Vertical free convective boundary-layer flow in a porous medium using a thermal nonequilibrium model: Elliptical effects

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Abstract

In this paper we study the effect of adopting a two-temperature model of microscopic heat transfer on the classical Cheng & Minkowycz [1] vertical free convection boundary-layer flow in a porous medium. Such a model, which allows the solid and fluid phases not to be in local thermal equilibrium, is found to modify substantially the behaviour of the flow relatively close to the leading edge. A companion paper deals with the (parabolic) boundary-layer theory, but the present work investigates in detail how elliptical effects are manifested. This is undertaken by solving the full equations of motion, rather than the boundary-layer approximation. In general, it is found that at any point in the flow, the temperature of the solid phase is higher than that of the fluid phase, and therefore that the thermal field of the solid phase is of greater extent than that of the fluid phase. The microscopic inter-phase heat transfer is characterised by the coefficient, H, and it is shown that these thermal non-equilibrium effects are strongest when H is small.
Original languageEnglish
Pages (from-to)437-448
Number of pages12
JournalZeitschrift für Angewandte Mathematik und Physik
Volume54
Issue number3
DOIs
Publication statusPublished - 2003

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boundary layer flow
Boundary layer flow
Boundary Layer Flow
Non-equilibrium
Porous Media
Porous materials
solid phases
Vertical
Fluids
fluids
boundary layers
Boundary layers
heat transfer
Heat transfer
leading edges
Natural convection
free convection
Fluid
Equations of motion
Heat Transfer

Cite this

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title = "Vertical free convective boundary-layer flow in a porous medium using a thermal nonequilibrium model: Elliptical effects",
abstract = "In this paper we study the effect of adopting a two-temperature model of microscopic heat transfer on the classical Cheng & Minkowycz [1] vertical free convection boundary-layer flow in a porous medium. Such a model, which allows the solid and fluid phases not to be in local thermal equilibrium, is found to modify substantially the behaviour of the flow relatively close to the leading edge. A companion paper deals with the (parabolic) boundary-layer theory, but the present work investigates in detail how elliptical effects are manifested. This is undertaken by solving the full equations of motion, rather than the boundary-layer approximation. In general, it is found that at any point in the flow, the temperature of the solid phase is higher than that of the fluid phase, and therefore that the thermal field of the solid phase is of greater extent than that of the fluid phase. The microscopic inter-phase heat transfer is characterised by the coefficient, H, and it is shown that these thermal non-equilibrium effects are strongest when H is small.",
author = "Rees, {D A S}",
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T1 - Vertical free convective boundary-layer flow in a porous medium using a thermal nonequilibrium model: Elliptical effects

AU - Rees, D A S

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PY - 2003

Y1 - 2003

N2 - In this paper we study the effect of adopting a two-temperature model of microscopic heat transfer on the classical Cheng & Minkowycz [1] vertical free convection boundary-layer flow in a porous medium. Such a model, which allows the solid and fluid phases not to be in local thermal equilibrium, is found to modify substantially the behaviour of the flow relatively close to the leading edge. A companion paper deals with the (parabolic) boundary-layer theory, but the present work investigates in detail how elliptical effects are manifested. This is undertaken by solving the full equations of motion, rather than the boundary-layer approximation. In general, it is found that at any point in the flow, the temperature of the solid phase is higher than that of the fluid phase, and therefore that the thermal field of the solid phase is of greater extent than that of the fluid phase. The microscopic inter-phase heat transfer is characterised by the coefficient, H, and it is shown that these thermal non-equilibrium effects are strongest when H is small.

AB - In this paper we study the effect of adopting a two-temperature model of microscopic heat transfer on the classical Cheng & Minkowycz [1] vertical free convection boundary-layer flow in a porous medium. Such a model, which allows the solid and fluid phases not to be in local thermal equilibrium, is found to modify substantially the behaviour of the flow relatively close to the leading edge. A companion paper deals with the (parabolic) boundary-layer theory, but the present work investigates in detail how elliptical effects are manifested. This is undertaken by solving the full equations of motion, rather than the boundary-layer approximation. In general, it is found that at any point in the flow, the temperature of the solid phase is higher than that of the fluid phase, and therefore that the thermal field of the solid phase is of greater extent than that of the fluid phase. The microscopic inter-phase heat transfer is characterised by the coefficient, H, and it is shown that these thermal non-equilibrium effects are strongest when H is small.

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DO - 10.1007/s00033-003-0032-4

M3 - Article

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JO - Zeitschrift für Angewandte Mathematik und Physik

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SN - 0044-2275

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ER -