MHD Flow of Second Grade Fluid with Heat Absorption and Chemical Reaction
Muhammad Ramzan,
Ahmad Shafique,
Mudassar Nazar
Issue:
Volume 8, Issue 2, April 2022
Pages:
30-39
Received:
26 January 2022
Accepted:
2 March 2022
Published:
18 March 2022
Abstract: The objective of this paper is to analyze the influence of thermo-diffusion on magnetohydrodynamics (MHD) flow of fractional second grade fluid immersed in a porous media over an exponentially accelerated vertical plate. In addition, other factors such as heat absorption and chemical reaction are used in the problem. More exactly, the fractional model has been developed using the generalized Fick’s and Fourier’s laws. The Caputo-Fabrizio (CF) fractional derivative has been used to solved the model. Initially, the flow modeled system of partial differential equations are transformed into dimensional form through suitable dimensionless variable and then Laplace transform technique has been used to solved the set of dimensionless governing equations for velocity profile, temperature profile, and concentration profile. The influence of different parameters like diffusion-thermo, fractional parameter, magnetic field, chemical reaction, heat obsorption, Schmidt number, time, Prandtl number and second grade parameter are discussed through numerous graphs. From figures, it is observed that fluid motion decreases with increasing values of Schmidt number, Prandtl number, magnetic parameter, and chemical reaction, whereas velocity field decreases with decreasing values of diffusion-thermo and mass grashof number. In order to check the athenticity of present work, we compare the present work with already published model graphically.
Abstract: The objective of this paper is to analyze the influence of thermo-diffusion on magnetohydrodynamics (MHD) flow of fractional second grade fluid immersed in a porous media over an exponentially accelerated vertical plate. In addition, other factors such as heat absorption and chemical reaction are used in the problem. More exactly, the fractional mo...
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On Distributional Solutions of a Singular Differential Equation of 2-order in the Space K’
Issue:
Volume 8, Issue 2, April 2022
Pages:
45-50
Received:
9 March 2022
Accepted:
1 April 2022
Published:
9 April 2022
Abstract: The main purpose of this work is to describe all the zero-centered solutions of the second order linear singular differential equation with Dirac delta function (or it derivatives of some order) in the second right hand side in the space K’. All the coefficients and the exponents of the polynomials under the unknown function and it derivatives up to second order respectively, are real and natural numbers in the considered equation. We conduct investigations for both the euler case and left euler case situations of this equation, when it is fulfilled some particular conditions in the relationships between the parameters A, B, C, m, n and r. In each of these cases, we look for the zero-centered solutions and substitute the form of the particular solution into the equation. We then after, determinate the unknown coefficients and formulate the related theorems to describe all the solutions depending of the cases to be investigated.
Abstract: The main purpose of this work is to describe all the zero-centered solutions of the second order linear singular differential equation with Dirac delta function (or it derivatives of some order) in the second right hand side in the space K’. All the coefficients and the exponents of the polynomials under the unknown function and it derivatives up t...
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, where l is a natural number not equal to zero, s a natural number, (ai)0≤i≤l real numbers and more al≠0, 
is the Dirac distributio...
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(as linear combination of Dirac delta functions and it derivatives) into the considered equation. This leads us to release the conditions of its solvency, formulated into a theorem and, let us analyze the algebraic system obtained for the determination of the unknown coefficients Cj. By this, we undertake the description of all zero-centered solutions of the considered equation into a theorem.