Rogério M. Saldanha da Gama

On the solutions of the energy transfer problem in a non-convex black body with convective/radiative boundary conditions☆

Abstract This paper considers the energy transfer phenomenon in a non-convex black body that exchanges energy, with the environment, by convection and by thermal radiation. Such non-linear problems arise when a body, surrounded by a fluid, is at high temperature levels and, therefore, the thermal radiant heat exchange can not be neglected. Since the body is not convex, there will exist a direct radiant interchange among points of the boundary of the body. A way for simulating such phenomena is presented, as well as proof of existence and uniqueness of the solution.

Numerical Simulation of Fins in a High Temperature Context

The present work shows the influence of the mutual heat transfer on the effectiveness of finned surfaces. Numerical simulations are carried out through a sequence of linear problems, possessing an equivalent minimum principle, that has as its limit the solution of the original problem. The presented tools allow the employment of realistic hypotheses. The problems are simulated with the aid of a finite difference approximation. This work accounts for the the steady state heat transfer process in rigid fins which experiences convective and radiative heat exchange. Some typical results are shown in order to illustrate the methodology. Results indicate that mutual radiation can significantly impact the actual heat transfer response of a fin.

A MATHEMATICAL MODEL FOR DESCRIBING THE THERMAL INTERCHANGE BETWEEN TWO BLACK BODIES IN A VACCUM

It is presented a linear procedure for constructing the solution of the coupled conduction/radiation heat transfer problem in a system of two black bodies in a vacuum. This nonlinear problem consists of two partial differential equations coupled by nonlinear boundary conditions. The proposed procedure regards the considered problem as the limit of well known linear heat transfer problems

Forced Convection Flow Through an Unsaturated Wellbore

This work studies the dynamics of the filling up of a rigid cylindrical shell porous matrix by a Newtonian fluid and the heat transfer associated phenomenon. A mixture theory approach is employed to obtain a preliminary local model for nonisothermal flows through a wellbore. The mixture consists of three overlapping continuous constituents: a solid (porous medium), a liquid and an inert gas included to account for the compressibility of the mixture as a whole. Assuming the convection flow on radial direction only, a set of four nonlinear partial differential equations describes the problem. Its hydrodynamic part — a nonlinear hyperbolic system — is approximated by means of a Glimm’s scheme, combined with an operator splitting technique, while an implicit finite difference scheme is used to simulate the thermal part.Copyright

Simulation of a Pollutant Transport in an Atmosphere With Shock Waves

In this work a model for transport phenomena in an environment representing the atmosphere containing a pollutant is presented by considering mass and linear momentum conservation for the air-pollutant mixture as well as the mass balance for the pollutant. The resulting mathematical description consists of a nonlinear system of hyperbolic equations that admits discontinuities in addition to smooth or classical solutions. The Riemann problem associated with a class of problems describing the transport of a pollutant in an ideal gas with constant temperature with a discontinuous mass density distribution as initial condition is discussed. Numerical approximations for this nonlinear system in which the problem is solved subjected to a discontinuous initial condition — a jump, originating, in most cases, shock waves — are obtained by employing Glimm’s method and considered in some numerical simulations.Copyright