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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]

Abstract: In this paper we investigate the onset of convection in a horizontally partitioned porous layer which is heated from below. Identical sublayers are separated by thin impermeable barriers. A linear stability analysis is performed, and dispersion relations are obtained directly and explicitly for two- and three-layer configurations. A systematic numerical procedure is devised to compute the dispersion relation for an arbitrary number of sublayers, but from this it is possible to guess the correct analytical form of the dispersion relation for general cases. Neutral stability curves are found to organise themselves into natural groups of N members when there are N sublayers. When the disturbance wavenumber, k, is large, each member of any group lies within an O(k −1) distance of all other members, but within an O(1) distance of other groups. When the number of sublayers is large, the system tends towards one with a critical Darcy–Rayleigh number of 12 and a critical wavenumber of zero; this is the well-known property of a single porous layer with constant heat flux boundary conditions. An asymptotic analysis is performed in order explore these two apparently disparate configurations. Finally, another asymptotic analysis is used to determine the critical Rayleigh number and its associated wavenumber when the number of sublayers is large. [Copyright &y& Elsevier]

Abstract: The convective heat transfer of SiO2/water colloidal suspensions (5–34wt.%) is investigated experimentally in a flow loop with a horizontal tube test section whose wall temperature is imposed. Experiments were performed at different inlet temperatures (20, 50, 70°C) in cooling and/or heating conditions at various flow rates (200

Abstract: This paper reports an analytical and numerical study of natural convection in a shallow rectangular cavity filled with nanofluids. Neumann boundary conditions for temperature are applied to the horizontal walls of the enclosure, while the two vertical ones are assumed insulated. The governing parameters for the problem are the thermal Rayleigh number, Ra, the Prandtl number Pr, the aspect ratio of the cavity, A and the solid volume fraction of nanoparticles, . For convection in an infinite layer , analytical solutions for the stream function and temperature are obtained using a parallel flow approximation in the core region of the cavity and an integral form of the energy equation. The critical Rayleigh number for the onset of supercritical convection of nanofluids is predicted explicitly by the present model. Furthermore, a linear stability analysis of the parallel flow solution is studied and the threshold for Hopf bifurcation is determined. Also, results are obtained from the analytical model for finite amplitude convection for which the flow and heat transfer is presented in terms of the governing parameters of the problem. Numerical solutions of the full governing equations are obtained for a wide range of the governing parameters. A good agreement is observed between the analytical model and the numerical simulations. [ABSTRACT FROM AUTHOR]

Abstract: The scope of the paper is an algorithm reconstructing the boundary conditions (heat flux and heat transfer coefficient) in the solidification of pure metals on the grounds of temperature measurements. For the verification of the algorithm experimental data derived in the course of the solidification of aluminum were used. An example of the application of the algorithm for designating the cooling conditions in continuous casting is provided, when the values of temperature at selected points on the boundary of the casting are known. [Copyright &y& Elsevier]

