Application of local meshless method for the solution of two term time fractional-order multi-dimensional PDE arising in heat and mass transfer

Ahmad, Imtiaz; Ahmad, Hijaz; İnç, Mustafa; Yao, Shao-Wen; Almohsen, Bandar

doi:10.2298/tsci20095a

Cited by 4 publications

(1 citation statement)

References 20 publications

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“…Hristov [18,19], Povstenko and Kyrylych [20,21], Zheng et al [22], Baleanu et al [23,24], and Hilfer [25] have a comprehensive description of the theory of fractional operators with their properties and applications. References [26][27][28][29][30][31][32][33][34][35][36][37][38] include mathematical observations and potential implementations and applications of the fractional differential Calculus.…”

Section: Introductionmentioning

confidence: 99%

Simultaneous Flow of n-Immiscible Fractional Maxwell Fluids with Generalized Thermal Flux and Robin Boundary Conditions

Rauf

Rubbab

Shah

et al. 2021

Advances in Mathematical Physics

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In a rectangular region, the multilayered laminar unsteady flow and temperature distribution of the immiscible Maxwell fractional fluids by two parallel moving walls are studied. The flow of the fluid occurs in the presence of Robin’s boundaries and linear fluid-fluid interface conditions due to the motion of the parallel walls on its planes and the time-dependent pressure gradient. The problem is defined as a mathematical model which focuses on the fluid memory, which is represented by a constituent equation with the Caputo time-fractional derivative. The integral transformations approach (the Laplace transform and the finite sine-Fourier transform) is used to determine analytical solutions for velocity, shear stress, and the temperature fields with fluid interface, initial, and boundary conditions. For semianalytical solutions, the algorithms of Talbot are used to calculate the Laplace inverse transformation. We used the Mathcad software for graphical illustration and numerical computation. It has been observed that the memory effect is significant on both fluid motion and temperature flow.

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Section: Introductionmentioning

confidence: 99%

Simultaneous Flow of n-Immiscible Fractional Maxwell Fluids with Generalized Thermal Flux and Robin Boundary Conditions

Rauf

Rubbab

Shah

et al. 2021

Advances in Mathematical Physics

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The Conical Radial Basis Function for Partial Differential Equations

Zhang

Wang

Hou

2020

Journal of Mathematics

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The performance of the parameter-free conical radial basis functions accompanied with the Chebyshev node generation is investigated for the solution of boundary value problems. In contrast to the traditional conical radial basis function method, where the collocation points are placed uniformly or quasi-uniformly in the physical domain of the boundary value problems in question, we consider three different Chebyshev-type schemes to generate the collocation points. This simple scheme improves accuracy of the method with no additional computational cost. Several numerical experiments are given to show the validity of the newly proposed method.

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Gaussian radial basis functions method for linear and nonlinear convection–diffusion models in physical phenomena

et al. 2021

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In this study, we propose a simple direct meshless scheme based on the Gaussian radial basis function for the one-dimensional linear and nonlinear convection–diffusion problems, which frequently occur in physical phenomena. This is fulfilled by constructing a simple ‘anisotropic’ space–time Gaussian radial basis function. According to the proposed scheme, there is no need to remove time-dependent variables during the whole solution process, which leads it to a really meshless method. The suggested meshless method is implemented to the challenging convection–diffusion problems in a direct way with ease. Numerical results show that the proposed meshless method is simple, accurate, stable, easy-to-program and efficient for both linear and nonlinear convection–diffusion equation with different values of Péclet number. To assess the accuracy absolute error, average absolute error and root-mean-square error are used.

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Application of local meshless method for the solution of two term time fractional-order multi-dimensional PDE arising in heat and mass transfer

Cited by 4 publications

References 20 publications

Simultaneous Flow of n-Immiscible Fractional Maxwell Fluids with Generalized Thermal Flux and Robin Boundary Conditions

Simultaneous Flow of n-Immiscible Fractional Maxwell Fluids with Generalized Thermal Flux and Robin Boundary Conditions

The Conical Radial Basis Function for Partial Differential Equations

Gaussian radial basis functions method for linear and nonlinear convection–diffusion models in physical phenomena

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