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This paper aims to present briefly a unified fractional step method for fluid dynamics, incompressible solid mechanics and heat transfer calculations. The proposed method is demonstrated by solving compressible and incompressible flows, solid mechanics and conjugate heat transfer problems.

The finite element method is used for the spatial discretization of the equations. The fluid dynamics algorithm used is often referred to as the characteristic‐based split scheme.

The proposed method can be employed as a unified approach to fluid dynamics, heat transfer and solid mechanics problems.

The idea of using a unified approach to fluid dynamics and incompressible solid mechanics problems is proposed. The proposed approach will be valuable in complicated engineering problems such as fluid‐structure interaction and problems involving conjugate heat transfer and thermal stresses.

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.

The purpose of the current paper is to develop a numerical methodology, based on the immersed boundary-lattice Boltzmann computational framework, for the Neumann and Dirichlet boundary conditions in problems involving natural and forced convection heat transfer.

The direct forcing immersed boundary method is extended to study the heat transfer by incompressible flow within the thermal lattice Boltzmann method (LBM) computational framework. The direct forcing and heating immersed boundary-LBM introduces a heat source term to the thermal LBM to account for the heat transfer occurring at the immersed boundary. New numerical treatments for the Neumann type of boundary condition and for the calculation of the local Nusselt number are developed. The developed methodologies have been applied to flows around immersed bodies with natural and forced convection, including steady as well as unsteady flows.

Numerical experiments involving immersed bodies in natural and forced convection have been performed in order to assess the validity of the direct heating IB-LBM. The flow cases studied also include steady and transient flow phenomena. Flow velocity field and isotherms have been used for qualitative comparisons with existing, published results. The surface averaged Nusselt number, Strouhal number, and lift coefficient (for the unsteady flow cases) have been used for quantitative comparison with published results. The results show that there are satisfactory agreements, qualitatively and quantitatively, between the results obtained by using the present method and those previously published.

Limited application of immersed boundary to thermal flows within the LBM has been studied by researchers; the few past studies were limited to Dirichlet boundary conditions and/or using of feedback forcing and heating approaches. In the current paper, the direct forcing and heating approach was used which helps to eliminate the arbitrary constants used in the feedback approaches. The developed new numerical treatments for the Neumann type of boundary condition and for the calculation of the local Nusselt number eliminate the need to determine surface normal and temperature gradient in the normal direction for heat transfer calculation, which is particularly beneficial in cases with deforming or changing boundaries.

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 investigate the effect of transient mixed convective flow interaction between circular cylinders and channel walls on heat transfer with three circular cylinders arranged in an isosceles right‐angled triangle within a horizontal channel.

This paper uses a semi‐implicit finite element method to solve the incompressible Navier‐Stokes equation, energy equation and continuity equation in primitive‐variable form by assuming the flow to be two‐dimensional and laminar.

Provides information indicating that the transient streamlines, isotherms, drag coefficient and time‐mean Nusselt number around the surfaces of three cylinders are affected by various gap‐to‐diameter ratio, Reynolds numbers and Grashof numbers. The results show that the maximum value of surface‐ and time‐mean Nusselt number along cylinders exists at S=0.75.

It is limited to two‐dimensional laminar flow for the transient mixed convective flow interaction between circular cylinders and channel walls in a horizontal channel.

A very useful source of information and favorable advice for people is applied to heat exchangers, space heating, power generators and other thermal apparatus.

The results of this study may be of interest to engineers attempting to develop thermal control of thermal apparatus and to researchers interested in the flow‐modification aspects of mixed convection between circular cylinders and channel walls in a horizontal channel.

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 modelling of steady‐state natural and mixed convection in obstructed channels is presented. The two‐dimensional numerical analysis is carried out with a finite element thermally coupled incompressible flow formulation written in terms of the primitive variables of the problem and solved via a generalized streamline operator technique. Natural convection is studied in several vertical channel configurations for a wide range of Rayleigh numbers while mixed convection is analysed in a horizontal channel with a built‐in rectangular cylinder for different Reynolds and Grashof numbers. The results obtained in this work are validated with available experiments and other existing numerical solutions.

This paper aims to provide an experimental/numerical analysis of free convection within a hollow/finned cavity.

The hollow square cavity is equipped with eight active fins which have a similar configuration and different temperatures. Furthermore, four different thermal arrangements are considered to determine the order of temperature for each fin. The coupled lattice Boltzmann method is used, which not only maintains the considerable advantages of standard lattice Boltzmann method such as accuracy but also enhances the stability of this method.

The cavity is filled with TiO₂-SiO₂/Water-Ethylene Glycol nanofluid. The thermal conductivity and dynamic viscosity of nanofluid are experimentally measured using high-precision devices in six concentrations of the nanoparticle. In this study, some main parameters, including a range of Rayleigh number (10³ < Ra < 10⁶), the concentration of nanofluid (0.5 to 3 Vol.%) and thermal arrangements of fins, are considered. The effects of these main parameters on the flow, isotherms, heat transfer performance and entropy generation are studied.

The originality of this paper is combining the numerical simulation (lattice Boltzmann method) using a modern approach with experimental observations of nanofluid’s properties.

The main purpose of this paper is to develop a novel thermal lattice Boltzmann method (LBM) based on finite volume (FV) formulation. Validation of the suggested formulation is performed by simulating plane Poiseuille, backward-facing step and flow over circular cylinder.

For this purpose, a cell-centered scheme is used to discretize the convection operator and the double distribution function model is applied to describe the temperature field. To enhance stability, weighting factors are defined as flux correctors on a D2Q9 lattice.

The introduction of pressure-temperature-dependent flux-control coefficients in the streaming operator, in conjunction with suitable boundary conditions, is shown to result in enhanced numerical stability of the scheme. In all cases, excellent agreement with the existing literature is found and shows that the presented method is a promising scheme in simulating thermo-hydrodynamic phenomena.

A stable and accurate FV formulation of the thermal DDF-LBM is presented.

This paper aims to investigate the free convection, heat transfer and entropy generation numerically and experientially. A numerical/experimental investigation is carried out to investigate the free convection hydrodynamically/thermally and entropy generation.

The coupled lattice Boltzmann method is used as a numerical approach which keeps the significant advantages of standard lattice Boltzmann method with better numerical stability. On the other hand, the thermal conductivity and dynamic viscosity are measured using modern devices in the laboratory.

Some correlations based on the temperature at different nanofluid concentration are derived and used in the numerical simulations. In this regard, the results will be accurate with respect to using theoretical properties of nanofluid, and close agreements will be detected between present results and the previous numerical and experimental works. The numerical investigation is done under the effect of Rayleigh number (103 < Ra < 106), volume concentration of nanofluid (?? = 0.5, 1, 1.5, 2, 2.5 and 3%) and thermal configuration of the cavity (Cases A, B, C and D).

The originality of the present work lies in coupling of the lattice Boltzmann method with experimental observations to analyse the free convection in a cavity.