Dual-Phase-Lagging and Porous-Medium Heat Conduction Processes

Wang, Liqiu; Xu, Mingtian; Wei, Xiu-Shen

doi:10.1007/978-1-4020-8178-1_1

Cited by 7 publications

(3 citation statements)

References 37 publications

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“…The dual-phase-lag heat shown in Equation ( 5 ) has been applied in mathematical modeling of the heat transfer in functionally graded materials [ 13 , 14 , 15 ], ultrafast pulse-laser heating problems [ 16 , 17 ], porous media [ 18 , 19 , 20 ], nanocomposites [ 21 , 22 ], and living tissue [ 23 , 24 , 25 ]. If

in Equation ( 5 ), then the classical parabolic heat conduction equation is obtained.…”

Section: Introductionmentioning

confidence: 99%

Fractional Order Dual-Phase-Lag Model of Heat Conduction in a Composite Spherical Medium

2022

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In the paper, a solution of the fractional dual-phase-lag heat conduction problem is presented. The considerations are related to the heat conduction in a multi-layered spherical medium with azimuthal symmetry. The final form of the analytical solution is given in a form of the double series of spherical Bessel functions and Legendre functions. Numerical calculations concern the study of the effect of the order of the Caputo derivative on the temperature distribution in a composite solid sphere, hemisphere and spherical cone.

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in Equation ( 5 ), then the classical parabolic heat conduction equation is obtained.…”

Section: Introductionmentioning

confidence: 99%

Fractional Order Dual-Phase-Lag Model of Heat Conduction in a Composite Spherical Medium

2022

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“…What makes the metal foams special within the class of porous media is precisely their high thermal conductivity, porosity and permeability. All these features drive the modelling of heat transfer in metal foams towards the framework of local thermal non-equilibrium [7][8][9][10][11][12][13][14][15]. The rationale is that the convection heat transfer in metal foams involves two phases, the fluid and the solid, with markedly different thermal conductivities [8,16].…”

Section: Introductionmentioning

confidence: 99%

Flow and Convection in Metal Foams: A Survey and New CFD Results

Pulvirenti

Celli

Barletta

2020

Fluids

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Metal foams are widely studied as possible tools for the enhancement of heat transfer from hot bodies. The basic idea is that a metal foam tends to significantly increase the heat exchange area between the hot solid body and the external cooling fluid. For this reason, this class of porous materials is considered as a good candidate for an alternative to finned surfaces, with different pros and cons. Among the pros, we mention the generally wider area of contact per unit volume between solid and fluid. Among the cons is the difficulty to produce different specimens with the same inner structure, with the consequence that their performance may be significantly variable. This paper will offer a survey of the literature with a focus on the main heat transfer characteristics of the metal foams and the energy balance model based on Local Thermal Non-Equilibrium (LTNE). Then, a numerical simulation of the heat transfer at the pore-scale level for an artificial foam with a spatially periodic structure will be discussed. Finally, these numerical results will be employed to assess the macroscopic modeling of the flow and heat transfer in a metal foam. More precisely, the Darcy–Forchheimer model and the LTNE model adopted to describe the momentum and energy transfer in metal foams have been validated for metallic periodic structures.

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“…Tzou (1995) proposed a dual phase lagging heat conduction equation to remedy this defect. Wang et al (2008) developed methods of measuring the phase lags of the heat flux and the temperature gradient and obtained analytical solutions for regular heat conduction domains under essentially arbitrary initial and boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

A Mathematical Model for Short-Time Filtration in Poroelastic Media with Thermal Relaxation and Two Temperatures

Sherief

Hussein

2011

Transp Porous Med

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In this work, we derive a set of governing equations for a mathematical model of generalized thermoelasticity in poroelastic materials. This model predicts finite speeds of propagation of waves contrary to the model of coupled thermoelasticity where an infinite speed of propagation is inherent. Next, we prove the uniqueness of solution of these equations under suitable conditions. We also obtain a reciprocity theorem for these equations. A thermal shock problem for a half-space composed of a poroelastic material saturated with a liquid is then considered. The surface of the half-space is assumed to be traction free, permeable, and subjected to heating. The Laplace transform technique is used to solve the problem. Numerical results for the temperature in the elastic body and fluid, displacement of the elastic body, velocity of the fluid, and stresses for both components are obtained and represented graphically.

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Dual-Phase-Lagging and Porous-Medium Heat Conduction Processes

Cited by 7 publications

References 37 publications

Fractional Order Dual-Phase-Lag Model of Heat Conduction in a Composite Spherical Medium

Fractional Order Dual-Phase-Lag Model of Heat Conduction in a Composite Spherical Medium

Flow and Convection in Metal Foams: A Survey and New CFD Results

A Mathematical Model for Short-Time Filtration in Poroelastic Media with Thermal Relaxation and Two Temperatures

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