Similarity solutions in free convection boundary-layer flows adjacent to vertical permeable surfaces in porous media: II prescribed surface heat flux

Chaudhary, M. A.; Merkin, J. H.; Pop, I.

doi:10.1007/bf01463925

Cited by 56 publications

(53 citation statements)

References 6 publications

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“…Numerical investigations can be found in [1], [6], [12], [14], [21], [22] and [27]. In view of all these papers, the following conclusions can be drawn.…”

Section: Resultsmentioning

confidence: 92%

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Recent Advances on Similarity Solutions Arising During Free Convection

Brighi¹,

Hoernel²

2005

Progress in Nonlinear Differential Equations and Their Applications

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This paper reviews results about free convection near a vertical flat plate embedded in some saturated porous medium. We focus on a third order autonomous differential equation that gives a special class of solutions called similarity solutions. Two cases are under consideration: in the first one we prescribe the temperature on the plate and in the second one we prescribe the heat flux on it. We will also see that the same equation appears in other industrial processes.

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“…Numerical investigations can be found in [1], [6], [12], [14], [21], [22] and [27]. In view of all these papers, the following conclusions can be drawn.…”

Section: Resultsmentioning

confidence: 92%

“…The second set of boundary conditions (1.3) with α = m + 2 and β = 2m + 1 for m ∈ R is for the prescribed surface heat flux as done in [10] and [13]. In both cases the solutions depend on two parameters: m, the power-law exponent and γ, the mass transfer parameter.…”

Section: Introductionmentioning

confidence: 99%

Recent Advances on Similarity Solutions Arising During Free Convection

Brighi¹,

Hoernel²

2005

Progress in Nonlinear Differential Equations and Their Applications

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“…with m ∈ R and A > 0, see [16], [18], [21], [28] and [32]. Secondly, the heat flux is prescribed along the plate that leads to…”

Section: The Semi-infinite Vertical Flat Plate Casementioning

confidence: 99%

“…For mathematical results about existence, nonexistence, uniqueness, nonuniqueness and asymptotic behavior, see [2], [5], [6] and [28] for γ = 0, and [9], [12], [15], [23] and [24] for the general case. Numerical investigations can be found in [2], [7], [16], [18], [28], [30] and [38].…”

Section: The Semi-infinite Vertical Flat Plate Casementioning

confidence: 99%

Steady Free Convection in a Bounded and Saturated Porous Medium

Akesbi¹,

Brighi²,

Hoernel³

2006

Recent Advances on Elliptic and Parabolic Issues

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In this paper we are interested with a strongly coupled system of partial differential equations that modelizes free convection in a two-dimensional bounded domain filled with a fluid saturated porous medium. This model is inspired by the one of free convection near a semi-infinite impermeable vertical flat plate embedded in a fluid saturated porous medium. We establish the existence and uniqueness of the solution for small data in some unusual spaces.

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“…Details about the physical background can be found, for example, in [13], [14], [15], [16], [19] and [22]. In these papers, the authors assume that convection takes place in a thin layer around the plate.…”

Section: Introductionmentioning

confidence: 99%