G. Spiga

A rigorous solution to a heat transfer two phase model in porous media and packed beds

Abstract The dynamic response of porous media and packed beds systems to an arbitrary time varying inlet temperature is investigated analytically. A two phase model is developed taking rigorously into account the fluid to solid heat capacity ratio. At first the initial value problem is solved, including initially non-uniform spatial temperature distributions. Then a general solution, relevant to operational modes in which the initial conditions are forgotten, is proposed. Some graphs are shown for simple situations such as delta, step, ramp response (for the initial value problem) and periodic sinusoidal inlet temperature.

Radiative transfer in an absorbing and anisotropically scattering slab with a reflecting boundary

Abstract Radiative transfer has been considered within a participating plane slab assuming the externallyapplied radiation to impinge normally on one boundary of the slab while the other boundary is assumed to reflect in a diffuse way. The linearly anisotropic and the Rayleigh modes of scattering have been both considered. A rigorous solution is developed following a constructive procedure based on projectional methods: the resulting computational formulae have been numerically processed to obtain the distribution of the physically relevant variables for some significant situations.

Effects of scattering and reflection of radiation on batch photochemical reaction in a slab geometry

Abstract Effects of scattering of radiation within the medium, boundary surface reflectivity and initial optical thickness of the medium on the conversion occurring in a batch photochemical reaction in plane-slab geometry are investigated analytically. Results are presented for the local and average conversion within the medium, reflectivity and transmissivity of the medium, and normalized optical thickness of the medium as a function of time. The scattering is found to reduce the conversion and tends to increase the uniformity of the distribution of the reactant within the medium.

Radiative transfer in an absorbing-scattering slab bounded by emitting and reflecting surfaces☆

Abstract An exact integral theory of the planar radiative transfer with isotropic scattering and general boundary conditions is presented in the paper. The analytical solution to the problem is numerically processed for two different specializations of the emissivity and reflectivity properties of the bounding surfaces. Results are given for the total and angular radiation intensities as well as for the net radiative flux.

Radiative heat transfer in plane participating media

Abstract The problem of radiative heat transfer through a nonisothermal scattering, absorbing and emitting grey medium between reflecting, absorbing and emitting plates is analytically investigated. The solution technique is based on a projectional procedure, equivalent to a variational approach. The results concern the most meaningful physical quantities, and get an improved accuracy with respect to the data available in literature, with extremely low computational time.

SUN DRIVEN PHOTOCHEMICAL REACTION IN A HORIZONTAL PLANE SLAB

Abstract The interaction between the solar radiation and a participating-reacting plane medium is studied, and the relevant mass balance and radiative transfer equations are solved by an analytical-numerical procedure. The system simulates a batch photochemical reactor for the exploitation or storage of solar energy. The roles played by the reaction and insolation characteristic times, as well as the effects of geometrical and physical properties of the reactor, are discussed. Some figures, showing the time and space variation of the most meaningful physical quantities, are reported as illustrative examples of the obtained numerical results.

Rigorous and simplified approach to the radiative transfer in an absorbing and anisotropically scattering slab with a reflecting boundary

Abstract Radiative transfer has been considered within a plane participating slab assuming diffuse emission at one boundary and diffuse reflection at the other boundary. The medium is assumed to be a zero temperature one so that emission is neglected and only absorption and scattering (according to a linearly anisotropic law) are assumed within the slab. A rigorous solution is developed following a constructive procedure based on projectional methods: the resulting formulae have been numerically processed to obtain the distribution of the physically relevant variables for some significant situations. The results from the rigorous approach are then used as reference values to test the reliability of the results from some of the simplified approaches used in the literature ( P 1 approximation and kernel substitution).

RELATIONSHIP BETWEEN NUCLEAR AND THERMOMECHANICAL ASPECTS IN FUEL ROD DESIGN

Abstract The aim of this paper is to provide an analytical determination of temperature and thermal stress in a cylindrical nuclear fuel rod with cladding, including the actual neutron flux distribution in a unit cell, fur a thermal reactor in steady state. The temperature and stresses are evaluated by solving a set of differential and integral equations, derived from the heat conduction and Hookes law. Some numerical applications are presented (with reference to a common pressurized water reactor) and discussed. The emphasis is placed on the influence of nuclear parameters on the thermal and mechanical behavior of the fuel element.

Integral form of the Boltzmann equation for the forced diffusion of charged particles in anisotropically scattering media

SommarioSulla base di una recente formulazione della teoria del trasporto di particelle in presenza di una forza esterna, il presente lavoro mostra come il problema considerato sia riconducibile, per varie e significative leggi di interazione tra le particelle e il mezzo in cui diffondono, a un sistema di equazioni integrali lineari in una variabile indipendente. Viene studiato soprattutto lo scattering anisotropo, e sono ricavati in forma esplicita i kernel del sistema integrale per alcuni modelli di interazione di maggiore interesse.SummaryAccording to a recently proposed integral formulation of the Boltzmann equation for test particles in an external force field, the present paper shows how it is actually possible to reduce the original transport problem to the solution of a system of linear integral equations in one variable for a wide and physically meaningful class of interaction laws between test particles and host medium. The feasibility study deals mainly with anisotropic scattering, and provides the kernels of the final integral system to be solved. The explicit analytic form of such kernels has been explicitly worked out for some interaction models of particular interest.

Functional analysis of integral transport equations in linear rarefied gas dynamics

SommarioIn questa nota vengono studiate le proprietà funzionali di alcune equazioni integrali lineari che regolano problemi basilari della dinamica dei gas rarefatti. Gli operatori integrali, relativi alle operazioni stesse, sono analizzati in dettaglio.SummaryA study is proposed on the functional properties of the solutions of an interesting class of linear integral equations governing linear problems in rarefied gas dynamics. The analysis is carried out through a systematic study of the integral operator generated by the kernel of the equations themselves.