Mixed convection boundary layer similarity solutions: prescribed wall heat flux

Merkin, J. H.; Mahmood, Tahir

doi:10.1007/bf00945309

Cited by 81 publications

(94 citation statements)

References 6 publications

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“…This leads us to consider the critical values in more detail. To calculate c c numerically we follow the approach given in [22], for example, whereby we make a linear perturbation to Eq. (9) resulting in a linear homogeneous equation subject to homogeneous boundary conditions and it is the solution to this eigenvalue problem that determines c c .…”

Section: Steady Statesmentioning

confidence: 99%

The effects of wall transpiration on the unsteady free convection boundary-layer flow near a stagnation point in a heat generating porous medium

Merkin

2017

Meccanica

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The natural convection boundary-layer flow near a stagnation point on a permeable surface embedded in a porous medium is considered when there is local heat generation within the boundary layer at a rate proportional to The initial-value problem reveals that, for 1 p\2, the nontrivial steady states are stable and the solution evolves to this state at large times. However, for p [ 2 these steady states are unstable and the solution either approaches the trivial state with the local heating dying out or a finite-time singularity develops for sufficiently large initial inputs.

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Section: Steady Statesmentioning

confidence: 99%

The effects of wall transpiration on the unsteady free convection boundary-layer flow near a stagnation point in a heat generating porous medium

Merkin

2017

Meccanica

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“…(primes denote differentiation with respect to ~7) Equations (7) have been discussed previously for values of the Prandtl number of order unity by Merkin and Mahmood [16]; in fact in [16] results were given for o-= 1. Also, it was shown in [16] that equations (7) possess a solution only if m > ½, and we will assume throughout that this condition is satisfied.…”

Section: Equationsmentioning

confidence: 99%

“…Also, it was shown in [16] that equations (7) possess a solution only if m > ½, and we will assume throughout that this condition is satisfied. We start by considering the behaviour of the similarity equations (7) for both small and large values of o-.…”

Section: Equationsmentioning

confidence: 99%

“…The arbitrary constant a 0 will be determined by the matching with the outer region. Note that (16) requires that a 0 be positive, which we will show to be the case for all m > 1. …”

Section: Similarity Equations (A) Solution For Large Prandtl Numbermentioning

confidence: 99%

“…We begin by discussing the similarity equations for this problem. These have been treated previously in some detail by Merkin and Mahmood [16] for Prandtl numbers of order unity. Here we examine the behaviour of their solution for both small and large Prandtl numbers.…”

Section: Introductionmentioning

confidence: 99%

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Mixed convection on a vertical surface with a prescribed heat flux: the solution for small and large Prandtl numbers

1991

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The mixed convection boundary-layer flow over a vertical surface with a prescribed surface heat flux is considered for both large and small values of the Prandtl number. The similarity equations are treated first. It is shown that, for large values of the Prandtl number, the solution approaches the forced convection limit with the free convection effects having only a small perturbation on this. The opposite is seen to be the case for small values of the Prandtl number, now free convection becomes the dominant heat transfer mechanism. A consequence of this is seen to be that the range of negative buoyancy parameter (opposed flow) over which a solution can exist decreases to zero as the Prandtl number is decreased.The scalings worked out for the similarity equations are then applied to the general boundary-layer flow, with the particular example of a uniform stream over a flat plate with uniform surface heat flux being treated in detail. Again it is seen that, for large Prandtl numbers, the solution approaches the forced convection limit whereas, for small Prandtl numbers, free convection dominates the flow. The effect of this is seen, for opposed flow, to delay the onset of separation for large Prandtl numbers, and to bring the separation point closer to the leading edge as the Prandtl number is decreased. An estimate for this effect is obtained.

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Free and Mixed Convection about a Vertical Plate with Prescribed Temperature or Heat Flux

1994

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Mixed convection boundary layer similarity solutions: prescribed wall heat flux

Cited by 81 publications

References 6 publications

The effects of wall transpiration on the unsteady free convection boundary-layer flow near a stagnation point in a heat generating porous medium

The effects of wall transpiration on the unsteady free convection boundary-layer flow near a stagnation point in a heat generating porous medium

Mixed convection on a vertical surface with a prescribed heat flux: the solution for small and large Prandtl numbers

Free and Mixed Convection about a Vertical Plate with Prescribed Temperature or Heat Flux

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