Fractional analysis of Jeffrey fluid over a vertical plate with time-dependent conductivity and diffusivity: A low-cost spectral approach

Usman, Muhammad; Alhejaili, Weaam; Hamid, Muhammad; Khan, Nawab

doi:10.1016/j.jocs.2022.101769

Cited by 12 publications

(3 citation statements)

References 24 publications

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“…Thenmozhi et al [5] formulated the boundary layer mathematical equations of MHD Jeffery fluid with heat transport passing on the stretched porous surface. Usman et al [6] presented a fractional analysis study of Jeffery fluid which is moving on the vertical plate and the thermal conduction and diffusion are depending on time. The exploration of flow properties for the two immiscible fluids (Jeffery fluid and Phan-Thien-Tanner models) was investigated by Huang et al [7] which is moving in a channel due to ciliary beating.…”

Section: Introductionmentioning

confidence: 99%

Stagnation point flow of MHD non-Newtonian fluid and thermal investigation with Joule heating, viscous dissipation and Soret effect

Awais,

Salahuddin

2024

Preprint

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The aim of this study is to analyze the numerical solution of magnetohydrodynamic Jeffery fluid past over the upper horizontal parabolic surface with the help of Adam-Milne Predictor Corrector method along with the RK method. Adams predictor-corrector technique is very significant because it improve accuracy of results as compared to using either method alone. The predictor step gives an initial approximation and the corrector step refines this approximation based on the implicit equation. The assumption based on the boundary layer and stagnation point flow of magnetohydrodynamic Jeffery fluid which is past on the melting upper horizontal parabolic surface and the physical aspects are examined with the variable fluid properties. The velocity slip effect on the surface of paraboloid is used to determine its influence on the movement of fluid. The thermal and solutal transfer rates has crucial role in the chemical reactions, climate changes, electronic devices, distillation and separation processes, water and air pollution. Therefore we considered both the thermal and solutal transfer rates with the effects of Joule heating, viscous dissipation, heat source/sink, activation energy and Soret effect. The implementation of all the assumption on the basic conservation laws gives us the governing equation in the form of PDE’s and then the similarity variables are translated these equations into the form of ODE’s. The numerical technique named as ‘Adams-Milne Predictor-Corrector method’ is adopted to solve the numerical solutions. The results are examined in the numerical and graphical forms. The graphical behavior of numerous parameters on the velocity, concentration and temperature regions are analyzed. The numerical findings of skin friction and Nusselt number are also placed here and compared the results with the Bvp5c and Adams-Milne (Predictor-Corrector) method. Graphical Abstract: The slip parameter, ratio of relaxation to retardation parameter, viscosity parameter, Deborah number and Hartmann number drops the velocity for both Newtonian and non-Newtonian cases whereas the velocity increases due to the stretching ratio parameter and melting surface coefficient. The heat source/sink parameter, Eckert number, viscosity parameter, thermal conduction coefficient and Hartmann number. The amplification in concentration region is examined by the consideration of Soret number, thermal diffusion and activation energy, while the reaction rate coefficient drops the concentration.

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Section: Introductionmentioning

confidence: 99%

Stagnation point flow of MHD non-Newtonian fluid and thermal investigation with Joule heating, viscous dissipation and Soret effect

Awais,

Salahuddin

2024

Preprint

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“…Nadeem [22] practiced the technique of the derivatives with fractional order on the periodic ows in an Oldroyd-B uid generated by an edge. Recently many researchers discussed the ows of non-Newtonian models by adopting distinct types of fractional derivatives [23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Fractional Nadeem trigonometric non-Newtonian (NTNN) fluid model based on Caputo-Fabrizio fractional derivative with heated boundaries

Nadeem,

Ishtiaq,

Alzabut

et al. 2023

Preprint

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The fractional model of Caputo-Fabrizio derivative in various physical flow problems has significant advantages with its implementations in manufacturing and engineering fields. This fractional derivative model provides realistic solutions to the flow system. Therefore, the current study has the main objective of implementation of Caputo-Fabrizio fractional derivative on the flow phenomenon of trigonometric non-Newtonian fluid. The time-dependent flow mechanism is assumed to be developed through a vertical infinite plate. The thermal radiation’s effects are incorporated into the analysis of heat transfer. With the help of mathematical formulations, the physical flow system is expressed. The governing equations of the flow system acquire the dimensionless form through the involvement of the dimensionless variables. The application of Caputo-Fabrizio derivative is implemented to achieve the fractional model of the dimensionless system. An exact solution of the fractional-based dimensionless system of the equations is acquired through the technique of the Laplace transform. Physical interpretation of temperature and velocity distributions relative to the pertinent parameters is visualized via graphs. The current study concludes that the higher values of fluid parameter improve the velocity field. Moreover, both distributions exhibit an accelerating nature corresponding to the order of the fractional operator.

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“…For instance, Usman et al [8] employed Gegenbauer polynomials to solve nonlinear physical models, while Chakraborty and Jung [9] utilized Hermite, Legendre, Laguerre, Jacobi, and generalized Laguerre polynomials to model the impact of continuous random variables described by normal, uniform, exponential, beta, and gamma probability distributions, respectively. Feinberg and Langtangen [10] discussed the application of orthogonal polynomials for uncertainty quantification.…”

Section: Introductionmentioning

confidence: 99%

Accelerated and Improved Stabilization for High Order Moments of Racah Polynomials

Mahmmod,

Abdulhussain,

Suk

et al. 2023

IEEE Access

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Discrete Racah polynomials (DRPs) are highly efficient orthogonal polynomials and used in various scientific fields for signal representation. They find applications in disciplines like image processing and computer vision. Racah polynomials were originally introduced by Wilson and later modified by Zhu to be orthogonal on a discrete set of samples. However, when the degree of the polynomial is high, it encounters numerical instability issues. In this paper, we propose a novel algorithm called Improved Stabilization (ImSt) for computing DRP coefficients. The algorithm partitions the DRP plane into asymmetric parts based on the polynomial size and DRP parameters. We have optimized the use of stabilizing conditions in these partitions. To compute the initial values, we employ the logarithmic gamma function along with a new formula. This combination enables us to compute the initial values efficiently for a wide range of DRP parameter values and large polynomial sizes. Additionally, we have derived a symmetry relation for the case when the Racah polynomial parameters are zero (a = 0, α = 0, β = 0). This symmetry makes the Racah polynomials symmetric about the main diagonal, and we present a different algorithm for this specific scenario. We have demonstrated that the ImSt algorithm works for a broader range of parameters and higher degrees compared to existing algorithms. A comprehensive comparison between ImSt and the existing algorithms has been conducted, considering the maximum polynomial degree, computation time, restriction error analysis, and reconstruction error. The results of the comparison indicate that ImSt outperforms the existing algorithms for various values of Racah polynomial parameters.

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Fractional analysis of Jeffrey fluid over a vertical plate with time-dependent conductivity and diffusivity: A low-cost spectral approach

Cited by 12 publications

References 24 publications

Stagnation point flow of MHD non-Newtonian fluid and thermal investigation with Joule heating, viscous dissipation and Soret effect

Stagnation point flow of MHD non-Newtonian fluid and thermal investigation with Joule heating, viscous dissipation and Soret effect

Fractional Nadeem trigonometric non-Newtonian (NTNN) fluid model based on Caputo-Fabrizio fractional derivative with heated boundaries

Accelerated and Improved Stabilization for High Order Moments of Racah Polynomials

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