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Abstract: Convection in a layer of fluid with a free surface due to a combination of thermocapillary stresses and buoyancy is one of the classic problems of fluid mechanics. Although extensively studied, it is still not fully understood. In particular, neither the effect of phase change nor the thermal boundary conditions at the liquid–vapor interface have been properly described. These two intimately related issues have a significant impact on the stability of the flow and transitions between different convective patterns. The objective of this paper is to develop and validate a comprehensive numerical model which properly describes both heat transfer and phase change at the liquid–vapor interface, as well as the transport of heat and vapor in the gas layer, which is ignored by the vast majority of theoretical studies with minimal justification. We present a numerical investigation of convection in a long cell filled with a volatile fluid and air, and investigate the changes in convective patterns due to with changes in the applied horizontal temperature gradient. We also explore how variations in the wetting properties of the fluid and lateral confinement (three-dimensionality) affect the flow. While the numerical results have been found to be in general agreement with existing experimental observations, we have also discovered an unexpected phenomenon: a region of evaporation near the cold wall and a region of condensation near the hot wall. [Copyright &y& Elsevier]

Abstract: Since the late seventies of the 20th century, several analytical models for combined heat and mass transfer in laminar falling film absorption have been proposed. Nevertheless the analytical solutions obtained with the Fourier method for the coupled process are complex and for short flow length a certain instability occurs which have been explained with the inconsistency of the initial and boundary conditions. Therefore boundary layer models have been justified in order to solve the transfer problem for short flow length. Moreover a linear approximation of the phase equilibrium is required. The analytical solutions for heat and mass transfer presented in this paper are obtained by using the Laplace transform to solve the partial differential equations for an isothermal as well as impermeable wall. An originally unknown constant temperature and mass fraction boundary condition at the interface are set. The temperature and mass fraction profile across the film are obtained formally independently. In order to determine the yet unknown interface temperature and mass fraction the phase equilibrium and the interface energy balance are applied, using averaged gradients with regard to the streamwise coordinate. The interface temperature and mass fraction obtained with this procedure are interpreted and treated as mean values. From the known evolution of the mean interface temperature and mass fraction, the local values are derived by inverting the first mean value theorem for integration. The results show very good agreement to the established analytical solutions. The solving procedure does not depend on the input parameters such as the Lewis number for instance, which is needed in order to determine the eigenvalues within the Fourier method. Moreover arbitrary correlations for the phase equilibrium are applicable. The present solution is mathematically stable and offer explicit expressions in order to calculate the mean heat and mass fluxes directly. Therefore this solution is favourable to implement entire absorption process simulation, yet describing the coupled heat and mass transfer process comprehensively. [Copyright &y& Elsevier]

Abstract: This paper proposes a solution method for inverse laser surface heating problem. By minimizing the mean square error between the experimental data obtained from inside the body and the estimated data from the derived analytical solution of a laser surface heating problem with time-dependent boundary conditions, the temperature function at the laser heating end can be determined. Consequently, the temperature distribution and the heat flux over the entire time and space domains can also be obtained. In addition, the integral transform and tedious numerical operations are not required in the proposed solution method. Mathematical and experimental examples are given to illustrate the simplicity, efficiency, and accuracy of the proposed method. [Copyright &y& Elsevier]

Abstract: The inverse heat conduction problem (IHCP) involves estimation of a surface heat flux from transient temperature measurements inside a heat conducting body. Commonly an insulated remote boundary or one with a known heat transfer coefficient is modeled. However, in many practical applications, the precise thermal condition at the remote boundary is not known. In this paper, a method of accounting for thermal action at the remote boundary using a second measured temperature history is presented. The measurement need not be at an actual boundary but can be at an interior point in the domain. The IHCP solution herein is achieved through the filter coefficient method, which uses filter coefficients in a convolution summation. By using the filter technique, near real-time heat flux measurements can be continuously obtained in manufacturing settings to enhance productivity. Also the filter concept opens the way for the development of new scientific instruments that incorporate inverse problem methods. [Copyright &y& Elsevier]

Abstract: This paper presents a simple and rapid mathematical model to calculate the non-steady-state startup process and study the isothermal characteristics of a particular heat pipe. The model takes into consideration the special structure and usage conditions, where vapor temperature in the heat pipe changes only over time. This vapor temperature change correlation is calculated numerically and is set as the temperature boundary condition for the working well. The temperature, velocity and pressure distribution in the working well are then solved using FLUENT. The results manifest that the time required for approaching steady condition are 450s, 550s and 600s with water bath temperatures of 330K, 340K and 350K, respectively. The comparison of the calculations and experimental data shows good agreement, and the maximum deviation is 3.7K. [Copyright &y& Elsevier]

Abstract: In this paper, effect of magnetic field on free convection heat transfer in an enclosure filled with nanofluid is studied. KKL (Koo-Kleinstreuer-Li) correlation is used for simulating effective thermal conductivity and viscosity of nanofluid. The inner cylinder is maintained at uniform heat flux and the outer cylinder has constant temperature. The governing equations are solved via Control Volume based Finite Element Method. The heat transfer between cold and hot regions of the enclosure cannot be well understood by using isotherm patterns so heatline visualization technique is used to find the direction and intensity of heat transfer in a domain. Effect of Hartmann number, volume fraction of nanoparticle, Rayleigh number and aspect ratio on streamline, isotherm and heatline are examined. The results show that as Hartmann number increases Nusselt number decreases while opposite trend is observed as nanoparticles volume fraction, Rayleigh number and aspect ratio increase. Domination of conduction mechanism causes heat transfer enhancement to increase. So enhancement in heat transfer increases with increase of Hartmann number and aspect ratio while it decreases with augment of Rayleigh number. [Copyright &y& Elsevier]

