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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.

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.

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.

The purpose of this study is to investigate the effects of heat generation or absorption on heat transfer and fluid flow within two- and three-dimensional enclosure for homogeneous medium filled with different metal liquid. Numerical results are presented and analyzed in terms of fluid flow, thermal field structures, as well as average Nusselt number profiles over a wide range of dimensionless quantities, Grashof number (Gr) (104 and 105), SQ (varied between −500 to 500) and Prandtl number (Pr = 0.015, 0.024 and 0.0321). The results indicate that when the conductive regime is established for a Grashof number Gr = 104, the 2D model is valid and predicts all three-dimensional results with negligible difference. This was not the case in the convective regime (Gr = 105) where the effect of the third direction becomes important, where a 2D-3D difference was seen with about 37 per cent. Also, in most cases, the authors find that the heat absorption phenomena have the opposite effect with respect to the heat generation.

Numerical results are presented and analyzed in terms of fluid flow, thermal field structures, as well as average Nusselt number profiles over a wide range of dimensionless quantities.

Grashof number (Gr) (104 and 105), SQ (varied between −500 to 500) and Prandtl number (Pr = 0.015, 0.024 and 0.0321).

The results indicate that when the conductive regime is established for a Grashof number Gr = 104, the 2D model is valid and predicts all three-dimensional results with negligible difference.

Three‐dimensional flows over backward facing s.tif are analysed by means of a finite element procedure, which shares many features with the SIMPLER method. In fact, given an initial or guessed velocity field, the pseudovelocities, i.e. the velocities that would prevail in the absence of the pressure field, are found first. Then, by enforcing continuity on the pseudovelocity field, the tentative pressure is estimated, and the momentum equations are solved in sequence for velocity components. Afterwards, continuity is enforced again to find corrections that are used to modify the velocity field and the estimated pressure field. Finally, whenever necessary, the energy equation is solved before moving to the next step.

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.

The purpose of this paper is to study numerically and experimentally incompressible Newtonian flow in a three‐dimensional cylindrical branching channel.

The flow configuration studied in the present investigation is such that a fully developed laminar flow enters an abruptly expanded cylinder and the flow leaves this cylinder by two identical cylindrical outlet branch pipes. A numerical analysis was performed by developing a three‐dimensional numerical code using the highly simplified marker and cell method. Representative velocities in the flow field are recorded by Laser Doppler Velocimeter measurements and volume flow rate from each outlet branch pipe is measured. Flow visualization in representative symmetrical planes is also carried out. Comparisons of numerical predictions and experimental data are presented and the reasonable agreement between the numerical and experimental results is encouraging.

The flow field in the three‐dimensional cylindrical branching channel is clarified within the range of laminar flow. The characteristics of the branch flow rate are obtained and show that there exist two distinct domains of strong asymmetric flow distribution from the outlet branch pipes, depending on the Reynolds numbers. It is further observed that the flow became time periodic as the Reynolds number is increased. It becomes apparent that the swirl flow component plays a key role in the flow phenomena.

The present investigation sheds light on the three‐dimensionality in the prevailing flow field for various inlet Reynolds numbers in the laminar flow range. Flow rate deflection characteristics in a three‐dimensional cylindrical branching channel are also obtained.

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.

Our recent results on stability and multiplicity of flow states for confined flows of an incompressible Newtonian fluid are surveyed. The considered laminar flows are caused by either thermal, mechanical, or electromagnetic effects and beyond the stability limit exhibit multiplicity of stable, steady or oscillatory, asymptotic states. Stability diagrams as well as examples of multiple flow states are given. It is concluded that beyond the critical value of the characteristic non‐dimensional parameter, and below the threshold to stochastic or turbulent state, multiple stable asymptotic flow states can be expected. This means that at such flow regimes, any computational (experimental) result may be strongly dependent on its initial condition and/or computational (experimental) path. Uncertainties of experimental and numerical modeling, which follow from this conclusion, are discussed. The global spectral Galerkin method using divergence free basis functions has been employed for the spatial approximation of the velocity and temperature fields. Several numerical experiments were performed comparing the present and other formulations, each of which confirmed the computational efficiency of the present approach over other classical numerical methods.

The cross‐correlation flow measurement technique, applied for measuring the coolant flow rate in a nuclear reactor, was calibrated with the use of numerical simulations of turbulent flow. The three‐dimensional domain was collapsed into two dimensions. With a two‐dimensional calculation of steady‐state flow with transient thermal characteristics the response of thermocouples to a temperature variation was calculated. By cross‐correlating the calculated thermocouple responses, the link between total flow rate and measured transit times was made. The reliability of the calibration was estimated at ±4.6%. In addition, a measured velocity profile effect was successfully predicted.