Gérard Jeandel

Radiative and conductive heat transfer in a nongrey semitransparent medium. Application to fire protection curtains

Abstract This paper deals with heat transfer in nongrey media which scatter, absorb and emit radiation. Considering a two dimensional geometry, radiative and conductive phenomena through the medium have been taken into account. The radiative part of the problem was solved using the discrete ordinate method with classical S n quadratures. The absorption and scattering coefficients involved in the radiative transfer equation (RTE) were obtained from the Mie theory. Conduction inside the medium was linked to the RTE through the energy conservation. Validation of the model has been achieved with several simulation of water spray curtains used as fire protection walls.

Heat transfer by radiation and conduction in fibrous media without axial symmetry

Coupled radiative and conductive heat transfer in a fibrous medium formed by silica fibres is investigated in this paper by not taking account of the axial symmetry for the distribution of fibres or the boundary conditions. Radiative properties of the medium are calculated by using the Mie theory. The model obtained depends only on optical parameters (indices of silica) and on morphological parameters (diameter and orientation of the fibres, density of the medium). Simulations make it possible to study the strongly anisotropic behaviour of the scattering of the radiation by a fibre and to study the influence of various parameters on the radiative properties of the medium. The results of the Mie theory make possible the simulation of the heat transfer coupled by radiation and conduction. To do this, we introduce a new numerical scheme able to simulate heat transfer in the lack of axial symmetry. With this model, we can show the effects of distribution of fibres and temperature on the thermal behaviour of the medium as well as showing the importance of the phenomenon of scattering in fibrous media.

Coupled radiative and conductive heat transfer in a non-grey absorbing and emitting semitransparent media under collimated radiation

Abstract This paper deals with heat transfer in non-grey semitransparent two-dimensional sample. Considering an homogeneous purely absorbing medium, we calculated the temperature field and heat fluxes of a material irradiated under a specific direction. Coupled radiative and conductive heat transfer were considered. The radiative heat transfer equation (RTE) was solved using a S8 quadrature and a discrete ordinate method. Reflection and absorption coefficients of the medium were calculated with the silica optical properties. The conduction inside the medium was linked to the RTE through the energy conservation. Validation of the model and two original cases are also presented.

Radiative and conductive heat exchanges in high-temperature glass melt with the finite-volume method approach. Influence of several spatial differencing schemes on RTE solution

ABSTRACT This article is devoted to heat transfer involving radiation and conduction. Considering a nongray, purely absorbing medium, the radiative heat transfer equation (RTE) and the energy balance equation are both solved with the finite-volume method (FVM). The energy equation is coupled to the RTE through the radiative source term. Several differencing scheme efficiencies are discussed for the case of strong opacities. Validation of the model with various benchmarks simulating high-temperature glass melting, including one- and two-dimensional geometries, is achieved.

CONVERGENCE OF A NUMERICAL SCHEME FOR A NONLINEAR COUPLED SYSTEM OF RADIATIVE-CONDUCTIVE HEAT TRANSFER EQUATIONS

In this paper, we prove the convergence of a numerical scheme for one-dimensional coupled system of nonlinear partial and ordinary integro-differential equations. This system describes the steady-state coupled radiative-conductive heat transfer for a non-grey anisotropically absorbing, emitting and scattering medium, with axial symmetry and nonhomogeneous Dirichlet boundary conditions. The convergence proof follows from monotonicity arguments and the application of a discrete fixed-point problem, involving only to the temperature fields.

A FVM BASED ON A CELL VERTEX SCHEME FOR THE SOLUTION OF THE RTE IN 3D COMPLEX GEOMETRIES

The angular discretization associated to the RTE is un form and the spatial domain of interest is divided into four-node tetrahedron elem ents. All dependent variables are stored at the nodes of the mesh, and the equation for each v riable is obtained from its discretized conservation equation written for a VP control volume surrounding node P. The discretized RTE (for a nonscattering gray mediu m) over VP and a k ∆Ω discrete solid angle associated to the Ω direction gives [1,2]:

Control of Transient Coupled Radiative-conductive Heat Transfer Equation

Control of the combined heat transfer process is presently under consideration for better glass manufacture with less defects. Solution of transient combined radiative and conductive heat transfer in a medium requires the solution of radiative transfer equation, which usually takes hours to converge using latest finite volume codes. Indeed transient combined radiative and conductive heat transfer in a medium is governed by nonlinear partial integro-differential equations. Simple models are necessary for real time control purposes. First this paper present a reduced model. It is obtained by a polynomial approximation for the combined heat transfer and a discretization of PDEs by finite difference method. Then a PI controller of the approximate plant is designed. Convergence is confirmed by simulation results.