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The purpose of this paper is to present two efficient immersed boundary methods (IBM) for simulation of thermal flow problems. One method is for given temperature condition (Dirichlet type), while the other is for given heat flux condition (Neumann type). The methods are applied to simulate natural and mixed convection problems to check their performance. The comparison of present results with available data in the literature shows that the present methods can obtain accurate numerical results efficiently.

The paper presents two efficient IBM solvers, in which the effect of thermal boundary to its surrounding fluid is considered through the introduction of a heat source/sink term into the energy equation. One is the temperature correction‐based IBM developed for problems with given temperature on the wall. The other is heat flux correction‐based IBM for problems with given heat flux on the wall. Note that in this solver, the offset of derivative condition is directly used to correct the temperature field.

As compared with existing solvers, the temperature correction‐based IBM determines the heat source/sink implicitly instead of pre‐calculated explicitly, so that the boundary condition for temperature is accurately satisfied. To the best of the authors' knowledge, the work of heat flux correction‐based IBM is the first endeavour for application of IBM to solve thermal flow problems with Neumann (heat flux) boundary condition. It was found that both methods presented in this work can efficiently obtain accurate numerical results for thermal flow problems.

The two methods presented in this paper are novel. They can effectively solve thermal flow problems with Dirichlet and Neumann boundary conditions.

The purpose of this study is to address a problem in cooling of an electronic package where the dissipating fins transfer the extra heat energy from the heat source (i.e. electronic devices) to the heat sink (i.e. environment). To this end, the convective heat transfer of nanofluid flow over dissipating fins is simulated using a numerical approach, whereas the properties of nanofluid are evaluated based on the experimental measurements and used in the numerical process.

To simulate the convective flow, the lattice Boltzmann method is used. Also, the curved boundary scheme is used to enhance the capability of lattice Boltzmann method (LBM) in the simulation of natural convection in curved boundaries. In addition, the second law analysis is used based on total and local approaches.

To improve the cooling performance of fins, a modern technique is used, which is using of nanofluid. For this purpose, samples of SiO₂-liquid paraffin with mass fractions of 0.01, 0.05, 0.1, 0.5 and 1 (Wt.%) in a temperature range of 25–60 °C are provided, and the required thermal and physical properties of samples including thermal conductivity and dynamic viscosity are measured during experimental work. The extracted results are used in the numerical simulations using derived correlations.

The originality of the present work is using a modern numerical method in the investigation of an engineering application and combining it with experimental data.

Performance of various k‐ε models on turbulent forced convection in a channel with periodic ribs is assessed.

The influence of the Yap correction and the non‐linear stress‐strain relation on the predictions of mean‐flow, turbulence quantities and local heat transfer rate is examined. The effect of thermal boundary conditions on the heat transfer predictions is investigated by employing both the prescribed heat flux approach and the conjugate heat transfer approach.

It was found that the inclusion of the Yap correction in the ε‐equation significantly improves the predictions of mean velocity and wall heat transfer for both high‐Reynolds number and low‐Reynolds number k‐ε models in the present ribbed channel flow with massive flow separation. The employment of the non‐linear stress‐strain relation only marginally improves the predictions of turbulence quantities: the turbulence anisotropy is reproduced although the level of turbulence intensity is still too low. In general, the conjugate heat transfer approach predicts better average Nusselt number than the prescribed heat flux approach. However, both approaches under‐predict the experimental value by about 28‐33 percent when the low‐Reynolds number k‐ε model of Lien and Leschziner (1999) with the Yap term is adopted.

Thorough numerical treatments of the thermal boundary conditions at the solid‐liquid interface, and detailed periodic condition in the periodic regime, were given in the paper to benefit researchers interested in solving similar problems.

To present conversion of the advection upwind splitting method (AUSM+) from the conventional density‐based and coupled formulation to the pressure‐based and segregated formulation.

The spatial discretization is done by a finite volume method. A collocated grid cell‐center formulation is used. The pressure‐correction procedure is set up in the usual way for a compressible flow problem. The conventional Rhie‐Chow interpolation methodology for the determination of the transporting velocity, and the conventional central interpolation for the pressure at the control volume faces, are replaced by AUSM+ definitions.

The AUSM+ flux definitions are spontaneously well suited for use in a collocated pressure‐correction formulation. The formulation does not require extensions to these flux definitions. As a consequence, the results of a density‐based fully coupled method, are identical to the results of a pressure‐based segregated formulation. The advantage of the pressure‐correction method with respect to the density‐based method, is the higher efficiency for low Mach number applications. The advantage of the AUSM+ flux definition for the transporting velocity with respect to the conventional Rhie‐Chow interpolation, is the improved accuracy in high Mach number flows. As a consequence, the combination of AUSM+ with a pressure‐correction method leads to an algorithm with improved performance for flows at all Mach numbers.

A new methodology, with obvious advantages, is composed by the combination of ingredients from an existing spatial discretization method (AUSM+) and an existing time stepping method (pressure‐correction).

Introduces the fourth and final chapter of the ISEF 1999 Proceedings by stating electric and magnetic fields are influenced, in a reciprocal way, by thermal and mechanical fields. Looks at the coupling of fields in a device or a system as a prescribed effect. Points out that there are 12 contributions included ‐ covering magnetic levitation or induction heating, superconducting devices and possible effects to the human body due to electric impressed fields.

