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Thermodynamic Analysis of Variable Viscosity MHD Unsteady Generalized Couette Flow with Permeable Walls
David Theuri,
Oluwole Daniel Makinde
Issue:
Volume 3, Issue 1, February 2014
Pages:
1-8
Received:
23 September 2013
Published:
20 January 2014
Abstract: The thermodynamic first and second law analyses of a temperature dependent viscosity hydromagnetic generalized unsteady Couette flow with permeable walls is investigated. The transient model problem for momentum and energy balance is tackled numerically using a semi-discretization method while the steady state boundary value problem is solved by shooting method together with Runge-Kutta-Fehlberg integration scheme. The velocity and the temperature profiles are obtained and are utilized to compute the skin friction coefficient, Nusselt number, entropy generation rate and the Bejan number. Pertinent results are presented graphically and discussed quantitatively.
Abstract: The thermodynamic first and second law analyses of a temperature dependent viscosity hydromagnetic generalized unsteady Couette flow with permeable walls is investigated. The transient model problem for momentum and energy balance is tackled numerically using a semi-discretization method while the steady state boundary value problem is solved by sh...
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Numerical Solution of Linear Volterra Integro-Differential Equation using Runge-Kutta-Fehlberg Method
Issue:
Volume 3, Issue 1, February 2014
Pages:
9-14
Received:
18 August 2013
Published:
20 February 2014
Abstract: In this paper a new fourth and fifth-order numerical solution of linear Volterra integro-differential equation is discussed. One popular technique that uses here for error control is called the Runge-Kutta-Fehlberg method for Ordinary Differential Equation (ODE) part and Newton-Cotes formulae for integral parts.
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Solution of a Diffusion Problem in a Non-Homogeneous Flow and Diffusion Field by the Integral Representation Method (IRM)
Hiroshi Isshiki,
Shuichi Nagata,
Yasutaka Imai
Issue:
Volume 3, Issue 1, February 2014
Pages:
15-26
Received:
10 January 2014
Published:
20 February 2014
Abstract: Integral representations are derived from a differential-type boundary value problem using a fundamental solution. A set of integral representations is equivalent to a set of differential equations. If the boundary conditions are substituted into the integral representations, the integral equations are obtained, and the unknown variables are determined by solving the integral equations. In other words, an integral-type boundary value problem is derived from the integral representations. An effective and flexible finite element algorithm is easily obtained from the integral-type boundary value problem. In the present paper, integral representations are obtained for the diffusion of a material or heat in the sea, where the convective velocity and diffusion constant change in space and time. A new numerical solution of an advection-diffusion equation is proposed based integral representations using the fundamental solution of the primary space-differential operator, and the numerical results are shown. An innovative generalization of the integral representation method: generalized integral representation method is also proposed. The numerical examples are given to verify the theory.
Abstract: Integral representations are derived from a differential-type boundary value problem using a fundamental solution. A set of integral representations is equivalent to a set of differential equations. If the boundary conditions are substituted into the integral representations, the integral equations are obtained, and the unknown variables are determ...
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Application of Optimal HAM for Solving the Fractional Order Logistic Equation
Issue:
Volume 3, Issue 1, February 2014
Pages:
27-31
Received:
8 December 2013
Published:
28 February 2014
Abstract: In this paper, we use the optimal homotopy analysis method (OHAM) for approximate solutions of the fractional order Logistic equation. The numerical results obtained are compared with the results obtained by using variational iteration method (VIM) and Adomian decomposition method (ADM). The fractional derivatives are described by Caputo's sense. Exact and/or approximate analytical solutions of these equations are obtained. The results reveal that this method is very effective and powerful to obtain the approximate solutions.
Abstract: In this paper, we use the optimal homotopy analysis method (OHAM) for approximate solutions of the fractional order Logistic equation. The numerical results obtained are compared with the results obtained by using variational iteration method (VIM) and Adomian decomposition method (ADM). The fractional derivatives are described by Caputo's sense. E...
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Existence and Uniqueness of Mild Solutions for Fractional Integrodifferential Equations
V. Dhanapalan,
M. Thamilselvan,
M. Chandrasekaran
Issue:
Volume 3, Issue 1, February 2014
Pages:
32-37
Received:
30 January 2014
Published:
10 March 2014
Abstract: The aim of this paper is to prove the existence and uniqueness of mild solution of a class of l nonlinear fractional integrodifferential equations {█((d^q u(t))/(dt^q )+Au(t)=∫_0^t▒f(t,s,x(s) )ds+∫_0^t▒〖a(t-s)g(s,y(s) )ds, t∈[0,T],〗@u(0)=u_(o.) )┤ in a Banach space X, where 0
Abstract: The aim of this paper is to prove the existence and uniqueness of mild solution of a class of l nonlinear fractional integrodifferential equations {█((d^q u(t))/(dt^q )+Au(t)=∫_0^t▒f(t,s,x(s) )ds+∫_0^t▒〖a(t-s)g(s,y(s) )ds, t∈[0,T],〗@u(0)=u_(o.) )┤ in a Banach space X, where 0...
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An Easy Computable Approximate Solution for a Squeezing Flow between Two Infinite Plates by using of Perturbation Method
U. Filobello-Nino,
H. Vazquez-Leal,
A. Perez-Sesma,
J. Cervantes-Perez,
V. M. Jimenez-Fernandez,
L. Hernandez-Martinez,
D. Pereyra-Diaz,
R. Castaneda-Sheissa,
J. Sanchez-Orea,
C. Hoyos-Reyes,
S. F. Hernandez-Machuca,
J. Huerta-Chua,
J. L. Rocha-Fernandez,
A. D. Contreras-Hernandez,
J. M. Mendez-Perez
Issue:
Volume 3, Issue 1, February 2014
Pages:
38-42
Received:
19 February 2014
Published:
10 March 2014
Abstract: This article proposes Perturbation Method (PM) to find an approximate solution for the problem of an axis symmetric Newtonian fluid squeezed between two large parallel plates. After comparing figures between approximate and exact solutions, we will see that the proposed solutions besides of handy, are highly accurate and therefore that PM is efficient.
Abstract: This article proposes Perturbation Method (PM) to find an approximate solution for the problem of an axis symmetric Newtonian fluid squeezed between two large parallel plates. After comparing figures between approximate and exact solutions, we will see that the proposed solutions besides of handy, are highly accurate and therefore that PM is effici...
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