S. Del Giudice

Thermal Aspects of Cryosurgery

Tissue reactions to cryosurgical procedures depend on temperature variations and on rates of temperature variations induced by freezing probes. In this paper thermal responses of biological systems undergoing freezing are obtained through the application of the finite element method to the solution of the nonlinear bio-equation. This model allows realistic predictions of isotherm fields and of rates of freezing in practically any cryosurgical procedure.

FINITE-ELEMENT SOLUTION OF THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS

A finite-element procedure is presented for the calculation of two-dimensional, viscous, incompressible flows of a recirculating nature. As in finite-difference procedures, velocity and pressure are uncoupled and the equations are solved one after the other. Velocity fields are determined by first calculating intermediate velocity values based on an estimated pressure distribution and then obtaining appropriate corrections to satisfy the continuity equation. Illustrative examples involving flow in the entrance region between parallel plates, lid-driven cavity flow, and flow around an obstacle demonstrate the accuracy and capabilities of the proposed technique.

LAMINAR FORCED CONVECTION IN THREE-DIMENSIONAL DUCT FLOWS

A finite-element procedure for the prediction of laminar forced convection in three-dimensional parabolic flows is presented. The procedure, based on the parabolized simplification of the complete Navier-Stokes equations, is first validated by comparing computed results with the available literature data for thermally and hydrodynamically developing flows in flat channels. Then, new results are presented for simultaneously developing flows in square duels, with

Finite element analysis of laminar mixed convection in the entrance region of horizontal annular ducts

, and

A (k-ε) MODEL OF TURBULENT FLOW

boundary conditions and Prandtl number ranging from 0.1 to 10.

Temperature-dependent viscosity and viscous dissipation effects in simultaneously developing flows in microchannels with convective boundary conditions

The laminar mixed convection in the entrance region of horizontal straight ducts of an annular cross section is studied by means of a generally applicable finite element procedure based on the parabolized simplification of the Navier-Stokes and energy equations and on the Boussinesq approximation of the buoyancy term. The procedure is validated through comparisons of computed results with available data from the literature. New results concern annuli with radius ratios equal to 0.25, 0.5, and 0.75 subjected to the fundamental boundary condition of the second and the third kinds, for Prandtl numbers equal to 0.7 and 7, and different values of Grashof number.

Thermal Design of Pavement Structures in Seasonal Frost Areas

A two-equation model of turbulence is employed where the transport of turbulence kinetic energy and the dissipation rate are depicted by transport-type equations, i.e., the two-equation model of turbulence. A finite-element discretization of the (k-e) turbulence model is described that relies on the sequential approach in the solution. As in finite-difference procedures, velocity and pressure are uncoupled and the equations are solved one after the other, computing the magnitude of the turbulent viscosity from turbulence kinetic energy and dissipation rate.

THREE-DIMENSIONAL LAMINAR FLOW IN DUCTS

The effects of viscous dissipation and temperature dependent viscosity in simultaneously developing laminar flows of liquids in straight microchannels are studied with reference to convective boundary conditions. Two different geometries, namely the circular tube and the parallel plate channel, are considered. Viscosity is assumed to vary with temperature according to an exponential relation, while the other fluid properties are held constant. A finite element procedure, based on a projection algorithm, is employed for the step-by-step solution of the parabolized momentum and energy equations. Axial distributions of the local overall Nusselt number and of the apparent Fanning friction factor are presented with reference to both heating and cooling conditions for two different values of the Biot number. Examples of radial temperature profiles at different axial locations and of axial distributions of centerline velocity and temperature are also shown.

DETERMINATION OF THERMAL WAVE DISTRIBUTIONS BY THE FINITE ELEMENT METHOD

In many practical situations, adequate thermal design of pavement structures in seasonal frost areas can be done by utilizing a model based on heat conduction alone. In this paper we present a system of computer programs which allow the solution of practically any nonlinear heat conduction problem in soils, provided that a two-dimensional description, plane or axisymmetric, is possible. The finite element method, together with the empirical correlations for thermal properties and boundary conditions, is used in the simulations. Predictions of the thermal regime in different structures are favorably compared with the results of experimental measurements, both for long-term and short-term temperature variations.

LAMINAR HEAT TRANSFER IN THE ENTRANCE REGION OF DUCTS

A finite-element marching procedure is presented for the calculation of transport processes in three-dimensional parabolic flows As in corresponding finite-difference procedures, equations are solved one after the other. Similarly, longitudinal and cross-stream pressure gradients are uncoupled. Velocity fields are determined by first calculating intermediate velocity values based on estimated pressure gradient distributions and then obtaining appropriate corrections so as to satisfy the continuity equation Illustrative examples concerning flow in the entrance region of straight ducts demonstrate the accuracy and reliability of the proposed technique.