Investigation of Oldroyd-B Fluid with Functional Effects of Permeability: Memory Effect Study Using Non-Singular Kernel Derivative Approach

Numerical investigation of MHD flow of Williamson nanofluid with variable viscosity pasting a wedge within porous media: A non‐Darcy model approach

Exact Symmetric Solutions of MHD Casson Fluid Using Chemically Reactive Flow with Generalized Boundary Conditions

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