Similarity solutions for unsteady free-convection flow from a continuous moving vertical surface

Abd‐el‐Malek, Mina B.; Kassem, M.; Mekky, Mohammad L.

doi:10.1016/s0377-0427(03)00638-1

Cited by 14 publications

(4 citation statements)

References 24 publications

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“…Abd-El-Malek et al [7] addressed the problem of drug diffusion via a thin membrane using a group theoretic method. Using group methods, in 2004 Abd-El-Malek et al [8] analysed another efficient technique for unstable free-convection flow on a vertical plate, moving continuously. Ece [9] came up with similarity solutions for temperature and velocity profiles with boundary layer for determining the magnetic field effect on surface heat flux and skin friction.…”

Section: Introductionmentioning

confidence: 99%

Group Method of Uniform Surface Heat Flux from a Vertical Cone Using Laminar Free Convection

Maheshwaran¹,

Pullepu²,

Pinelas³

2023

MMEP

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In this study, the Group Transformation method is employed to simulate the laminar free convection problem involving a viscous incompressible fluid on a vertically oriented cone with a uniform heat flux on its surface. The non-dimensional governing partial differential equations (PDEs) and their boundary conditions are reduced to ordinary differential equations (ODEs) with corresponding appropriate conditions. To solve the resulting non-linear ODEs, the Range-Kutta shooting method is applied. The temperature and velocity fields are graphically presented for various parameters, such as the semi-vertical angle and Prandtl number. Furthermore, the local Nusselt number and skin fraction are analyzed numerically.

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Section: Introductionmentioning

confidence: 99%

Group Method of Uniform Surface Heat Flux from a Vertical Cone Using Laminar Free Convection

Maheshwaran¹,

Pullepu²,

Pinelas³

2023

MMEP

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“…Group methods, as a class of methods which assuage to a reduction of the number of independent variables, were first presented in [22,23]. Moran and Gaggioli [24,25] indicated a general systematic group formalism for similarity study, where a given combination of partial differential equations was reduced to a system of ordinary differential equations [25][26][27][28][29][30][31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

Similarity Solutions for Flow and Heat Transfer of Non-Newtonian Fluid over a Stretching Surface

Sojoudi

Mazloomi

Saha

et al. 2014

Journal of Applied Mathematics

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Similarity solutions are carried out for flow of power law non-Newtonian fluid film on unsteady stretching surface subjected to constant heat flux. Free convection heat transfer induces thermal boundary layer within a semi-infinite layer of Boussinesq fluid. The nonlinear coupled partial differential equations (PDE) governing the flow and the boundary conditions are converted to a system of ordinary differential equations (ODE) using two-parameter groups. This technique reduces the number of independent variables by two, and finally the obtained ordinary differential equations are solved numerically for the temperature and velocity using the shooting method. The thermal and velocity boundary layers are studied by the means of Prandtl number and non-Newtonian power index plotted in curves.

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“…In this method developed by Morgan [11] Greek characters β volumetric coefficient of expansion with concentration ν = µ/ρ kinematic viscosity of fluid ρ fluid density ψ stream function η similarity variable assumed group generates a set of simple simultaneous equations whose solution determines the specific form for the invariants see [6,10]. This method adopted by Abd El Malek proved [1] to be efficient [2][3][4]14,15] for the analysis of various boundary layer flow problems.…”

Section: Introductionmentioning

confidence: 99%

Group analysis for natural convection from a vertical plate

Rashed

Kassem

2008

Journal of Computational and Applied Mathematics

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The steady laminar natural convection of a fluid having chemical reaction of order n past a semi-infinite vertical plate is considered. The solution of the problem by means of one-parameter group method reduces the number of independent variables by one leading to a system of nonlinear ordinary differential equations. Two different similarity transformations are found. In each case the set of differential equations are solved numerically using Runge-Kutta and the shooting method. For each transformation different Schmidt numbers and chemical reaction orders are tested.

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Similarity solutions for unsteady free-convection flow from a continuous moving vertical surface

Cited by 14 publications

References 24 publications

Group Method of Uniform Surface Heat Flux from a Vertical Cone Using Laminar Free Convection

Group Method of Uniform Surface Heat Flux from a Vertical Cone Using Laminar Free Convection

Similarity Solutions for Flow and Heat Transfer of Non-Newtonian Fluid over a Stretching Surface

Group analysis for natural convection from a vertical plate

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