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The purpose of this paper is to develop new semi-empirical heat transfer correlations for turbulent flow of liquid metals in the tubes, and then to compare these correlations with the experimental data. The Prandtl and Reynolds numbers can vary in the ranges: 0.0001 ≤ Pr ≤ 0.1 and 3000 ≤ Re ≤ 10⁶.

The energy conservation equation averaged by Reynolds was integrated using the universal velocity profile determined experimentally by Reichardt for the turbulent tube flow and four different models for the turbulent Prandtl number. Turbulent heat transfer in the circular tube was analyzed for a constant heat flux at the inner surface. Some constants in different models for the turbulent Prandtl number were adjusted to obtain good agreement between calculated and experimentally obtained Nusselt numbers. Subsequently, new correlations for the Nusselt number as a function of a Peclet number was proposed for different models of the turbulent Prandtl number.

The inclusion of turbulent Prandtl number greater than one and the experimentally determined velocity profile of the fluid in the tube while solving the energy conservation equation improved the compatibility of calculated Nusselt numbers, with Nusselt numbers determined experimentally. The correlations proposed in the paper have a sound theoretical basis and give Nusselt number values that are in good agreement with the experimental data.

Heat transfer correlations proposed in this paper were derived assuming a constant heat flux at the inner surface of the tube. However, they can also be used for a constant wall temperature, as for the turbulent flow (Re > 3,000), the relative difference between the Nusselt number for uniform wall heat flux and uniform wall temperature is very low.

Unified, systematic approach to derive correlations for the Nusselt number for liquid metals was proposed in the paper. The Nusselt number was obtained from the solution of the energy conservation equation using the universal velocity profile and eddy diffusivity determined experimentally, and various models for the turbulent Prandtl number. Four different relationships for the Nusselt number proposed in the paper were compared with the experimental data.

The aim of this work is to quantify the relative importance of the turbulence modelling for cavitating flows in thermal regime. A comparison of various transport-equation turbulence models and a study of the influence of the turbulent Prandtl number appearing in the formulation of the turbulent heat flux are proposed. Numerical simulations are performed on a cavitating Venturi flow for which the running fluid is freon R-114 and results are compared with experimental data.

A compressible, two-phase, one-fluid Navier–Stokes solver has been developed to investigate the behaviour of cavitation models including thermodynamic effects. The code is composed by three conservation laws for mixture variables (mass, momentum and total energy) and a supplementary transport equation for the volume fraction of gas. The mass transfer between phases is closed assuming its proportionality to the mixture velocity divergence.

The influence of turbulence model as regard to the cooling effect due to the vaporization is weak. Only the k – ε Jones–Launder model under-estimates the temperature drop. The amplitude of the wall temperature drop near the Venturi throat increases with the augmentation of the turbulent Prandtl number.

The interaction between Reynolds-averaged Navier–Stokes turbulence closure and non-isothermal phase transition is rarely studied. It is the first time such a study on the turbulent Prandtl number effect is reported in cavitating flows.

This study is concerned with the computation of turbulent flow and heat transfer in U‐bends of strong curvature. Following the earlier studies within the authors' group on flows through round‐ended U‐bends, here attention is turned to flows through square‐ended U‐bends. Flows at two Reynolds numbers have been computed, one at 100,000 and the other at 36,000. In the heat transfer analysis, the Prandtl number was either 0.72 (air) or, in a further departure from our earlier studies, 5.9 (water). The turbulence modelling approaches examined, include a two‐layer and a low‐Re k‐ε model, a two‐layer and a low‐Re version of the basic differential stress model (DSM) and a more recently developed, realisable version of the differential stress model that is free of wall‐parameters. For the low‐Re effective viscosity model (EVM) and DSMs, an alternative, recently proposed length‐scale correction term, independent of wall distance has also been tested. Even the simplest model employed – two‐layer EVM – reproduces the mean flow development with reasonable accuracy, suggesting that the mean flow development is mainly influenced by mean pressure rather than the turbulence field. The heat transfer parameters, on the other hand, show that only the low‐Re DSMs produce reliable Nusselt number predictions for both Prandtl numbers examined.

The purpose of this paper is to numerically study heated channel flow using direct numerical simulation (DNS) and large eddy simulation (LES) method. Using different domain size and different grid resolution it is show that filtering procedure is influenced and may results in very different solutions.

Turbulent non-isothermal fully developed channel flow has been investigated using LES. The filtered Navier-stokes and energy equations were numerically solved with dynamic subgrid scale (SGS) model, standard Smagorinsky model or without additional model for the turbulent SGS stress and heat flux required to close the governing equations.

The numerical LES results in comparison with the DNS data demonstrate that the LES computations may not always offers a reliable prediction of non-isothermal turbulent flow in open channel. It has been found that, even though the models reproduces accurately results for the flow field the thermal field computed using LES do not necessary match the DNS results. Introducing SGS model for scalar do not always show large improvement. One of the reason is thickness of hydrodynamic and thermal boundary layer. In the cases when boundary layers are very different it is not easy optimally set up control volumes in the domain.

This is one of the first instance in which a results of numerical computations for different grid resolution, different stretching, SGS model is employed for non-isothermal turbulent channel flow. It shows that in the cases when boundary layers hydrodynamic and thermal are very different it is hardly find optimal grid resolution or stretching

A numerical study is performed to investigate turbulent Couette flow and heat transfer characteristics in concentric annuli with a slightly heated inner cylinder moving in the flow direction. A two‐equation k‐ε turbulence model is employed to determine the turbulent viscosity and the turbulent kinetic energy. The turbulent heat flux is expressed by Boussinesq approximation in which the eddy diffusivity for heat is given as functions of the temperature variance t^2‐ and the dissipation rate of temperature fluctuations ε_t, together with k and ε. The governing boundary‐layer equations are discretized by means of control volume finite‐difference technique and numerically solved using a marching procedure. It is disclosed from the study that the streamwise movement of the inner core causes substantial reductions in the turbulent kinetic energy and the temperature variance, particularly near the inner wall region, resulting in the deterioration of the Nusselt number, and that an attenuation in heat transfer performance is induced by the velocity ratio of the moving inner cylinder to the fluid flow.

