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To introduce a novel numerical calculation procedure for periodically fully developed heat and fluid flow, which can treat three‐dimensional velocity and temperature fields, using a two‐dimensional storage.

The three‐dimensional Navier‐Stokes equation and energy equation have been transformed into quasi‐three‐dimensional forms. An appropriate set of explicit periodic boundary conditions have been obtained for thermally fully developed flow through a general three‐dimensional periodic structure, exploiting the volume averaging theory.

The proposed numerical procedure has been found inexpensive and efficient. Its validity has been proved by comparing the results obtained for a bank of long cylinders in yaw against available experimental data.

Since no explicit sets of periodic boundary conditions of this kind have been reported before, they will be exploited by researchers and practitioners interested in efficient numerical computations of three‐dimensional periodic heat and fluid flows.

A three‐dimensional, two‐phase computational model for simulating boiling‐enhanced mixed convection in free‐surface flows is presented. The associated constitutive models for the thermophysical and transport properties are described. A computational model incorporating the discrete‐element analysis was used to simulate the multi‐dimensional, two‐phase flow around a heated chip in a test tank filled with Freon‐(R113). Two and three‐dimensional simulations of both natural convection and nucleate boiling heat transfer regimes are presented. The velocity field, the temperature distribution, and the vapour concentration profiles are evaluated and discussed. The simulated heat fluxes are compared with the available experimental data. While the heat fluxes from the two‐dimensional simulation agree with the fluxes calculated for the three‐dimensional case, the flow in the tank is essentially three‐dimensional. The results show that there are secondary flows which cannot be captured by a two‐dimensional model. The heat flux in the boiling heat transfer regime is only about ten times larger than that in the natural convection regime due to the small vapour concentration in tank.

In part I of this study, a three‐dimensional finite difference iterative solver capable of handling the coupled Navier‐Stokes and energy equations for incompressible viscous flows was described and validated with two‐ and three‐dimensional benchmarks. Part II describes the results of the computational study of two distinct complex geometries: 1) two‐dimensional and three‐dimensional natural convection in cavity whose surface is cooled while two internal blocks are heated; 2) two‐dimensional and three‐dimensional natural convection in the region defined by two interconnected cavities of different sizes which are differentially heated. All computations have been performed for a Prandtl number of 1.0, and different values of the Rayleigh number ranging between 10³ and 10⁶ depending on the problem. In the first problem, three‐dimensional effects in the top region of the cavity trap fluid in vortices near the top of the heated blocks adversely affecting heat transfer in the region while enhancing it in the region between the two heated blocks. In the second problem, the sudden expansion of fluid as it leaves the top cavity and enters the bottom one generates three‐dimensional wakes in the bottom cavity that enhance the convective heat transfer across the system walls near them. These studies tend to suggest that three‐dimensional effects play a very important role in the enhancement of convective heat transfer in complex geometries, especially at higher Rayleigh numbers.

This bibliography is offered as a practical guide to published papers, conference proceedings papers and theses/dissertations on the finite element (FE) and boundary element (BE) applications in different fields of biomechanics between 1976 and 1991. The aim of this paper is to help the users of FE and BE techniques to get better value from a large collection of papers on the subjects. Categories in biomechanics included in this survey are: orthopaedic mechanics, dental mechanics, cardiovascular mechanics, soft tissue mechanics, biological flow, impact injury, and other fields of applications. More than 900 references are listed.

In part I uses an iterative point successive over‐relaxation (PSOR) finite difference scheme to solve the coupled unsteady Navier‐Stokes and energy equations for incompressible, viscous and laminar flows in their primitive variable form. Presents the details concerning the derivation of the solution scheme, as well as details on its computer implementation. For validation purposes, includes the results of the two‐dimensional and three‐dimensional benchmark problem of natural convection in a cavity with differentially heated vertical walls. Benchmark computations have been performed for a Prandtl number of 0.71, and different values of the Rayleigh number ranging between 10³ and 10⁶ depending on the problem. By comparison with other approaches in the literature, the scheme has been found to be accurate even for large Rayleigh numbers.

