A three-dimensional enthalpic lattice Boltzmann formulation for convection–diffusion heat transfer problems in heterogeneous media

In this paper, an enthalpic lattice Boltzmann method formulation for 3D unsteady convection–diffusion heat transfer problems is used to overcome discontinuity issues in heterogeneous media. The new formulation is based on the appearance of a source term added to the collision step. The major achievement of the proposed enthalpic LB formulation is avoiding any interface treatments or geometry considerations even when dealing with complex geometries. The performance of the present method is tested for several three-dimensional convection–diffusion problems. Comparisons are made with the control volume method, and numerical results show excellent agreements.     

An alternative space–time meshless method for solving transient heat transfer problems with high discontinuous moving sources

ABSTRACT

The aim of this work is the development of a space–time diffuse approximation meshless method (DAM) to solve heat equations containing discontinuous sources. This work is devoted to transient heat transfer problems with static and moving heat sources applied on a metallic plate and whose power presents temporal discontinuities. The space–time DAM using classical weight function is convenient for continuous transient heat transfer. Nevertheless, for problems including discontinuities, some spurious oscillations for the temperature field occur. A new weight function, respecting the principle of causality, is used to eradicate the physically unexpected oscillations.     

On the numerical solution of generalized convection heat transfer problems via the method of proper closure equations – part II: Application to test problems

ABSTRACT

In part I of this paper, a new physical-based computational approach for the solution of convection heat transfer problems on co-located non-orthogonal grids in the context of an element-based finite volume method was discussed. The test problems are presented here, in part II of the paper. These problems include five steady two-dimensional convection heat transfer problems. In all test cases, the convergence history, the required under-relaxations for the iterative solution of the linearized equations, and the order of accuracy of the method are discussed and the streamlines as well as isotherms are presented. The computational results show that the proposed method is second order accurate and might occasionally need mild under-relaxation in relatively complex problems. Excellent match between the computational results and the corresponding reliable published results is observed.     

A lattice Boltzmann method for simulation of liquid–vapor phase-change heat transfer

A lattice Boltzmann model for the liquid–vapor phase change heat transfer is proposed in this paper. Two particle distribution functions, namely the density distribution function and the temperature distribution function, are used in this model. A new form of the source term in the energy equation is derived and the modified pseudo-potential model is used in the proposed model to improve its numerical stability. The commonly used Peng–Robinson equation of state is incorporated into the proposed model. The problem of bubble growth and departure from a horizontal surface is solved numerically based on the proposed model.     

On the numerical solution of generalized convection heat transfer problems via the method of proper closure equations – part I: Description of the method

ABSTRACT

The purpose of this paper is to introduce a new physical-based computational approach for the solution of convection heat transfer problems on co-located non-orthogonal grids in the context of an element-based finite volume method. The approach has already been presented in the context of two-dimensional incompressible flow problems without heat transfer. It has been shown that the pressure–velocity coupling on co-located grids can be correctly modeled via the so-called method of proper closure equations (MPCE). Here, MPCE is extended to the numerical simulation of natural, forced, and mixed convection heat transfer problems. It is shown that the couplings between pressure, velocity, and temperature can be conveniently handled on co-located grids by resorting again to the modified forms of the governing equations, i.e., the proper closure equations. The set of discrete equations is solved in a fully coupled manner in this study. Here, in part I of the paper, only the basic methodology is described; in part II, the results of application of the method to some test problems are presented.     

A high-order finite volume scheme for unsteady convection-dominated convection–diffusion equations

Abstract

A finite volume scheme with high-order accuracy is proposed for solving the unsteady convection-dominated transport problems. In this scheme, some weighting parameters are introduced in discretizing both the convection term and time integral. These parameters are determined analytically by making the truncation error of the proposed scheme as small as possible. Since the discretization equations of the proposed scheme share the same band structure as that of the traditional finite volume method based on the central differencing scheme, the proposed scheme does not increase computing cost. Numerical results show that the proposed scheme not only can achieve sixth-order accuracy but also avoids any unphysical oscillations in the steep gradient region of the solutions of the linear and nonlinear convection-dominated convection–diffusion problems.     

Marangoni convection flow and heat transfer characteristics of water–CNT nanofluid droplets

ABSTRACT

The heat transfer characteristics of liquid droplets are influenced by the hydrophobicity of the surfaces. Fluid properties and surface energy play important roles in heat transfer assessment. In the present study, the influence of the contact angle on the flow field developed inside a nanofluid droplet consisting of a mixture of water and carbon nanotubes (CNT) is investigated. Flow field and heat transfer characteristics are simulated numerically in line with the experimental conditions. It is found that the flow velocity predicted numerically is in good agreement with the experimental data. Nusselt and Bond numbers increase at large contact angles and Marangoni force dominates over buoyancy force.     

