Bivariate Spectral Local Linearisation Method (BSLLM) for Unsteady MHD Micropolar-Nanofluids with Homogeneous–Heterogeneous Chemical Reactions Over a Stretching Surface

Sithole, Hloniphile; Mondal, Hiranmoy; Magagula, Vusi Mpendulo; Sibanda, Precious; Motsa, S. S.

doi:10.1007/s40819-018-0593-8

Cited by 13 publications

(6 citation statements)

References 14 publications

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“…Motsa [63] and Magagula et al [65] proposed a bivariate-SQLM (BI-SQLM) to solve nonlinear PDEs. Jamil et al [66] studied the unsteady MHD micropolar-nanofluids with homogeneousheterogeneous chemical reactions over a stretching surface using the BI-SLLM. Since both BI-SQLM and BI-SLLM face challenges with problems of large time scales, Motsa et al [67] and Magagula et al [68] proposed the nonoverlapping multidomain spectral collocation methods, i.e., multidomain BI-SLLM [69] and multidomain BI-SQLM [65,70].…”

Section: Introductionmentioning

confidence: 99%

A Novel Multivariate Spectral Local Quasilinearization Method (MV-SLQLM) for Modelling Flow, Moisture, Heat, and Solute Transport in Soil

Mwakilama

Magagula

Gathungu

2023

Journal of Applied Mathematics

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Conventionally, the problem of studying the transport of water, heat, and solute in soil or groundwater systems has been numerically solved using finite difference (FD) or finite element (FE) methods. FE methods are attractive over FD methods because they are geometrically flexible. However, recent studies demonstrate that spectral collocation (SC) methods converge exponentially faster than FD or FE methods using a few grid points or on coarse grids. This work proposes and applies a multivariate spectral local quasilinearization method (MV-SLQLM) to model the transportation and interaction of soil moisture, heat, and solute concentration in a nonbare soil ridge. The MV-SLQLM uses a quasilinearization method (QLM) to linearize any nonlinear equations and then employs a local linearization method (LLM) to decouple the linearized system of PDEs to form a sequence of equations that are solved in a computationally efficient manner. The MV-SLQLM is thus an extension of the bivariate spectral local linearization method (BI-SLLM) that fails to deal with a 2D problem and is a modification of the MV-SQLM whose efficiency is compromised when operating on high dense solution matrices. We use the residual error norms of the difference between successive iterations to affirm convergence to the expected solution. To illustrate the application and check the solution accuracy, we conduct systematic analyses of the effect of model parameters on distribution profiles. Findings are in good agreement with theory and literature, thereby revealing suitability of the MV-SLQLM to solve coupled nonlinear PDEs with environmental fluid dynamics applications.

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Section: Introductionmentioning

confidence: 99%

A Novel Multivariate Spectral Local Quasilinearization Method (MV-SLQLM) for Modelling Flow, Moisture, Heat, and Solute Transport in Soil

Mwakilama

Magagula

Gathungu

2023

Journal of Applied Mathematics

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“…The bivariate spectral local linearization method has been applied to solve systems of non-similar boundary layer equations [11]. The method was also employed for unsteady magnetohydrodynamic micropolar-nanofluids with homogeneous-heterogeneous chemical reactions over a stretching surface [12]. The BSLLM also solved an unsteady two-dimensional boundary layer flow with heat and mass transfer, in another study [13] Due to the overall advantages bivariate Chebyshev spectral methods have, as observed in the literature, this work employs the same approach with a new linearization technique to develop a method to solve nonlinear partial differential equations.…”

Section: Introductionmentioning

confidence: 99%

A Bivariate Spectral Linear Partition Method for Solving Nonlinear Evolution Equations

Khumalo,

Motsa,

Magagula

2023

Preprint

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This work develops a method for solving nonlinear evolution equations. The method, termed a bivariate spectral linear partition method, BSLPM, combines the Chebyshev spectral collocation method, bivariate Lagrange interpolation, and a linear partition technique as an underlying linearization method. It is developed for an n th order nonlinear differential equation and then used to solve three known evolution problems. The results are compared with known exact solutions from literature. The method’s applicability, reliability, and accuracy are confirmed by the congruence between the numerical and exact solutions. Tables, error graphs, and convergence graphs were generated using MATLAB (R2015a), to confirm the order of accuracy of the method and verify its convergence. The performance of the method is also observed against other methods performing well in these types of differential equations and is found to be comparable in terms of accuracy. The proposed method is also efficient as it uses minimal computation time.

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“…They successfully obtained only one solution. Some advances of the micropolar nanofluid can be seen in these articles in which researchers obtained a single solution [13][14][15][16][17][18][19][20]. Further, the dual solutions of micropolar nanofluid on the vertical surface were investigated by Lund et al [21] in which they found that dual solutions are only possible in some ranges of the suction parameter.…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis and Dual Solutions of Micropolar Nanofluid over the Inclined Stretching/Shrinking Surface with Convective Boundary Condition

et al. 2020

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The present study accentuates the heat transfer characteristics of a convective condition of micropolar nanofluid on a permeable shrinking/stretching inclined surface. Brownian and thermophoresis effects are also involved to incorporate energy and concentration equations. Moreover, linear similarity transformation has been used to transform the system of governing partial differential equations (PDEs) into a set of nonlinear ordinary differential equations (ODEs). The numerical comparison has been done with the previously published results and found in good agreement graphically and tabular form by using the shooting method in MAPLE software. Dual solutions have been found in the specific range of shrinking/stretching surface parameters and the mass suction parameter for the opposing flow case. Moreover, the skin friction coefficient, the heat transfer coefficient, the couple stress coefficient, and the concentration transfer rate decelerate in both solutions against the mass suction parameter for the augmentation of the micropolar parameter respectively. The first (second) solution is the stable (unstable) solution and can (not) be considered as a real solution as the values of the smallest eigenvalues are positive (negative).

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Bivariate Spectral Local Linearisation Method (BSLLM) for Unsteady MHD Micropolar-Nanofluids with Homogeneous–Heterogeneous Chemical Reactions Over a Stretching Surface

Cited by 13 publications

References 14 publications

A Novel Multivariate Spectral Local Quasilinearization Method (MV-SLQLM) for Modelling Flow, Moisture, Heat, and Solute Transport in Soil

A Novel Multivariate Spectral Local Quasilinearization Method (MV-SLQLM) for Modelling Flow, Moisture, Heat, and Solute Transport in Soil

A Bivariate Spectral Linear Partition Method for Solving Nonlinear Evolution Equations

Stability Analysis and Dual Solutions of Micropolar Nanofluid over the Inclined Stretching/Shrinking Surface with Convective Boundary Condition

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