Abstract: The present paper discusses steady three dimensional flow and heat transfer of viscous fluid on a rotating disk stretching in radial direction. Using Lie group theory symmetries of the governing equations are calculated. Imposing restrictions from the boundary conditions it is shown that the similarity in the problem can be achieved for two types of radially stretching velocities namely; linear and power-law. Linear stretching has already been discussed in the literature; however power-law stretching is discussed here for the first time. Using new similarity transformations, the governing partial differential are transformed into a system of ordinary differential equations which are later treated both analytically and numerically. Exact analytical solutions are found for the case of pure stretching and the large stretching parameter case, for power-law stretching index n =3. Numerical solutions are obtained for combined effects of stretching and rotation for all values of n using Keller box method. Comparison of numerical solution with the corresponding analytical solution (for n =3) shows an excellent agreement. The quantities of physical interest, such as azimuthal and radial skin friction and also Nusselt number are presented and discussed physically. [Copyright &y& Elsevier]

Abstract: The steady laminar boundary layer flow along a vertical stationary plate with convective surface boundary condition is investigated in this paper. The heat transfer coefficient is considered either constant or variable along the plate and the problem is either non-similar or similar. The results are obtained with the direct numerical solution of the governing equations. The problem is governed by Prandtl number and a convective parameter and the influence of these parameters on the results are presented in tables and figures. There are differences in the results between the non-similar and similar case at low values of the convective parameter but as this parameter increases the differences decrease and the flow tends to the classical natural convection along a vertical isothermal plate. [Copyright &y& Elsevier]

Abstract: Nowadays, consumers look for minimally processed, additive-free food products that maintain their organoleptic properties. This has led to the development of new technologies for food processing. One emerging technology is high hydrostatic pressure, as it proves to be very effective in prolonging the shelf life of foods without losing its properties. Recent research has involved modelling and simulating the effect of combining thermal and high pressure processes (see Denys et al. (2000) [3], Infante et al. (2009) [5], Knoerzer et al. (2007) [6], Otero et al. (2007) [9]). The focus is mainly on the inactivation of certain enzymes and microorganisms that are harmful to food. Various mathematical models that study the behaviour of these enzymes and microorganisms during a high pressure process have been proposed (see Infante et al. (2009) [5], Knoerzer et al. (2007) [6]). Such models need the temperature and pressure profiles of the whole process as an input. In this paper we present two dimensional models, with different types of boundary conditions, to calculate the temperature profile for solid type foods. We give an exact solution and propose several simplifications, in both two and one dimensions. The temperature profile of these simplified two and one dimensional models is calculated both numerically and analytically, and the solutions are compared. Our results show a very good agreement for all the approximations proposed, and so we can conclude that the simplifications and dimensional reduction are reasonable for certain parameter values, which are specified in this work. [Copyright &y& Elsevier]

Abstract: In this paper, the heat transfer characteristics of porous material adopted in the receiver of a concentrated solar power (CSP) with different structure parameters are numerically investigated. The commercial software FLUENT and the user defined function program (UDF) are adopted to implement the simulation. The porous material geometry is represented by periodic structures formed with packed tetrakaidecahedron. The air flow and heat transfer characteristics under the boundary conditions of constant heat flux and constant wall temperature are studied. The field synergy principle (FSP) and the entransy dissipation extremum principle (EDEP) are used to analyze the flow and heat transfer performance of the composite porous material. From the numerical results the best composite of the porous material is obtained. The effects of different boundary conditions are revealed. It is also demonstrated that the FSP and the EDEP are inherently consistent. [Copyright &y& Elsevier]

Abstract: A face-based smoothed finite element method (FS-FEM) is formulated for transient thermal mechanical analyses of 3-D solids with nonlinearity. For this face-based smoothed finite element method, the problem domain is first discretized into a set of tetrahedral elements, and the face-based smoothing domains are further formed along the faces of the tetrahedral meshes. The smoothing operations are performed in these smoothing domains. Several numerical examples with different kinds of boundary conditions are investigated in this paper. Compared with the 4-node tetrahedral FEM, the FS-FEM can achieve much better accuracy and higher convergence when dealing with the thermal mechanical analyses of 3-D solids. [Copyright &y& Elsevier]

Abstract: This work presents a detailed numerical analysis of electro-osmotic flows inside silicon microchannels characterized by an elliptical cross-section. A finite element method is used to solve the governing equations and perform an extensive parametric study. Particular attention is given to the effect of the aspect ratio of the elliptical cross-section, the electro-kinetic diameter, the ratio of the Joule heating to the imposed wall heat flux on the dynamic and thermal behavior of electro-osmotic flows in the case of H1 boundary conditions. The analysis presented in this paper can be useful to optimize design and thermal performances of silicon micro heat sinks based on electro-osmotic flows. Results point out that as the electro-kinetic diameter increases, the influence of the Joule heating on the temperature distribution becomes less relevant. This trend becomes more pronounced as the aspect ratio increases. Numerical results also show that an increment of the electro-kinetic diameter leads to an enhancement of the convective heat transfer. A comparison between numerical results obtained for electro-osmotic flows through elliptical and rectangular geometries is finally shown and discussed. Such comparison highlights that rectangular microchannels have better performances at small values of the aspect ratio, while elliptical microchannels are more effective for greater values of aspect ratio. [Copyright &y& Elsevier]