Large‐eddy simulation (LES) of a turbulent channel flow is performed using different subfilter‐scale (SFS) models and test filter functions. The SFS models used are the dynamic Smagorinsky model (DSM) and the dynamic mixed model (DMM). The DMM is a linear combination between the scale‐similarity model and the DSM. The test filter functions investigated are the sharp cut‐off (in spectral space) and smooth filter that is commutative up to fourth‐order. The filters are applied either in the homogeneous directions or in all three spatial directions. The governing equations are discretized using a fourth‐order energy‐conserving finite‐difference scheme. The influence from the test filter function and the SFS model on the LES results are investigated and the effect of two‐dimensional versus three‐dimensional test filtering are investigated. The study shows that the combination of SFS model and filter function highly influences the computational results; even the effect on the zeroth‐order moment is large.

This paper gives a review of the finite element techniques (FE) applied in the area of material processing. The latest trends in metal forming, non‐metal forming, powder metallurgy and composite material processing are briefly discussed. The range of applications of finite elements on these subjects is extremely wide and cannot be presented in a single paper; therefore the aim of the paper is to give FE researchers/users only an encyclopaedic view of the different possibilities that exist today in the various fields mentioned above. An appendix included at the end of the paper presents a bibliography on finite element applications in material processing for 1994‐1996, where 1,370 references are listed. This bibliography is an updating of the paper written by Brannberg and Mackerle which has been published in Engineering Computations, Vol. 11 No. 5, 1994, pp. 413‐55.

This paper describes a study concerning the numerical simulation of a sonic helium jet through a transverse nozzle in a flat plate exhausting normally into a supersonic air flow. Three‐dimensional Reynolds‐averaged Navier—Stokes equations coupled with the modified Baldwin‐Lomax algebraic turbulence model and relevant species equations are solved by using a finite‐volume upwind scheme. In this approach, Roe’s flux function, explicit multi‐stage integration and multi‐block procedure are applied to achieve the steady state solution efficiently. The Roe’s flux function is modified to suit the simulation of helium‐air mixing. The comparison between two‐dimensional calculated results with experimental data of surface pressure shows good agreement. The results of three‐dimensional computations for square, circular and rectangular jets are presented, and the essential flow features including induced shocks, upstream separations, and downstream primary and secondary vortices are adequately simulated.

This paper gives a review of the finite element techniques (FE) applied in the area of material processing. The latest trends in metal forming, non‐metal forming and powder metallurgy are briefly discussed. The range of applications of finite elements on the subjects is extremely wide and cannot be presented in a single paper; therefore the aim of the paper is to give FE users only an encyclopaedic view of the different possibilities that exist today in the various fields mentioned above. An appendix included at the end of the paper presents a bibliography on finite element applications in material processing for the last five years, and more than 1100 references are listed.

The purpose of this paper is to develop a combined method for three-dimensional incompressible flow and heat transfer by the spectral collocation method (SCM) and the artificial compressibility method (ACM), and further to study the performance of the combined method SCM-ACM for three-dimensional incompressible flow and heat transfer.

The partial differentials in space are discretized by the SCM with Chebyshev polynomial and Chebyshev–Gauss–Lobbatto collocation points. The unsteady artificial compressibility equations are solved to obtain the steady results by the ACM. Three-dimensional exact solutions with trigonometric function form and exponential function form are constructed to test the accuracy of the combined method.

The SCM-ACM is developed successfully for three-dimensional incompressible flow and heat transfer with high accuracy that the minimum value of variance can reach. The accuracy increases exponentially along with time marching steps. The accuracy is also improved exponentially with the increasing of nodes before stable accuracy is achieved, while it keeps stably with the increasing of the time step. The central processing unit time increases exponentially with the increasing of nodes and decreasing of the time step.

It is difficult for the implementation of the implicit scheme by the developed SCM-ACM. The SCM-ACM can be used for solving unsteady impressible fluid flow and heat transfer.

The SCM-ACM is applied for two classic cases of lid-driven cavity flow and natural convection in cubic cavities. The present results show good agreement with the published results with much fewer nodes.

The combined method SCM-ACM is developed, firstly, for solving three-dimensional incompressible fluid flow and heat transfer by the SCM and ACM. The performance of SCM-ACM is investigated. This combined method provides a new choice for solving three-dimensional fluid flow and heat transfer with high accuracy.