MHD flows on irregular boundary over a diverging channel with viscous dissipation effect

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Iyyappan G. ◽  
Abhishek Kumar Singh
Keyword(s):  
Heat Transfer ◽  
Finite Difference ◽  
Difference Scheme ◽  
Skin Friction ◽  
Viscous Dissipation ◽  
Finite Difference Scheme ◽  
Uniform Mesh ◽  
Irregular Boundary ◽  
Content Type ◽  
Diverging Channel

Purpose The purpose of this paper is to analyse the force convection laminar boundary layer flow on irregular boundary in diverging channel with the presence of magnetic field effects. Effects of various fluid parameters such as suction/injection, viscous dissipation, magnetic parameter and heat source/sink on velocity and temperature profiles are numerically analyzed. Moreover, numerically investigated on skin-friction and heat transfer coefficients when suction/injection occur. Design/methodology/approach The governing coupled partial differential equations are transformed to dimensionless form using non-similarity transformations. The non-dimensional partial differential equations are linearized by quasi-linearization technique and solved by varga's algorithm with numerical finite difference scheme on a non-uniform mesh. Findings The computation results are presented in terms of temperature, heat transfer and skin friction coefficients; these are useful for determining surface heat requirements. It was found that, in finite difference scheme for non-uniform mesh with quasi-linearization technique method gives smoothness of solution compared to finite difference scheme for uniform mesh, and this evidence is graphically represented in Figure 2. Originality/value The impacts of viscous dissipation (Ec) and magnetic parameter (Ha) on temperature profiles, skin friction and heat transfer are analyzed, which determine the heat generation/absorption to ensure the MHD flow of the laminar boundary layer on irregular boundary over a diverging channel.

A parameter-uniform finite difference scheme for singularly perturbed parabolic problem with two small parameters

2021 ◽  
Author(s):  
Tesfaye Aga Bullo ◽  
Guy Aymard Degla ◽  
Gemechis File Duressa
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Variable Parameter ◽  
Accurate Solution ◽  
Singularly Perturbed ◽  
Finite Difference Approximation ◽  
Parabolic Problems ◽  
Difference Approximation ◽  
Uniform Mesh

A parameter-uniform finite difference scheme is constructed and analyzed for solving singularly perturbed parabolic problems with two parameters. The solution involves boundary layers at both the left and right ends of the solution domain. A numerical algorithm is formulated based on uniform mesh finite difference approximation for time variable and appropriate piecewise uniform mesh for the spatial variable. Parameter-uniform error bounds are established for both theoretical and experimental results and observed that the scheme is second-order convergent. Furthermore, the present method produces a more accurate solution than some methods existing in the literature.   

Numerical identification of temperature dependent thermal conductivity using least squares method

2019 ◽  
Vol 30 (6) ◽  
pp. 3083-3099
Author(s):  
Anna Ivanova ◽  
Stanislaw Migorski ◽  
Rafal Wyczolkowski ◽  
Dmitry Ivanov
Keyword(s):  
Thermal Conductivity ◽  
Finite Difference ◽  
Heat Equation ◽  
Difference Scheme ◽  
Least Squares ◽  
Finite Difference Scheme ◽  
Nonlinear Heat Equation ◽  
Temperature Dependent ◽  
Content Type ◽  
Temperature Dependent Thermal Conductivity

Purpose This paper aims to considered the problem of identification of temperature-dependent thermal conductivity in the nonstationary, nonlinear heat equation. To describe the heat transfer in the furnace charge occupied by a homogeneous porous material, the heat equation is formulated. The inverse problem consists in finding the heat conductivity parameter, which depends on the temperature, from the measurements of the temperature in fixed points of the material. Design/methodology/approach A numerical method based on the finite-difference scheme and the least squares approach for numerical solution of the direct and inverse problems has been recently developed. Findings The influence of different numerical scheme parameters on the accuracy of the identified conductivity coefficient is studied. The results of the experiment carried out on real measurements are presented. Their results confirm the ones obtained earlier by using other methods. Originality/value Novelty is in a new, easy way to identify thermal conductivity by known temperature measurements. This method is based on special finite-difference scheme, which gives a resolvable system of algebraic equations. The results sensitivity on changes in the method parameters was studies. The algorithms of identification in the case of a purely mathematical experiment and in the case of real measurements, their differences and the practical details are presented.

scholarly journals SCHEMES CONVERGENT Ε-UNIFORMLY FOR PARABOLIC SINGULARLY PERTURBED PROBLEMS WITH A DEGENERATING CONVECTIVE TERM AND A DISCONTINUOUS SOURCE

2015 ◽  
Vol 20 (5) ◽  
pp. 641-657 ◽  
Author(s):  
Carmelo Clavero ◽  
Jose Luis Gracia ◽  
Grigorii I. Shishkin ◽  
Lidia P. Shishkina
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Euler Method ◽  
Singularly Perturbed ◽  
Uniform Mesh ◽  
Interior Layer ◽  
Convective Term ◽  
Singularly Perturbed Problems ◽  
First Order

We consider the numerical approximation of a 1D singularly perturbed convection-diffusion problem with a multiply degenerating convective term, for which the order of degeneracy is 2p + 1, p is an integer with p ≥ 1, and such that the convective flux is directed into the domain. The solution exhibits an interior layer at the degeneration point if the source term is also a discontinuous function at this point. We give appropriate bounds for the derivatives of the exact solution of the continuous problem, showing its asymptotic behavior with respect to the perturbation parameter ε, which is the diffusion coefficient. We construct a monotone finite difference scheme combining the implicit Euler method, on a uniform mesh, to discretize in time, and the upwind finite difference scheme, constructed on a piecewise uniform Shishkin mesh condensing in a neighborhood of the interior layer region, to discretize in space. We prove that the method is convergent uniformly with respect to the parameter ε, i.e., ε-uniformly convergent, having first order convergence in time and almost first order in space. Some numerical results corroborating the theoretical results are showed.

scholarly journals Finite difference scheme for singularly perturbed reaction diffusion problem of partial delay differential equation with nonlocal boundary condition

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sekar Elango ◽  
Ayyadurai Tamilselvan ◽  
R. Vadivel ◽  
Nallappan Gunasekaran ◽  
Haitao Zhu ◽  
...  
Keyword(s):  
Boundary Condition ◽  
Finite Difference ◽  
Difference Scheme ◽  
Boundary Layers ◽  
Finite Difference Scheme ◽  
Nonlocal Boundary ◽  
Singularly Perturbed ◽  
Uniform Mesh ◽  
Integral Boundary ◽  
Delay Term

AbstractThis paper investigates singularly perturbed parabolic partial differential equations with delay in space, and the right end plane is an integral boundary condition on a rectangular domain. A small parameter is multiplied in the higher order derivative, which gives boundary layers, and due to the delay term, one more layer occurs on the rectangle domain. A numerical method comprising the standard finite difference scheme on a rectangular piecewise uniform mesh (Shishkin mesh) of $N_{r} \times N_{t}$ N r × N t elements condensing in the boundary layers is suggested, and it is proved to be parameter-uniform. Also, the order of convergence is proved to be almost two in space variable and almost one in time variable. Numerical examples are proposed to validate the theory.

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