Abstract: Solar thermal energy is currently used for low temperature heating applications using flat plate collectors. The absorbed solar energy is transferred to the working fluid flowing in the pipe. The performance of the system is influenced by heat transfer from tube to working fluid, with minimum convective losses, which has to be considered as one of the primary design factor. In tube and channel flows, to enhance the rate of heat transfer to the working fluid, passive augmentation techniques such as twisted tapes and swirl generators are used in the fluid flow path. In this paper, convective heat transfer analysis for a horizontal circular pipe with fluid in mixed laminar flow range is performed using experimental simulation under constant heat flux boundary condition. The variation of heat transfer coefficient and pressure drop in the pipe flow for water and water based Al2O3 nanofluids at different volume concentrations and twisted tapes are studied. The dependence of particle concentration and Reynolds number for enhancement in heat transfer and increase in the pumping power due to pressure drop is analysed in the range of parameters considered. [Copyright &y& Elsevier]

Abstract: In this paper, a new boundary-domain integral equation for solving energy equation in convective heat transfer problems is derived. The derived integral equation accounts for fluid velocity which is computed using the velocity boundary-domain integral equations presented in [2,3] (X.W. Gao, 2004, 2005). Numerical implementation of these integral equations is discussed for steady incompressible fluid flows, in which the velocity and pressure integral equations are uncoupled from the temperature equation, and thus can be solved separately. By substituting the velocity, velocity gradient, and pressure integral equations into the energy integral equation, temperatures can be computed without iterative processes. Two numerical examples for 2D problems are given to validate the proposed method. [Copyright &y& Elsevier]

Abstract: In this paper we formulate three inverse design, isoperimetric, shape optimization problems leading to optimum geometries that maximize the heat transfer rate. We examine both semi-infinite and finite, two-dimensional domains. The former is bounded from below by an isothermal periodic boundary while a constant heat flux is assumed at the far field; the latter is bounded by a periodic boundary at the bottom and a flat isothermal surface at the top. The objective is to find the optimum shape of the periodic boundary such that the heat transfer rate is maximized. We consider three different applications: (i) the optimal shape of corrugations (surface “roughness”), (ii) the optimal shape of high conductivity inserts (inverted fins) and (iii) the optimal shape of high conductivity fins. As expected, the optimum geometries have the shape of a depression, however the details of the geometries are quite interesting. In particular, the shape optimization problem associated with the inverse design of a high-conductivity extended surface/fin has led to some interesting results, with practical implications. [Copyright &y& Elsevier]

Abstract: The prescription of turbulent inflow boundary condition for large-eddy simulation (LES) is critical to obtain accurate predictions. In this paper, a stochastic model for generating inflow turbulence is implemented and compared to the method of generating inflow turbulence with random fluctuations. The LES studies of the effect of inflow boundary conditions are performed using a semi-implicit Legendre spectral element method. Two different backward-facing step configurations are simulated at Reynolds numbers 5000 and 28,000 utilizing the technique of implicit LES with no sub-grid model. Frequency analysis is performed at various points in the boundary layer and in the shear layer to study the effect of inflow boundary condition. The spectral method requires correlated velocity input data generated by the stochastic model for predicting the correct transition to turbulence at Re =5000, while the random fluctuations predict a delayed transition to turbulence. At Re =28,000, the two techniques of generating inflow turbulence give similar results. In addition, it is also observed that at Re =5000, the semi-implicit method requires small time step size to correctly predict transition to turbulence. The large time step size leads to laminarization of the flow in the inlet channel. This effect of the time step size is not observed in the case of Re =28,000. [Copyright &y& Elsevier]

Abstract: This paper reports an analytical and numerical study of natural convection in a shallow enclosure filled with a non-Newtonian fluid. Thermal boundary conditions of the Neumann type are applied on the horizontal walls of the enclosure while the vertical walls are assumed adiabatic. A power law model is used to characterize the non-Newtonian fluid behavior of the fluid. The governing parameters for the problem are the thermal Rayleigh number Ra, power-law index n, Prandtl number Pr and cavity aspect ratio A. An analytical solution, valid for an infinite layer, is derived on the basis of the parallel flow approximation. Rigid–rigid, free–free and rigid–free hydrodynamic boundary conditions are considered. It is demonstrated that, for shear-thinning fluids, the onset of convection is subcritical. For shear thickening fluids, convection is found to occur at a supercritical Rayleigh number equal to zero. The effects of the non-Newtonian behavior on the fluid flow, temperature field and heat transfer are discussed. A good agreement is found between the analytical predictions and the numerical results obtained by solving the full governing equations. [Copyright &y& Elsevier]

Abstract: The determination of thermophysical properties from an inverse method is an attractive technique both from the experimental and methodological point of view. The aim of this paper is to identify simultaneously the thermal conductivity and the thermal diffusivity of liquids and the heat transfer coefficient by the utilization of the well-known flash method which is coupled to an inverse parameter identification method. To be characterized, a thin layer of the liquid is sandwiched between two metal plates and a cylindrical sample holder. Then it is subjected on its front face to a heat flux density during a short time. The temperature evolution of the rear face of the container is measured during and after the thermal excitation. The identification procedure based on the inverse method consists in the minimization of an objective function that represents the errors between the measured temperature at the rear face and a theoretical model that describes the temperature evolution of the system (liquid and container). The theoretical model, which is a function of the unknown thermophysical properties of the three layer system, is calculated by the use of the thermal quadrupoles formalism. To minimize the objective function, a genetic algorithm is developed and used. Genetic algorithm is categorized as global search heuristics. It is an iterative procedure which borrows the ideas of natural selection and survival of the fittest from natural evolution which were first described by Darwin. The identification procedure based on the use the flash method and the developed genetic algorithm is used in this work to identify thermophysical properties of distilled water, glycerol, acetone, and ethylene glycol. A good agreement is found between our experimental results and the thermophysical properties indicated in the literature of the studied liquids. [Copyright &y& Elsevier]