Hybrid formulation and solution for transient conjugated conduction–external convection

This work presents a hybrid numerical–analytical solution for transient laminar forced convection over flat plates of non-negligible thickness, subjected to arbitrary time variations of applied wall heat flux at the fluid–solid interface. This conjugated conduction–convection problem is first reformulated through the employment of the coupled integral equations approach (CIEA) to simplify the heat conduction problem on the plate by averaging the related energy equation in the transversal direction. As a result, an improved lumped partial differential formulation for the transversally averaged wall temperature is obtained, while a third kind boundary condition is achieved for the fluid from the heat balance at the solid–fluid interface. From the available steady velocity distributions, a hybrid numerical–analytical solution based on the generalized integral transform technique (GITT), under its partial transformation mode, is then proposed, combined with the method of lines implemented in the Mathematica 5.2 routine NDSolve. The interface heat flux partitions and heat transfer coefficients are readily determined from the wall temperature distributions, as well as the temperature values at any desired point within the fluid. A few test cases for different materials and wall thicknesses are defined to allow for a physical interpretation of the wall participation effect in contrast with the simplified model without conjugation.     

Heat transfer in a reaction–diffusion system with a moving heat source

A general formulation is presented for a moving boundary problem in which heat is generated at the boundary due to an exothermic reaction involving a species which diffuses into a dispersed phase from an external medium of finite volume. The speed of the moving boundary is prescribed based on the solution of the mass diffusion problem and an analysis is presented of the thermal dynamics of the system. The set of equations describing heat transport leads to a Green’s function type problem with time dependent boundary conditions and the Galerkin finite element method is employed to develop a numerical solution. Transformations are introduced to freeze the moving boundary and partition the domain for ease of computation, and an iterative scheme is defined to satisfy the heat flux jump boundary condition and match the temperature field across the moving boundary. The numerical results are used to set the limits of applicability of an analytical perturbation solution. Essential aspects of thermal dynamics in the system are described and parametric regions resulting in a local temperature hot spot are delineated. Computed contour plots describing thermal evolution are presented for different combinations of parameter values. These may be of utility in the prediction of thermal development, for control and avoidance of hot spot formation, and in physical parameter estimation.     

Prediction of convection heat transfer in converging–diverging tube for laminar air flowing using back-propagation neural network

The ability of an artificial neural network (ANN) model for heat transfer analysis in a converging–diverging tube is studied. Back propagation learning algorithm, the most common method for ANNs, was used in training and testing/validation the network. It is trained with selected values of the Reynolds numbers (Re), Prandtl numbers (Pr), half taper angle (θ), aspect ratio (L_cyc/D_max), and Nusselt number (Nu). The trained network is the used to make predictions of the Nusselt numbers. The accuracy between selected data and ANNs results was achieved with a mean absolute relative error less than 1.5%. This shows that well trained neural network model provided fast, accurate and consistent results.     

Improved social spider optimization algorithms for solving inverse radiation and coupled radiation–conduction heat transfer problems

A novel bio-inspired swarm algorithm, social spider optimization (SSO), is introduced to solve the inverse transient radiation and coupled radiation–conduction problems for the first time. Based on the original model, five improved SSO (ISSO) algorithms are developed to enhance search ability and convergence velocity. The sensitivity analysis of measured signals with respect to the physical parameters of the medium are described. After which, the SSO and ISSO algorithms are applied to solve the inverse estimation problems in a one-dimensional participating medium. Two cases concerns radiative transfer problems are investigated, in which the radiative source term, extinction coefficient, scattering albedo, and scattering symmetry factor are reconstructed. Furthermore, the coupled radiation–conduction heat transfer model is considered and the main parameters such as the conduction–radiation parameter, boundary emissivity, and scattering albedo are retrieved. All retrieval results show that SSO-based algorithms are robust and effective in solving inverse estimation problems even with measurement errors. Findings also show that the proposed ISSO algorithms are superior to the original SSO model in terms of computational accuracy and convergence velocity.     

Inverse analysis applied to retrieval of parameters and reconstruction of temperature field in a transient conduction–radiation heat transfer problem involving mixed boundary conditions

This article deals with the application of the inverse method for simultaneous retrieval of parameters and reconstruction of the temperature field in a transient conduction–radiation problem with mixed boundary conditions. The conducting–radiating medium is absorbing, emitting and isotropically scattering. The boundaries are diffuse gray. One boundary of the planar medium is at a prescribed temperature, while the other boundary is at a prescribed heat flux. A method involving lattice Boltzmann method (LBM), the finite volume method (FVM) is used to obtain the temperature field in the mixed boundary problem which in the present work is termed as the direct method. Next, random perturbations are imposed on this exact temperature field and then simultaneous reconstruction of the same and estimation of properties are accomplished by minimizing the square of the error between the exact and guessed temperature fields. This error, that in the present work is termed as the objective function, is minimized using the genetic algorithm (GA). The impact of different genetic parameters on the accuracy of the estimation is also investigated. It is observed that subject to the proper selection of the genetic parameters, simultaneous reconstruction of the temperature field along with a reasonably good estimation of the unknown parameters can be achieved using the LBM–FVM–GA.     