The paper presents a numerical technique for the simulation of the effects of grey‐diffusive surface radiation on fluid flow using a finite volume procedure for two‐dimensional (plane and axi‐symmetric) geometries. The governing equations are solved sequentially, and the non‐linearities and coupling of variables are accounted for through outer iterations (coefficients updates). In order to reduce the number of outer iterations, a multigrid algorithm was implemented. The radiating surface model assumes a non‐participating medium, semi‐transparent walls and constant elementary surface temperature and radiation fluxes. The calculation of view factors is based on the analytical evaluation for the plane geometry and numerical integration for axi‐symmetric geometry. Ashadowing algorithm was implemented for the calculation of view factors in general geometries. The method for the calculation of view factors was first tested by comparison with available analytical solutions for a complex geometric configuration. The flow prediction code combined with radiation heat transfer was verified by comparisons with analytical one‐dimensional solutions. Further test calculations were done for the flow and heat transfer in a cavity with a radiating submerged body. As an example of the capabilities of the method, transport processes in metalorganic chemical vapour deposition (MOCVD) reactors were simulated.

The purpose of the paper is to analyse the performances of closures and compressibility corrections classically used in turbulence models when applied to highly-compressible turbulent boundary layers (TBLs) over flat plates.

A direct numerical simulation (DNS) database of TBLs, covering a wide range of thermodynamic conditions, is presented and exploited to perform a priori analyses of classical and recent closures for turbulent models. The results are systematically compared to the “exact” terms computed from DNS.

The few compressibility corrections available in the literature are not found to capture DNS data much better than the uncorrected original models, especially at the highest Mach numbers. Turbulent mass and heat fluxes are shown not to follow the classical gradient diffusion model, which was shown instead to provide acceptable results for modelling the vibrational turbulent heat flux.

The main originality of the present paper resides in the DNS database on which the a priori tests are conducted. The database contains some high-enthalpy simulations at large Mach numbers, allowing to test the performances of the turbulence models in the presence of both chemical dissociation and vibrational relaxation processes.

The present work is to investigate nucleate boiling heat transfer at high heat fluxes, which is characterized by the existence of macrolayer. Two‐region equations are proposed to simulate both thermo‐capillary driven flow in the liquid layer and heat conduction in the solid wall. The numerical simulation results can clearly describe the activities of several multi vorticies in the macrolayer. These vorticies and evaporation at the vapor‐liquid interface constitute a very efficient heat transfer mechanism to explain the high heat transfer coefficient of nucleate boiling heat transfer near CHF. This study also explores the flow pattern of macrolayer with a high conducting solid wall, e.g. copper, and hence the temperature is uniform at the liquid‐solid interface, and the heat fluxes and the evaporation coefficient are found to have significant effect on flow pattern in the liquid layer. Furthermore, a parameter “evaporation fraction” as well as “aspect ratio” is proposed as an index to investigate the thermo‐capillary driven flow system. The model prediction agrees reasonably well with the experimental data in the literature.

The purpose of this paper is to focus on the application of the Trefftz method to the calculation of the two-dimensional (2D) temperature field in the boiling refrigerant flow through an asymmetrically heated vertical minichannel with a rectangular cross-section. The considerations were limited to determining the temperature of the continuous phase – liquid for bubbly and bubbly-slug flow. The numerical solution found with the Trefftz methods was compared with the simplified solution. For nucleate boiling, heat transfer coefficient at the heating foil – liquid contact was determined.

The Trefftz method was used to determine 2D temperature distributions for the glass pane, the heating foil and the boiling liquid. The temperature fields were approximated by the sum of the particular solution and the linear combination of suitable Trefftz functions. Coefficients of linear combination were computed using experimental data, including heating foil temperature measurements obtained with the liquid-crystal method and experimentally determined void fraction. The computations were based on the Trefftz method supplemented with the adjustment calculus.

The way of solving direct and inverse problems of heat conduction in solid bodies (isolating glass, heating foil) and in liquids (boiling refrigerant flowing through the minichannel) was presented. For the first time, both 2D temperature fields for the heating foil and the boiling liquid were calculated while simultaneously using the Trefftz method. The known temperature values of the foil and liquid allowed the calculation of the heat transfer coefficient and the heat flux at the heating foil-liquid contact. Adjustment calculus implemented into the Trefftz method was used to smooth the measurement data and to reduce their errors.

The approach proposed in the paper can be applied to determining 2D temperature field, heat flux and heat transfer coefficient in direct and inverse problems concerning two-phase flowing miniature compact heat exchangers.

The paper presents a novel implementation of the Trefftz method to simultaneous solving an inverse problem in the heating foil and the contacting flowing liquid.

A numerical investigation has been undertaken to study fluid flow and heat transfer through artificially rib‐roughened channels. Such flows are of particular interest in internal cooling of advanced gas turbine blades. The main objective is to test the suitability of recently developed variants of the cubic non‐linear k‐ε model for the prediction of cooling flows through ribbed passages. The numerical approach used in this study is the finite‐volume method together with the SIMPLE algorithm. For the modelling of turbulence, the Launder and Sharma low‐Re k‐ε model and a new version of the non‐linear low‐Re two equation model that have been recently shown to produce reliable thermal predictions in impinging jet flows and also flows through pipe expansions, have been employed. Both models have been used with the form of the length‐scale correction term to the dissipation rate originally proposed by Yap and also more recently developed differential version, NYap. The numerical results over a range of flow parameters have been compared with the reported experimental data. The mean flow predictions show that both linear and non‐linear k‐ε models with NYap can successfully reproduce the distribution of the measured streamwise velocity component, including the length and width of the separation bubble, formed downstream of each rib. As far as heat transfer predictions are concerned, the recent variant of the non‐linear k‐ε leads to marked improvements in comparison to the original version of Craft et al. Further improvements in the thermal prediction result through the introduction of a differential form of the turbulent length scale correction term to the dissipation rate equation. The version of the non‐linear k‐ε that has been shown in earlier studies to improve thermal predictions in pipe expansions and impinging jets; it is thus found to also produce reasonable heat transfer predictions in ribbed passages.