Abstract: In order to study the influence of moisture transfer on the wall internal surface temperature, a coupled heat and moisture transfer transient model was proposed in this paper. Relative humidity and temperature were chosen as the driving potentials. The accuracy of the proposed model was verified by comparing the simulated results with the experimental data. By employing the developed model, the internal surface temperature of walls made of different materials was evaluated under the constant and variable boundary conditions. The results show that the effect of moisture transfer on the wall internal surface temperature is significant. When the moisture transfer is taken into account, the internal surface temperature has cooling effect on the indoor air and is beneficial to improve the indoor thermal environment during the working hours in summer, which lays a scientific basis for low energy building design. [Copyright &y& Elsevier]

Abstract: This paper considers the heat and mass transfer characteristics of some nanofluid flows past a vertical infinite flat plate. The radiation effect for two distinct types of thermal boundary conditions is also taken into account. Derivation of exact analytical solutions are aimed for different water-based nanofluids containing Cu, Ag, CuO, Al2O3, and TiO2. The velocity and temperature profiles, skin friction coefficient and Nusselt number are easily examined and discussed via the closed forms obtained which may be further used to verify the validity of obtained numerical solutions for more complicated transient free convection nanofluid flow problems. [Copyright &y& Elsevier]

Abstract: A method for solving nonlinear transient inverse heat conduction problems is presented. To overcome the nonlinearity of the problem, not only the time domain is divided into several sub-domains, but also the geometrical domain. By using an inverse method, the unknown variables are determined in each sub-domain. The finite element method (FEM) is used for the sensitivity analyses in the sub-domains. The ill-posedness of the inverse problem in each sub-domain is much less than that corresponding to the original domain and hence the inverse problem is solved efficiently in each sub-domain. Three nonlinear transient problems are analyzed by both the method presented in this paper and the conventional method. According to the results obtained, it is shown that the proposed domain decomposition method (DDM) is more stable, accurate and faster than the conventional method with a single domain. [Copyright &y& Elsevier]

Abstract: A good understanding of the details of hydrodynamic and heat transport conditions and their impact on temperature polarisation and pressure drops is essential for optimum design of membrane distillation (MD) modules. To this end, the present work reports on initial progress in the development of a tool for 3D simulation of spacer-filled MD channels based on the open source CFD code library OpenFOAM. The paper discusses a number of modelling and implementation aspects including model geometry and computational domain, choice of boundary conditions, and discretisation schemes. The results pertaining to the effect of three different spacer types on the fluid dynamics and heat transfer inside the channel are presented and discussed in order to highlight the impact of spacer geometrical features on temperature polarisation and pressure drop. Of the three spacer types considered, the 3-layer spacer with the wall-adjacent filament layers aligned with the flow direction was found to cause the lowest pressure drop while producing a robust symmetrical temperature profile. The 2-layer flow aligned square spacer was found to be the least desirable design, producing asymmetric temperature and velocity profiles and high pressure drops. [Copyright &y& Elsevier]

Abstract: In this paper, we construct solutions for model describing heat transfer in longitudinal rectangular fins. The imposed boundary conditions are the step change in the base temperature and the step change in base heat flow. Both the thermal conductivity and the heat transfer coefficients are assumed to be power law temperature dependent. We employ the local and nonlocal symmetry techniques to analyze the problem at hand. In one case the reduced equation transforms to the tractable Ermakov–Pinney equation. Nonlocal symmetries are admitted when some arbitrary constants appearing in the governing equations are specified. The exact analytical steady state solutions which satisfy the prescribed boundary conditions are constructed. Since the obtained general exact analytical solutions for the transient state satisfy only the zero initial temperature and adiabatic boundary condition at the fin tip, we sort numerical solutions. The effects of the thermo-geometric fin parameter and the power law exponent on temperature distribution are studied. [Copyright &y& Elsevier]

Abstract: The paper deals with modeling the convective drying process. A relevant and reliable mathematical model that captures the history and distribution of temperature is presented. The attention is focused on the simultaneous heat and mass transfer occurring during drying where dry and hot air flows about the food. In the present study, external resistance to mass transfer is considered negligible. As a result, the drying curve is almost independent of the boundary conditions, which means that drying is diffusion-controlled. The main connotation of present study regards to undertake analytical procedure to establish the novel model for practical applications. The results show that the temperature evolution can be evaluated from an advanced analytical solution in a quick and efficient manner. The model is validated with the literature experimental data obtained for carrot and mango slabs. A good agreement is obtained between the model predictions and the available experimental results. [Copyright &y& Elsevier]

Abstract: Nanofluids are a novel strategy to improve heat transfer characteristics of fluids by the addition of solid particles with diameters below 100nm. Experimental measurements have shown that this approach can greatly increase heat conductivity, even above that predicted by Maxwell’s theory. However, it is still not clear what mechanism accounts for this increase, mainly in thermal conductivity, thus great effort is being put into investigating the different phenomena occurring inside the fluid. This paper shows a direct numerical simulation of the flow and thermal behaviour of a nanofluid loaded with alumina nanoparticles which considers the effects of particle–particle and particle–fluid interactions. The boundary element method is used given its capabilities to deal with moving boundary problems. This formulation was employed to simulate the behaviour and time evolution of a 30nm alumina/water nanofluid at six different particle concentrations, looking to observe flow fields, temperature distributions and total heat flow through the domain. Results showed strong convective currents caused by the presence of the nanoparticles, which in time increased total heat flow in the cavity. As expected, particle concentration increased the total heat flow affecting not only the conductive part of heat transfer, but the convective part as well. [Copyright &y& Elsevier]