Prediction of transient heat and mass transfer in a closed metal–hydrogen reactor

The metal–hydrogen reactor is usually composed of a porous medium (hydride bed) and an expansion volume (gaseous phase). During the sorption process, the hydrogen flow and the heat transfer in the expansion part are badly known and can have some effects on the sorption phenomena in the hydride medium. At our knowledge, the hypothesis that neglects those effects is typically used. In this paper, a 2D study of heat and mass transfer has been carried out to investigate the transient transport processes of hydrogen in the two domains of a closed cylindrical reactor. A theoretical model is conducted and solved numerically by the control-volume-based finite element method (CVFEM). The result on temperature and hydride density distribution are presented and discussed. Moreover, this paper discusses in detail the effects of some governing operating conditions, such as dimensions of the expansion volume, height to the radius reactor ratio, and the initial hydrogen to metal atomic ratio, on the evolution of the pressure, fluid flow, temperature and the hydrogen mass desorbed.     

Two-level meshless local Petrov Galerkin method for multi-dimensional nonlinear convection–diffusion equation based on radial basis function

Abstract

In this article, a two-level meshless local Petrov Galerkin method (MLPG) is proposed to analyze nonlinear convection–diffusion equation based on the radial basis function (RBF) collocation method. Two-level method is employed to save the computation time, solving one small linearized convection–diffusion equation in a coarse nodal distribution by Newton iterative scheme and then processing one linear equation on a fine nodal distribution. The convergence analysis for the MLPG method and the two-level method is proven by applying the RBF interpolation method. Finally, the numerical examples provide a sufficient support and show that the proposed method is efficient for solving nonlinear convection–diffusion equation.     

Rayleigh–Benard convection in water-based alumina nanofluid: A numerical study

Rayleigh–Benard (R-B) convection in water-based alumina (Al₂O₃) nanofluid is analyzed based on a single-component non-homogeneous volume fraction model (SCNHM) using the lattice Boltzmann method (LBM). The present model accounts for the slip mechanisms such as Brownian and thermophoresis between the nanoparticle and the base fluid. The average Nusselt number at the bottom wall for pure water is compared to the previous numerical data for natural convection in a cavity and a good agreement is obtained. The parameters considered in this study include the Rayleigh number of the nanofluid, the volume fraction of alumina nanoparticle and the aspect ratio of the cavity. For the Al₂O₃/water nanofluid, it is found that heat transfer rate decreases with an increase of the volume fraction of the nanoparticle. The results are demonstrated and explained with average Nusselt number, isotherms, streamlines, heat lines, and nanoparticle distribution. The effect of nanoparticles on the onset of instability in R-B convection is also analyzed.     

A hybrid GA–PS–SQP method to solve power system valve-point economic dispatch problems

This study presents a new approach based on a hybrid algorithm consisting of Genetic Algorithm (GA), Pattern Search (PS) and Sequential Quadratic Programming (SQP) techniques to solve the well-known power system Economic dispatch problem (ED). GA is the main optimizer of the algorithm, whereas PS and SQP are used to fine tune the results of GA to increase confidence in the solution. For illustrative purposes, the algorithm has been applied to various test systems to assess its effectiveness. Furthermore, convergence characteristics and robustness of the proposed method have been explored through comparison with results reported in literature. The outcome is very encouraging and suggests that the hybrid GA–PS–SQP algorithm is very efficient in solving power system economic dispatch problem.     

Direct numerical simulation of interphase heat and mass transfer in multicomponent vapour–liquid flows

A Volume-of-Fluid methodology for direct numerical simulation of interface dynamics and simultaneous interphase heat and mass transfer in systems with multiple chemical species is presented. This approach is broadly applicable to many industrially important applications, where coupled interphase heat and mass transfer occurs, including distillation. Volume-of-Fluid interface tracking allows investigation of systems with arbitrarily complex interface dynamics. Further, the present method incorporates the full interface species and energy jump conditions for vapour–liquid interphase heat and mass transfer, thus, making it applicable to systems with multiple phase changing species. The model was validated using the ethanol–water system for the cases of wetted-wall vapour–liquid contacting and vapour flow over a smooth, stationary liquid. Good agreement was observed between empirical correlations, experimental data and numerical predictions for vapour and liquid phase mass transfer coefficients. Direct numerical simulation of interphase heat and mass transfer offers the clear advantage of providing detailed information about local heat and mass transfer rates. This local information can be used to develop accurate heat and mass transfer models that may be integrated into large scale process simulation tools and used for equipment design and optimization.