Computational Results With Non-singular and Non-local Kernel Flow of Viscous Fluid in Vertical Permeable Medium With Variant Temperature

Riaz, Muhammad Bilal; Saeed, Syed Tauseef; Băleanu, Dumitru; Ghalib, Muhammad Mansha

doi:10.3389/fphy.2020.00275

Cited by 17 publications

(12 citation statements)

References 26 publications

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“…Mickens. These rules benefit in designing the dynamically consistent numerical schemes which hold the stability of equilibria and positive solution of the underlying system [10][11][12].…”

Section: Methodsmentioning

confidence: 99%

A Reliable Numerical Analysis of Transmission Dynamics of Chicken Pox (Varicella Zoster Virus)

et al. 2020

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Solutions generated through numerical techniques are great in solving real-world problems. This manuscript deals with the numerical approximation of the epidemic system, describing the transmission dynamics of the Vercilla Zoster Virus (VZV) through the impact of vaccination. To discretize the continuous dynamical system, we proposed a novel numerical technique that preserves the true dynamics of the VZV epidemic model. The proposed technique is established in such a manner that it sustains all necessary physical traits depicted by the epidemic model under study. The designed technique is named a nonstandard finite difference (NSFD) scheme. Theoretical analysis of the designed NSFD technique is presented which describes its strength over the standard numerical procedures which are already being used for such purposes. The graphical solutions of all the numerical techniques are presented which verify the efficacy of the proposed NSFDS technique.

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“…Mickens. These rules benefit in designing the dynamically consistent numerical schemes which hold the stability of equilibria and positive solution of the underlying system [10][11][12].…”

Section: Methodsmentioning

confidence: 99%

A Reliable Numerical Analysis of Transmission Dynamics of Chicken Pox (Varicella Zoster Virus)

et al. 2020

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“…The numerical and computational techniques are used to evaluate the Laplace inverse via Stehfest's 43 and Tzou's algorithms. 38,43 The Stehfest's algorithm can be written as…”

Section: Atangana-baleanu Time Derivativesmentioning

confidence: 99%

“…They consider the Maxwell fluid and investigate the heat and mass transfer with the integer and noninteger-order derivative. Some further investigation of fluid flows and their properties equipped with FD is established in References [29][30][31][32][33][34][35][36][37][38][39][40][41][42]. Applications of combined impact of heat and mass transfer in engineering, applied sciences, and FC, since they are connected to the historical data (memory effect).…”

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confidence: 99%

Heat and mass transport impact on MHD second‐grade fluid: A comparative analysis of fractional operators

et al. 2021

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The effect of the magnetic flux plays a major role in convective flow. The process of heat transfer is accompanied by a mass transfer process; for instance, condensation, evaporation, and chemical process. Due to the applications of the heat and mass transfer combined effects in different fields, the main aim of this paper is to do a comprehensive analysis of heat and mass transfer of magnetohydrodynamic (MHD) unsteady second-grade fluid in the presence of ramped conditions. The new governing equations of MHD second-grade fluid have been fractionalized by means of singular and nonsingular differentiable operators. To have an accurate physical significance of imposed conditions on the geometry of second-grade fluid, the constant concentration with ramped temperature and ramped velocity is considered. The fractional solutions of temperature, concentration, and velocity have been investigated by means of integral transform and inversion algorithm. The influence of physical parameters and flow is analyzed graphically via computational software (MATHCAD-15). The velocity profile decreases by increasing the Prandtl number. The existence of a Prandtl number may reflect the control of the thickness and enlargement of the thermal effect.

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“…We prefer to apply Laplace transform given in ( 8) on equation (23). e resultant form of the above expression is…”

Section: Velocity Profile Via Fractional Operatorsmentioning

confidence: 99%

“…In context with fractional differential operators, convective flow with ramped wall temperature for nonsingular kernel was analyzed by Riaz et al [23]. Moreover, Riaz et al [24] investigated the study of heat and mass transfer in the MHD Oldroyd-B fluid with ramped wall temperature using local and nonlocal differential operators.…”

Section: Introductionmentioning

confidence: 99%

Study of Heat Transfer under the Impact of Thermal Radiation, Ramped Velocity, and Ramped Temperature on the MHD Oldroyd-B Fluid Subject to Noninteger Differentiable Operators

Saeed

Khan

Riaz

et al. 2020

Journal of Mathematics

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This theoretical study explores the impact of heat generation/absorption with ramp wall velocity and ramp wall temperature on the magnetohydrodynamic (MHD) time-dependent Oldroyd-B fluid over an unbounded plate embedded in a porous surface. The mathematical analysis of fractional governing partial differential equations has been established using systematic and powerful techniques of Laplace transform with its numerical inversion algorithms. The fractionalized solutions have been traced out separately through all fractional differential operators. Nondimensional parameters along with Laplace transformation are used to find the solution of temperature and velocity profiles. Fractional time derivatives are used to analyze the impact of fractional parameters (memory effect) on the dynamics of the fluid. While making a comparison, it is observed that the fractional-order model is the best to explain the memory effect as compared to classical models. The obtained solutions are plotted graphically for different values of physical parameters. Our results suggest that the velocity profile decreases by increasing the effective Prandtl number. Furthermore, the existence of an effective Prandtl number may reflect the control of the thickness of momentum and enlargement of thermal conductivity.

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Computational Results With Non-singular and Non-local Kernel Flow of Viscous Fluid in Vertical Permeable Medium With Variant Temperature

Cited by 17 publications

References 26 publications

A Reliable Numerical Analysis of Transmission Dynamics of Chicken Pox (Varicella Zoster Virus)

A Reliable Numerical Analysis of Transmission Dynamics of Chicken Pox (Varicella Zoster Virus)

Heat and mass transport impact on MHD second‐grade fluid: A comparative analysis of fractional operators

Study of Heat Transfer under the Impact of Thermal Radiation, Ramped Velocity, and Ramped Temperature on the MHD Oldroyd-B Fluid Subject to Noninteger Differentiable Operators

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