Abstract: In this paper a novel simulation technique is presented to perform Direct Numerical Simulation (DNS) of fluid flow and heat transfer in dense fluid–particle systems. The unique feature of our fluid–solid coupling technique is the direct (i.e., implicit) incorporation of the boundary condition (with a second-order method) at the surface of the particles at the level of the discrete momentum and thermal energy equations of the fluid. Contrary to lattice Boltzmann or other commonly used immersed boundary implementations, our method does not require using any effective diameter. A fixed (Eulerian) grid is utilized to solve the Navier–Stokes equations for the entire computational domain. Dissipative particle–particle and/or particle-wall collisions are accounted via a hard sphere discrete particle approach using a three-parameter particle–particle interaction model accounting for normal and tangential restitution and tangential friction. Following the detailed verification of the method several dense multi-particle systems are studied in detail involving stationary arrays of particles and fluidized particles. [Copyright &y& Elsevier]

Abstract: This paper investigates the numerical simulation of non-Fourier transient heat transfer in a two-dimensional sub-100nm metal-oxide-semiconductor field-effect transistor (MOSFET). The dual-phase-lag (DPL) model with a specific normalization procedure is introduced for the modeling of nanoscale heat transport. The boundary conditions are selected similar to what existed in a real MOSFET device, both uniform and non-uniform heat generations within the transistor are applied, and the end parts of the top boundary which are in contact with the metallic material are left open. A temperature-jump boundary condition is used on all boundaries in order to consider the boundary phonon scattering at micro and nanoscale. A three-level finite difference scheme has been employed to generate the numerical results which are illustrated for a silicon sub-100nm MOSFET corresponding to the Knudsen number of 10. The results are presented at real times less than 50ps to avoid the three-dimensional effects. It is concluded that the combination of the DPL model with mixed-type temperature boundary condition is able to predict the heat flux and temperature distribution obtained from the Boltzmann transport equation (BTE) more accurate than the ballistic-diffusive equations (BDE). After verification of our results, the thermal field and the hotspot temperature within the bulk silicon are presented and the effect of adding a layer of silicon-dioxide to the transistor on its thermal behavior has been investigated. [Copyright &y& Elsevier]

Abstract: This paper presents an analytical analysis of both Fourier and non-Fourier heat conduction in the absorber plates of a flat-plate solar collector. Separation of variables was employed to develop the model. For the analysis, a repetitive heat transfer module was used for the solution of parabolic and hyperbolic equations. From the practical point of view, two types of boundary conditions were separately chosen. A numerical technique based on the finite difference method was employed to determine the temperature for validation purposes. A comparative investigation was carried out to understand the requirements for use of the non-Fourier heat conduction model easily. A significant difference in the temperatures obtained from the Fourier and non-Fourier models was observed for lower values of the Fourier number and higher values of the Vernotte number. Finally, the effect of the boundary conditions on the Fourier and non-Fourier heat transfer was demonstrated. [Copyright &y& Elsevier]

Abstract: Given the importance of water temperature on the physical, chemical, and biological processes, there is a consistent desire to improve our ability to predict instream temperature responses and understand significant heat fluxes and contributions. While there have been advances in understanding the contributions from various heat sources and sinks (e.g., atmospheric and transient storage exchanges), methods to determine the influences of boundary and initial conditions on downstream predictions have been absent. This paper provides two analytical solutions to the advection–dispersion equation (ADE) that includes terms accounting for atmospheric exchanges. In order to solve the ADE using integral transforms, two of the atmospheric flux terms had to be linearized. The influence of this step on predictions was tested and an initial analytical solution was developed. However, an additional simplifying assumption of constant windspeed was tested and resulted in a second, simpler analytical solution. The linearization step resulted in minimal differences in the total atmospheric exchange fluxes and consequently was found to be acceptable in developing the analytical solutions. The assumption of constant windspeed was also found acceptable and provided nearly identical predictions to the original analytical solution during low variability or no wind conditions. Both analytical solutions developed provide insight into the individual contributions from the boundary and initial conditions on spatial and temporal predictions. While the contribution from initial conditions quickly decays in time, the influence of the boundary condition persists a considerable distance downstream and illustrates the importance of gathering calibration data at locations far enough downstream to ensure the influence of the boundary conditions is sufficiently small. [Copyright &y& Elsevier]

Abstract: This paper presents heat transfer characteristics of supercritical carbon dioxide flow inside vertical circular pipe surrounded by highly conducting material, and develops an adequate tool to test the performance of available heat transfer correlations with. The possible situations are illustrated for the nuclear power plant to which the above-mentioned geometric configuration might be applicable. An experimental loop with vertical circular geometry is designed and constructed to test the upward flow in supercritical state when the axial heat transfer is enhanced by the surrounding metals, resulting in a wall boundary condition between the constant heat flux and temperature. The set of correlations and important findings are critically reviewed from extensive literature survey. Incorporating nondimensional groups resorting to past insights from the available literature, a convective heat transfer correlation is proposed. The optimization procedure is described which utilizes a random walk method along with the in-house finite element heat transfer code to determine the coefficients of the proposed heat transfer correlation. The proposed methodology can be applied to evaluation of heat transfer when the heat transfer coefficient data cannot directly be determined from the experiment. [Copyright &y& Elsevier]

