Rogério Martins Saldanha da Gama

Modelling of hydraulic transient in damageable elasto-viscoplastic piping systems

Abstract This paper is concerned with the modelling of the damage induced by pressure transients in liquid-filled pipes at high temperatures. The fluid dynamics and pipewall deformation are modelled by the classical water hammer theory, whereas pipewall mechanical behavior is described by an internal variable constitute theory. The resulting nonlinear system of hyperbolic equations is solved by means of a numerical technique based on Glimms method. Numerical examples concerning the damage evolution induced by pressure transients are presented and analyzed to demonstrate the applicability of the theory.

On the modelling of momentum and energy transfer in incompressible mixtures

Abstract Although many papers concerning the continuum theory of mixtures have been produced in the last years, the adequate form for the first and second laws of thermodynamics is still a controversial subject. In this paper, the basic principles that govern the evolution of a continuous mixture are postulated and used to develop a systematic procedure to obtain thermodynamically admissible objective constitutive equations. The prescription of five thermodynamic potentials is sufficient to define a complete set of constitutive relations. Two examples concerning the thermal analysis of a binary mixture of rigid solids and fluid flow in a porous channel bounded by two isothermal impermeable plates are presented. They illustrate the possibilities of effective practical use of the proposed theory.

Modelling and simulation of energy transfer in a saturated flow through a porous medium

Abstract Using the continuum theory of mixtures (a generalization of classical continuum mechanics), a model for a local description of the energy transfer in a saturated flow of a newtonian fluid through a rigid porous medium is proposed. It considers the fluid and the porous matrix as continuous constituents of a binary (solid-fluid) mixture. Both constituents coexist superposed in the whole volume of the mixture, so there exist simultaneously at each spatial point two temperatures and two velocities, giving rise to an energy generation and a momentum generation, which provide thermal and dynamical interactions, respectively. The forced convection heat transfer between the fluid and the solid constituents, when the fluid flows past a porous channel bounded by two isothermal parallel plates, is simulated by using a finite difference approach. The effects of some dimensionless parameters, such as β (relating the heat transfer between both constituents to the fluid constituent conduction), γ (relating both constituents conduction), the aspect ratio, the fluid constituents Peclet number, and the solid constituents Nusselt number (at the channels inlet and outlet) are discussed.

An alternative mathematical modelling for coupled conduction/radiation energy transfer phenomenon in a system of N gray bodies surrounded by a vacuum

In this work the energy transfer process among N rigid, opaque and gray bodies is considered. The energy transfer phenomenon takes place by conduction (inside each body) and by thermal radiation (among the boundaries of the bodies). All the bodies can emit and reflect thermal radiant energy and, hence, at each point of each boundary, the reflected and the emitted thermal radiant energy coming from the N bodies of the system must be taken into account. This complex phenomenon, with infinitely many practical applications, is described by a set of N partial differential equations coupled by a set of 2N non-linear equations defined on the boundaries of the bodies. A new mathematical modelling for the phenomenon is proposed that allows the construction of the solution in an easy way and provides proofs of existence and uniqueness of the solution. Some inconveniences of the classical modelling are presented, providing an expressive support for the proposed new modelling.

A new mathematical model for energy transfer problems with radiative boundary conditions

Abstract In this paper a new mathematical model is proposed for describing conduction heat transfer with radiative boundary conditions. This model, thermodynamically equivalent to the classical one, allows the construction of a minimum principle, which is employed for demonstrating the existence and uniqueness of the solution and provides a way for simulating the considered nonlinear energy transfer phenomenon.

A model for heat transfer in rigid continuous mixtures

Abstract In this paper an alternative viewpoint is presented for describing the heat conduction phenomenon in rigid composed solids through a continuum theory of mixtures, in which a composed material is regarded as a mixture of N continuous constituents. This viewpoint allows simulations that are not available in the classical theory. New parameters are introduced and their physical meanings are discussed in a direct comparison with the classical heat conduction theory. The theory is established in such a way that it is coincident with classical theory when there exists only one constituent.

A linear scheme for simulating conduction heat transfer problems with nonlinear boundary conditions

Abstract A scheme for constructing the solution of conduction heat transfer problems with nonlinear boundary conditions is presented through the solution of problems with linear boundary conditions. The proposed procedure provides an efficient and easy way for carrying out numerical simulations of nonlinear heat transfer problems. In order to illustrate the procedure a particular problem is simulated by means of a (linear) finite difference scheme.

An upper bound estimate for a class of conduction heat transfer problems with nonlinear boundary conditions

Abstract This work is concerned with the previous establishment of an upper bound for the solution of a large class of steady-state heat transfer problems, represented by a partial differential equation subjected to nonlinear boundary conditions. Within this class we have the conduction/radiation heat transfer problems in gray bodies. It is presented a general upper bound estimate obtained with the aid of a (conveniently chosen) auxiliary function and of a given (bounded) set. The employed procedure is based on the partial differential inequality div(k grad(T-W))⩾0 and its features.

Simulation of momentum and energy transfer in a porous medium nonsaturated by an incompressible fluid

Abstract This work studies the transport phenomena in a nonsaturated flow of a newtonian fluid through a rigid porous matrix. A mixture theory approach is used in the modelling of the fluid flow and the heat, transfer problem. The mixture consists of three overlapping continuous constituents: a solid (porous medium), a liquid and an inert gas, assumed with zero mass density and thermal conductivity. A set of four nonlinear partial differential equations describes the problem which is approximated by means of a Glimms scheme, combined with an operator splitting technique, for the hyperbolic equations and a finite-difference scheme for the elliptic ones.

Mathematical modelling of the non-linear heat transfer process in a gray shell surrounded by a non-participating medium

Abstract This paper is concerned with the construction of an adequate mathematical model for describing the conduction/radiation heat transfer phenomenon in a thin and opaque shell surrounded by a non-participating medium. The heat transfer phenomenon is represented by a non-linear integro-differential system of equations with two independent variables. It is shown that the solution exists, is unique and may be constructed through a systematic procedure. Two typical examples are presented.