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Theoretical study of heat transfer effects on flow past a parabolic started vertical plate in the presence of chemical reaction of first order

Muthucumaraswamy R., Velmurugan S.

International Journal of Applied Mechanics and Engineering

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2014

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Vol. 19, no. 2

275--284

EN

An exact solution of an unsteady flow past a parabolic starting motion of an infinite vertical plate with variable temperature and mass diffusion, in the presence of a homogeneous chemical reaction of first order has been studied. The plate temperature as well as concentration level near the plate are raised linearly with time t. The dimensionless governing equations are solved using the Laplace-transform technique. The effects of velocity profiles are studied for different physical parameters such as the chemical reaction parameter, thermal Grashof number, mass Grashof number, Schmidt number and time. It is observed that the velocity increases with increasing values of the thermal Grashof number or mass Grashof number. The trend is just reversed with respect to the chemical reaction parameter.

2

Radiative flow past a parabolic started isothermal vertical plate with uniform mass diffusion

Muthucumaraswamy R., Lakshmi V.

International Journal of Applied Mechanics and Engineering

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2014

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Vol. 19, no. 1

195--202

EN

A theoretical solution of thermal radiation effects on an unsteady flow past a parabolic starting motion of an infinite isothermal vertical plate with uniform mass diffusion has been studied. The plate temperature as well as the concentration level near the plate are raised uniformly. The dimensionless governing equations are solved using the Laplace-transform technique. The fluid considered here is a gray, absorbing-emitting radiation but a non-scattering medium. The effects of velocity profiles are studied for different physical parameters such as the thermal radiation parameter, thermal Grashof number, mass Grashof number and Schmidt number. It is observed that the velocity increases with increasing values the thermal Grashof number or mass Grashof number. The trend is just reversed with respect to the thermal radiation parameter.

3

Classical and weak solutions for semilinear parabolic equations with Preisach hysteresis

Jais M.

Opuscula Mathematica

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2008

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Vol. 28, no. 1

47-62

EN

We consider the solvability of the semilinear parabolic differential equation [formula] in a cylinder D = Ω x (0, T), where Ρ is a hysteresis operator of Preisach type. We show that the corresponding initial boundary value problems have unique classical solutions. We further show that using this existence and uniqueness result, one can determine the properties of the Preisach operator Ρ from overdetermined boundary data.

4

Explicit difference schemes for nonlinear differential functional parabolic equations with mixed derivatives-convergence analysis

Poliński A.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

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2005

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Vol. 45, [Z] 2

205--217

EN

We study the initial-value problem for parabolic equations with mixed partial derivatives and constant coefficients, and with nonlinear and nonlocal right-hand sides. Nonlocal terms appear in the unknown function and its gradient. We analyse convergence of explicit finite difference schemes by means of discrete fundamental solutions.