Abstract: This paper discusses the problem of blade cooling system optimization connected with conjugate heat transfer (CHT) analysis for reliable thermal field prediction within a steam cooled component. Since the full CHT solution, which involves the main flow, blade material and the coolant flow domains is computationally expensive from the point of view of optimization process, it was decided to reduce the problem by fixing the boundary conditions at the blade surface and solving the task for the interior only (both solid material and coolant). Such assumption, on one hand, makes the problem computationally feasible, and on the other, provides more reliable thermal field prediction than it used to be with the empirical relationships. The analysis involves shape optimization of internal cooling passages within an airfoil. The cooling passages are modeled with a set of four Bezier splines joined together to compose a closed contour. Each passage is fed with cooling steam of constant parameters at the inlet. In the present study the airfoil profile is taken as aerodynamically optimal. The search problem is solved with evolutionary algorithm and the final configuration is to be found among the Pareto optimal cooling candidates. [Copyright &y& Elsevier]

Abstract: In the precision glass moulding process, the heat transfer and the resulting transient temperature distributions of the molten glass are of great importance because they significantly affect the productivity as well as the thermally induced residual stresses in the final product. Thermal modelling of the heating system in the glass moulding process considering detailed heating mechanisms therefore plays an important part in optimizing the heating system and the subsequent pressing stage in the lens manufacturing process. The current paper deals with three-dimensional transient thermal modelling of the multi-stage heating system in a wafer based glass moulding process. In order to investigate the importance of the radiation from the interior and surface of the glass, a simple finite volume code is developed to model one dimensional radiation–conduction heat transfer in the glass wafer for an extreme case with very high temperature difference considering temperature dependant thermal conductivity and heat capacity. Afterwards, by using three-dimensional FEM modelling along with a predefined experimental test, the equivalent glass–mould interface contact resistance is determined for two different pressures. Finally, the three-dimensional modelling of the multi-stage heating system in the wafer based glass moulding process is simulated with the FEM software ABAQUS for a particular industrial application for mobile phone camera lenses to obtain the temperature distribution in the glass wafer. In the numerical modelling, the interface boundary conditions for each heating stage are changed according to the determining heat transfer mechanism(s). Numerical results are compared with experimental data to show the validity of the numerical modelling. The obtained results show that the right thermal modelling is highly dependent on the proper choice of thermal boundary conditions in different stages according to the real physical phenomena behind the process. [Copyright &y& Elsevier]

Abstract: This study deals with an experimental investigation on the thermo-physical properties and overall performance of MWCNT/heat transfer oil nanofluids flow inside vertical helically coiled tubes. Data were acquired for the laminar flow in the thermal entrance region, while the temperature of the tube wall was constant at around 95°C leading to isothermal boundary condition. Pure heat transfer oil and nanofluids with particle weight concentrations of 0.1%, 0.2% and 0.4% were utilized as the working fluids. It was observed that most conventional models fail to predict the thermo-physical properties of the applied nanofluids accurately, especially in case of the specific heat capacity. Therefore, rough empirical correlations were developed to estimate such properties for the working fluids. In addition, the overall performance of the tested helically coiled tubes was assessed based on the performance index and optimum work conditions were determined. High overall performance index of up to 6.4 was obtained for the simultaneous utilization of both heat transfer enhancement techniques considered in this paper. Hence, applying the methods studied here could be considered as a good choice in practical applications. [Copyright &y& Elsevier]

Abstract: In this paper, natural convective flow within a rectangular enclosure has been investigated numerically. All the walls of the enclosure are adiabatic except the bottom wall, which is partially heated and cooled by sinusoidal temperature profile. Both situations: medium is hydro-dynamically isotropic and anisotropic are considered. The governing equations are written under assumption of Brinkman-extended non-Darcy model, including material derivative, and then solved by numerically using spectral element method (SEM). Main emphasize is given on effect of periodicity parameter (N) on local heat transfer rate (Nu x ) as well as flow mechanism in the enclosure. The result shows that, as the periodicity is decreased on increasing N, the absolute value of Nu x at the bottom left corner point increases in both situations. For odd values of N, the local heat transfer profile is symmetric about the line X =0.5. The entire flow is governed by two type convective cells: (i) rotating clockwise (ii) rotating anticlockwise. Furthermore, increasing of N increases the multiple cellular structures in the form of N +1. The relative impact of media permeability on Nu x at (0,0) shows that enhancement of media permeability along Y-direction is much more effective than the same along X-direction. In contrast to isotropic porous media, the effect of the permeability and permeability orientation angle on the flow is complex and often non intuitive. In particular the present analysis shows that, different periodicity of temperature boundary condition has significant effect on the flow mechanism and consequently on the heat transfer rate for both situations. [Copyright &y& Elsevier]

Abstract: In this paper, mixed convection flow and heat transfer around a long cylinder of square cross-section under the influence of aiding buoyancy are investigated in the vertical unconfined configuration (Reynolds number, Re =1–40 and Richardson number, Ri =0–1). The semi-explicit finite volume method implemented on the collocated grid arrangement is used to solve the governing equations along with the appropriate boundary conditions. The onset of flow separation occurs between Re =1–2, between Re =2–3 and between Re =3–4 for Ri =0, 0.5 and 1, respectively. The flow is found to be steady for the range of conditions studied here. The friction, pressure and total drag coefficients are found to increase with Richardson number, i.e., as the influence of aiding buoyancy increases drag coefficients increase at the constant value of the Reynolds number. The temperature field around the obstacle is presented by isotherm contours at the Prandtl number of 0.7 (air). The local and average Nusselt numbers are calculated to give a detailed study of heat transfer over each surface of the square cylinder and an overall heat transfer rate and it is found that heat transfer increases with increase in Reynolds number and/or Richardson number. The simple expressions for the wake length and average cylinder Nusselt number are obtained for the range of conditions covered in this work. [Copyright &y& Elsevier]

