Symmetry groups and similarity solutions for a free convective boundary-layer problem

Kalpakides, V.K.; Balassas, K.G.

doi:10.1016/j.ijnonlinmec.2004.01.006

Cited by 23 publications

(13 citation statements)

References 21 publications

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“…They [23] have obtained exact solutions of boundary layer equations of a special non-Newtonian fluid over a stretching sheet. Kalpakides and Balassas [13] studied the free convective boundary layer problem of an electrically conducting fluid over an elastic surface using group theoretic method. Ibrahim et al [11] investigated the similarity reductions for problems of radiative and magnetic field effects on free convection and mass-transfer flow past a semi-infinite flat plate.…”

Section: Introductionmentioning

confidence: 99%

Lie group analysis of unsteady MHD three dimensional by natural convection from an inclined stretching surface saturated porous medium

El-Kabeir

El-Hakiem

Rashad

2008

Journal of Computational and Applied Mathematics

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Lie group method is investigated for solving the problem of heat transfer in an unsteady, three-dimensional, laminar, boundarylayer flow of a viscous, incompressible and electrically conducting fluid over inclined permeable surface embedded in porous medium in the presence of a uniform magnetic field and heat generation/absorption effects. A uniform magnetic field is applied in the y-direction and a generalized flow model is presented to include the effects of the macroscopic viscous term and the microscopic permeability of porous medium. The infinitesimal generators accepted by the equations are calculated and the extension of the Lie algebra for the problem is also presented. The restrictions imposed by the boundary conditions on the generators are calculated. The investigation of the three-independent-variable partial differential equations is converted into a two-independent-variable system by using one subgroup of the general group. The resulting equations are solved numerically with the perturbation solution for various times. Velocity, temperature and pressure profiles, surface shear stresses, and wall-heat transfer rate are discussed for various values of Prandtl number, Hartmann number, Darcy number, heat generation/absorption coefficient, and surface mass-transfer coefficient.

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Section: Introductionmentioning

confidence: 99%

Lie group analysis of unsteady MHD three dimensional by natural convection from an inclined stretching surface saturated porous medium

El-Kabeir

El-Hakiem

Rashad

2008

Journal of Computational and Applied Mathematics

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“…They also presented numerical results for the nonuniform magnetic field case. Kalpakides and Balassas [8] studied the free convective boundary-layer problem of an electrically conducting fluid over an elastic surface by group theoretic method. Their results agree with the existing result for the group of scaling symmetry.…”

Section: Introductionmentioning

confidence: 99%

Lie Group Analysis on Brownian Motion and Thermophoresis Effect on Free Convective Boundary-Layer Flow on a Vertical Cylinder Embedded in a Nanofluid-Saturated Porous Medium

Ferdows¹,

Hamad²,

Ali

2015

Journal of Applied Mathematics

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Natural convective boundary-layer flow of a nanofluid on a heated vertical cylinder embedded in a nanofluid-saturated porous medium is studied. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. Lie groups analysis is used to get the similarity transformations, which transform the governing partial differential equations to a system of ordinary differential equations. Two groups of similarity transformations are obtained. Numerical solutions of the resulting ordinary differential systems are obtained and discussed for various values of the governing parameters.

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“…Kalpakides and Balassas [2] also studied the free convective boundary layer problem using Lie group analysis. Radiative and magnetic effects on free convection and mass transfer flow past a flat plate are studied by Ibrahim et al [3].…”

Section: Introductionmentioning

confidence: 99%

Free convection flow in an inclined plate with variable thermal conductivity by scaling group transformations

Bhuvaneswari¹,

Sivasankaran²

2014

AIP Conference Proceedings

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Abstract. The Lie group analysis of natural convection flow over an inclined semi-infinite plate with variable thermal conductivity is studied. The fluid thermal conductivity is assumed to vary as a linear function of temperature. A scaling group of transformation is applied to the governing partial differential equations and then used to reduce them to a system of ordinary differential equations. Numerical solutions of the ordinary differential equations are also obtained. From the numerical results it is found that the momentum and thermal boundary layer thicknesses increase with thermal conductivity parameter. The velocity increases and temperature decreases with increasing the Grashof number.

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Symmetry groups and similarity solutions for a free convective boundary-layer problem

Cited by 23 publications

References 21 publications

Lie group analysis of unsteady MHD three dimensional by natural convection from an inclined stretching surface saturated porous medium

Lie group analysis of unsteady MHD three dimensional by natural convection from an inclined stretching surface saturated porous medium

Lie Group Analysis on Brownian Motion and Thermophoresis Effect on Free Convective Boundary-Layer Flow on a Vertical Cylinder Embedded in a Nanofluid-Saturated Porous Medium

Free convection flow in an inclined plate with variable thermal conductivity by scaling group transformations

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