This study aims to investigate numerically a two-dimensional fully developed mean turbulent fluid flow, and heat transfer in a circular duct is numerically investigated using FORTRAN 95 code that applies the finite difference method to solve the thermal problem for the two thermal boundary conditions, constant surface temperature, constant heat and steady, axisymmetric flow. Several important results have been drawn and discussed from thermal analysis. Finally, the numerical results of the model developed in the document have been validated in good accuracy by comparing them with some correlation results available in the specialized literature.

The methodology of solving the thermal problem is based on the equation of energy for a fluid of constant properties while taking into consideration the hypothesis of the axisymmetric and fully developed pipe flow in steady state. The global equation and the initial and boundary conditions acting on the problem have been configured here in dimensionless form to predict the turbulent behavior of the fluid inside the tube. Thus, using Thomas' algorithm, a program in FORTRAN version 95 was developed to numerically solve the discretized form of the system of equations describing the problem.

The profiles of the solutions are provided from which the authors infer that the numerical and literature correlation agreed very well. Another result that they obtained from this study is the number of Nusselt in the thermal entrance region to which a parametric study based on Reynolds and Peclet numbers, and the longitudinal coordinate, was carried out and discussed well for the impact of the scientific contribution.

The novelty of the work is the application of the finite difference method programed on the FORTRAN code, as a sequential numerical method of an ODEs system, to determine the number of Nusselt in both uniform wall temperature and wall heat flux uniform.

Because the local Re numbers, ratio of inertia to viscous forces, are not same at different regions of the enclosures, the present study aims to deal with the influences of using the turbulent/transition models on numerical results of the natural convection and flow field within a trapezoidal enclosure.

The three-dimensional (3D) trapezoidal enclosure with different inclined side walls of 75, 90 and 105 degrees are considered, where the side walls are heated and cooled at Ra = 1.5 × 10⁹ for all cases. The turbulent models of the k-ε-RNG, k- ω-shear-stress transport (SST) and the newly developed transition/turbulent model of Re_θ-γ-transition SST are utilized to analyze the fluid flow and heat transfer characteristics within the enclosure and compared their results with validated results.

Comprehensive comparisons have been carried out for all cases in terms of flow and temperature fields, as well as turbulent quantities, such as turbulent kinetic energy and turbulent viscosity ratio. Furthermore, the velocity and thermal boundary layers have been investigated, and the approximate transition regions for laminar, transitional and turbulent regimes have been determined. Finally, the heat transfer coefficient and skin friction coefficient values have been presented and compared in terms of different turbulent models and configurations. The results show that the transition/turbulence model has better prediction for the flow and heat fields than fully turbulent models, especially for local parameters for all abovementioned governing parameters.

The originality of this work is to analyze the 3D turbulent/transitional natural convection with different turbulence/transition models in a trapezoidal enclosure.

A numerical scheme that has already proved to be efficient and accurate for laminar heat transfer is extended for turbulent, axisymmetric heat transfer calculations. The extended scheme is applied to the steady‐state heat transfer of axisymmetric turbulent jets, impinging onto a flat plate. Firstly, the low‐Reynolds version of the standard k‐ε model is employed. As is well known, the classical k‐ε turbulence model fails to predict the heat transfer of impinging jets adequately. A non‐linear k‐ε model, with improved ε‐equation, yields much better results. The numerical treatment of the higher order terms in this model is described. The effect on the heat transfer predictions of a variable turbulent Prandtl number is shown to be small. It is also verified that the energy equation can be simplified, without affecting the results. Results are presented for the flow field and the local Nusselt number profiles on the plate for impinging jets with different distances between the pipe exit and the flat plate.

In this paper a numerical simulation, based on finite difference techniques, has been developed in order to analyse turbulent natural and mixed convection of air in internal flows. The study has been restricted to two‐dimensional cavities with the possibility of inlet and outlet ports, and with internal heat sources. Turbulence is modelled by means of two‐equation k‐ε turbulence models, both in the simplest form using wall functions and in the more general form of low‐Reynolds‐number k‐ε models. The couple time average governing equations (continuity, momentum, energy, and turbulence quantities) are solved in a segregated manner using the SIMPLEX method. An implicit control volume formulation of the differential equations has been employed. Some illustrative numerical results are presented to study the influence of geometry and boundary conditions in cavities. A comparison of different k‐ε turbulence models has also been presented.

Presents a novel theoretical approach, based on extension of ideas associated with the generalized integral transform technique, for obtaining accurate analytic solutions for fully developed steady forced convection inside circular ducts with turbulent flow and constant wall surface temperature conditions. Within the temperature field, reports the thermal response of the fluid in terms of hybrid solutions for bulk fluid temperature and Nusselt number distributions along the thermal entrance region of the duct. Further, in assessing the accuracy and validity of the theoretical work, critically examines predicated analytical solutions of thermally developed Nusselt numbers and compares them with results from reliable empirical correlations of the open literature. For the investigated cases, satisfactory agreement prevailed between the theoretically and empirically derived heat transfer parameters, exhibiting a maximum difference of 9.58 per cent for the range of system variables analysed.