Abstract: The overall heat transfer performance of a tube bank fin heat exchanger is very important for engineering applications. Developing a fin pattern with good heat transfer performance for tube bank fin heat exchanger needs more our intensive effort. There are two methods to obtain the heat transfer performances of a fin pattern, i.e., one is experimental method, and the other is numerical method. If numerical method is used, the thermal boundary condition on the fin surfaces is necessary. Generally, there are two ways to treat the thermal boundary, i.e., one is to treat fin surface with uniform temperature, and the other is to use a conjugate numerical method. The former is very easy to be applied in numerical method, but the latter needs more numerical effort. This paper reports the condition under which whether a conjugate numerical method or a numerical method just specifying uniform temperature thermal boundary condition should be used. It is found that such condition is the fin efficiency. When the fin efficiency is less than 0.8, a conjugate numerical method must be used. Otherwise, the numerical results obtained by applying an uniform temperature thermal boundary condition on the fin surfaces has only slightly differences with the results obtained by a conjugate numerical method. The reported results will provide a criterion for the researchers to choose a suitable numerical method in finding a fin pattern more efficiently and reliably. [Copyright &y& Elsevier]

Abstract: This paper aims to study the gravity effects on the mixed convection heat transfer in a microchannel using lattice Boltzmann method. To include these effects, hydrodynamic boundary condition equations are modified. In this problem, cold fluid enters the microchannel and leaves it after cooling the hot walls. For a wide range of inlet Knudsen number (Kn), computations are performed, and for validation, appropriate comparisons between present and previous available results are made. As the results, stream lines, longitudinal variations of friction coefficient, Nusselt number, slip velocity and temperature jump, and velocity and temperature profiles in different cross sections are presented. The results show that lattice Boltzmann method can be used to simulate mixed convection in a microchannel, and the effects of buoyancy forces are important for Kn < 0.05, specially for hydrodynamic properties, and thus should be included. For Kn > 0.05, these effects can be ignored. In addition, it is observed that buoyancy forces generate a rotational cell in the microchannel flow, leading to the negative slip velocity at Kn = 0.005. [Copyright &y& Elsevier]

Abstract: This paper focuses on a theoretical investigation of the coupling mechanism of heat transfer and liquid moisture diffusion in chitosan-treated porous fibrous material. The porous fibrous materials made of cotton with different porosities are modified by chitosan solution with different concentrations. The moisture regain of the chitosan-treated porous fibrous material increases and the contact angle of the chitosan-treated fiber decreases significantly after modification. For comparison, the simultaneous heat and liquid moisture transfer in porous fibrous materials with different porosities modified by chitosan solution with different concentration are discussed. With specification of initial and boundary conditions, the distributions of the water vapor concentration in the void spaces, the volume fraction of the liquid water in the void spaces, the distribution of the water content in fibers and the temperature changes in chitosan-treated porous fibrous material are obtained numerically. The comparison with the experimental measurements shows the superiority of the numerical model in resolving the coupled heat and mass transfer in chitosan-treated porous fibrous material. Analysis of the computational and experimental results illustrates that the heat and mass transfer in chitosan-treated porous fibrous material is influenced by chitosan concentration and fabric porosity significantly. [Copyright &y& Elsevier]

Abstract: In this paper, the possible optimal thickness of a heat sink base has been explored numerically with different convective heat transfer boundary conditions in a dimensionless three dimensional heat transfer model. From the numerical results, relations among different heat transfer mechanisms (natural or forced, air or liquid), different area ratios of a heat sink to a heating source, and the lowest thermal resistance have been obtained and discussed. Also a simple correlation for these three parameters from data fitting is given for guiding a heat sink design. [Copyright &y& Elsevier]

Abstract: We study a steady laminar 2-D MHD viscous incompressible flow over a permeable flat plate with thermal convective boundary condition and radiation effects. The viscosity and thermal conductivity of fluid are assumed to vary linearly with temperature. Similarity representation of the governing partial differential equations is obtained via group method. Similarity equations are then solved numerically by implicit finite difference technique. Effects of convective heat transfer parameter (b), radiation parameter (R,) magnetic field parameter (M), the thermal conductivity parameter (S), suction parameter (fw), Prandtl number (Pr) and Schmidt number (Sc) on the dimensionless axial velocity, temperature, concentration, wall temperature, the rate of heat transfer and the rate of mass transfer are investigated. Good agreement is found between the numerical results of the present paper with published result for special case. [Copyright &y& Elsevier]

Abstract: In this paper the laminar free convection in a hot outer square enclosure containing a cold inner sinusoidal circular cylinder at different amplitudes and number of undulations and different angle, is investigated by means of thermal lattice Boltzmann method (TLBM). Both square enclosure and cylinder are maintained at constant temperature and air filled the enclosure. Boundary conditions for fluid flow and temperature fields at curved boundaries are second order schemes. The buoyancy effect is modeled by applying the Boussinesq approximation to the density distribution function. The computed results show that by increasing amplitude or number of undulations or changing the angle might change the heat transfer coefficient and has profound influence on the temperature and fluid field. [Copyright &y& Elsevier]

Abstract: This paper presents a 3D FEM model to predict the thermal behaviour of a high speed motor spindle. This model allows a transient simulation which considers complex boundary conditions like heat sources as well as contact and convective heat transfer between spindle parts. Verification experiments are implemented on a test spindle. Compared with the measured data, it is shown that the developed model can predict well the thermal behaviour of the test spindle. [Copyright &y& Elsevier]

Abstract: The paper presents a model-based investigation of a metal hydride reactor applied as a solid state hydrogen storage device. The elements of a metal hydride reactor are hydrogen supply duct, internal hydrogen distribution, hydride bed, reactor shell and the flow domain of the heat transfer fluid. Internal hydrogen distribution and hydride bed are porous media. Therefore, hydrogen flows through non-porous and porous regions during its reversible exothermic absorption and endothermic desorption, respectively. The interface between porous and non-porous regions is a discontinuity with respect to energy transport mechanisms. Hence, Danckwerts-type boundary conditions for the energy balance equation are introduced. Application of the first and second law of thermodynamics to the interface reveals that temperature jumps may occur at the hydrogen inlet but are not allowed at the hydrogen outlet. Exemplarily the loading behavior of a metal hydride storage tank based on sodium alanate is analyzed. It is demonstrated and experimentally validated that only Danckwerts-type boundary conditions predict the important cooling effect of the inlet hydrogen on the exothermic absorption process correctly. [Copyright &y& Elsevier]

Abstract: In this paper, the regulation problem of convection governed dynamical processes described by linear distributed parameter models with position-independent inputs is addressed by combining the method of characteristics (MC) and the Malek-Zavarei and Jamshidi theorem. In this approach, the MC is used to transform the first order partial differential equations model of such processes into a set of time-delayed ordinary differential equations whose elements are used to generate certain matrices that satisfy linear matrix inequalities that render the proportional integral (PI) control parameters that guarantee the process stability. The performance of the proposed PI controller is tested via numerical simulations in the temperature regulation of a linear heat exchanger and compared to a tightly tuned classical PI controller. The application of the proposed controller is extended to regulate the outlet concentration in a nonlinear non-isothermal plug flow reactor. It is shown that the proposed controller is able to handle the infinite dimensional nature of the process model yielding smooth and unsaturated responses around the predetermined set-point trajectory in the face of load changes, time varying boundary conditions and set-point changes. [Copyright &y& Elsevier]

Abstract: The reliable estimation of buildings energy needs for cooling is a crucial issue in the implementation of the EPB Directive 2010/31/EU (formerly 2002/91/EC), especially in central and southern Europe climates. On this purpose one of the main topics is to predict the behavior of the opaque envelope subjected to variable boundary conditions. The EN ISO 13786:2007 technical standard assumes sinusoidal boundary conditions and introduces dynamic thermal characteristics. The aim of this paper is to assess the deviation arising by the use of different approaches for the calculation of the dynamic thermal characteristics of an opaque envelope element under periodic non sinusoidal boundary conditions. The EN ISO 13786 procedure has been firstly applied by decomposing the external forcing temperature by means of the Fast Fourier Transform (FFT) analysis. A comparison with different approaches, such as Finite Difference Methods (FDM) and Transfer Function Methods (TFM), has been carried out. The predictions of the EN ISO 13786 with a sinusoidal forcing temperature (i.e., standard approach) have also been assessed, comparing the results to the ones obtained through the FFT analysis. Furthermore, corrections to the periodic thermal transmittance and to the time shift have been proposed, in order to improve the explicative worth of those parameters. [Copyright &y& Elsevier]

Abstract: The exact analytical solution of the unsteady impulsive Thermo-Fluid Dynamic field arising in a two-dimensional channel with thick solid walls is presented when the thermal field in the fluid is coupled with the thermal field in the solid (conjugated heat transfer). The cases studied in this paper depend on the boundary conditions imposed on the unwetted sides of the channel walls: assigned temperature and adiabatic condition. Moreover the case of a given heat loss at the unwetted wall is also considered in an appendix. The temperature and heat flux at the solid–fluid interface are analyzed as function of time and of the nondimensional parameters governing the problem. [Copyright &y& Elsevier]

Abstract: This paper reports the results of a numerical study on heat and moisture transport through a buffer layer made of clay as used in nuclear waste repository. Galerkin''s weighted residual finite element method along with Newton-Raphson method has been used for the solution of the non-linear coupled governing equations used to represent the heat and moisture transport through unsaturated clay material. After validating the code numerical simulation results were obtained for heat and moisture variations within the buffer material for Dirichlet temperature boundary conditions in the range, 50oC

Abstract: Temperature variations have strong effects on structure vibrations, urging the need for accurate real-time temperature identification. The work presented here deals with the reconstruction of the thermal field inside a structure, given pointwise temperature measurements. This is achieved by reconstructing both the initial and boundary conditions. The numerical procedure uses the adjoint method, which is unable, in its usual L 2 setting, to provide accurate results at the end of the observation period. This paper shows how the introduction of regularity assumptions yields an accurate and stable real-time temperature reconstruction while keeping the generality and flexibility of the usual adjoint method. [Copyright &y& Elsevier]

Abstract: In this paper, we propose efficient and suitable effective surface models for steady laminar flows with heat transfer over rough surfaces. These models are developed in the frame of a domain decomposition method and consist in replacing the rough boundaries by effective smooth surfaces on which effective boundary conditions or wall laws are prescribed. The associated effective properties, namely the effective friction and heat transfer coefficients, are determined by the resolution of local closure problems over a representative pattern of the roughnesses. The impact of the flow parameters on these effective coefficients is analyzed, which allows to obtain useful estimates in some specific cases. Finally, two-dimensional numerical experiments are performed for a natural convection problem in a stamp shaped cavity to assess the validity of the proposed effective surface models. Throughout these tests, we also study numerically the impact of the position of the effective surface on momentum and heat transfers. [Copyright &y& Elsevier]

Abstract: This paper presents a two-step up-scaling approach to determine the jump relations that must be imposed at the interface between a homogeneous porous domain and a free domain. We study convective heat transfer at such an interface under the assumption of local thermal equilibrium. The two-step approach has the capability of providing closed jump relations depending on intrinsic characteristic of the interface. In addition, from the resulting jump relations, it is possible to determine a particular interface location where the condition of continuity are sufficient. Thus, the use of jump or continuity conditions depend only on the interface location inside the fluid–porous transition region. [Copyright &y& Elsevier]