Abstract: This paper investigates the cooling process of water in a circular enclosure subjected to non-uniform boundary conditions. Half of the enclosure boundary is maintained at a constant temperature, while the other half is well insulated. The enclosure is cooled from its top, bottom, or left side. The problem is solved numerically using the finite element method. The examined Rayleigh numbers are 1 × 105, 1 × 106, and 1 × 107, and the effect of maximum density at 4 °C is considered. The results indicate that the natural convection flow plays a significant role on the cooling process of water. The effects of the cooling side and Rayleigh number on the cooling process are presented. For Ra = 1 × 105, the results indicate that the bottom cooling side has the lowest cooling time, but it has the highest cooling time for Ra = 1 × 107. For Ra = 1 × 106 and 1 × 107, the left cooling shows lowest cooling time. For Ra = 1 × 105, the bottom cooling case takes 52.97% less time than the top cooling case to complete the cooling process. The density inversion near 4 °C creates a unique natural convection flow, and high resolution capturing of temperature contours and natural convection flow is presented. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, fluid flow and heat transfer across a long equilateral triangular cylinder placed in a horizontal channel is studied for Reynolds number range 1–80 (in the steps of 5) and Prandtl number of 0.71 for a fixed blockage ratio of 0.25. The governing Navier-Stokes and energy equations along with appropriate boundary conditions are solved by using a commercial CFD solver FLUENT (6.3). The computational grid is created in a commercial grid generator GAMBIT. The flow and temperature fields are presented by stream-line and isotherm profiles, respectively. The wake/recirculation length, mean drag coefficient and average Nusselt number, etc. are calculated for the above range of conditions studied here. The critical value of the Reynolds number (i.e., transition to transient) is found to lie between Re=58 and Re=59. The average Nusselt number and the wake length increase with increasing value of the Reynolds number; however, the mean drag coefficient decreases with increasing value of the Reynolds number. Finally, simple correlations for wake length, mean drag coefficient and average Nusselt number are obtained for the range of conditions studied here. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to present heat transfer measurements of gas in a tube under rarefied condition. The measurements are made in a circular tube of inner diameter 25mm for approximately constant wall temperature boundary conditions, with nitrogen, oxygen, argon, and helium as the working fluids. The range of Knudsen and Reynolds numbers covered in this study are 0.0022–0.032 and 0.13–14.7, respectively. Whereas the continuum values are correctly reproduced in our setup, the measured values for Nusselt numbers are very small in the slip regime. The measured values are two-five orders of magnitude smaller than the corresponding values in the continuum regime, and suggest that the Nusselt number is a strong function of Reynolds, Knudsen and Brinkmann numbers in the slip flow regime. These are among the first heat transfer measurements in the slip flow regime and the current theoretical and simulation models are inadequate to explain such low values of Nusselt number. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a numerical investigation of two-dimensional coupled heat and mass transfer during desorption of hydrogen in a cylindrical metal hydride reactor containing MmNi6.4Al0.4 is presented. By considering the variation in heat transfer fluid temperature along the axial direction (variable wall temperature boundary condition), the changes in hydride bed temperature at different axial locations are presented. The effect of variable wall temperature boundary condition on hydrogen desorption rate for different hot fluid temperatures and hydride bed thicknesses is investigated. The rate of hydrogen desorption at different hot fluid temperatures showed good agreement with the experimental data reported in the literature. As the desorption progresses, the change in heat transfer fluid temperature along the axial direction is found to decrease with time and becomes unchanged at the end of the process. The effect of variable wall temperature boundary condition on desorption time is found to be significant for the hydride bed thicknesses of about 7.5mm and more. For a given bed thickness of 17.5mm, the maximum difference in desorption time between variable wall and constant wall temperature convective boundary conditions is about 375s at 303K. [ABSTRACT FROM AUTHOR]

Abstract: This paper focuses on the investigation of the 3D mathematical model to simulate the coupled heat and liquid moisture transfer in hygroscopic porous fibrous media. The flow of the liquid moisture, the water vapor sorption/desorption by fibers and the diffusion of the water vapor are taken into account in this 3D model. Prediction-corrector method is used to solve the 3D governing equations. A series of computational results of the coupled heat and moisture transfer are obtained with the specific initial conditions and boundary conditions. The distribution 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 changes of the temperature in porous fibrous media are computed. It is shown that the effects of the gravity and capillary actions are significant in hygroscopic porous fibrous media. The comparison with the experimental measurements shows the reasonable agreement between the two. The results illustrate that the 3D model of the coupled heat and liquid moisture transfer in hygroscopic porous fibrous media is satisfactory. [Copyright &y& Elsevier]

Abstract: In this paper the two main drawbacks of the heat balance integral methods are examined. Firstly we investigate the choice of approximating function. For a standard polynomial form it is shown that combining the heat balance and refined integral methods to determine the power of the highest order term will either lead to the same, or more often, greatly improved accuracy on standard methods. Secondly we examine thermal problems with a time-dependent boundary condition. In doing so we develop a logarithmic approximating function. This new function allows us to model moving peaks in the temperature profile, a feature that previous heat balance methods cannot capture. If the boundary temperature varies so that at some time t >0 it equals the far-field temperature, then standard methods predict that the temperature is everywhere at this constant value. The new method predicts the correct behaviour. It is also shown that this function provides even more accurate results, when coupled with the new CIM, than the polynomial profile. Analysis primarily focuses on a specified constant boundary temperature and is then extended to constant flux, Newton cooling and time dependent boundary conditions. [Copyright &y& Elsevier]

Abstract: In this paper, we study the unsteady flow and heat transfer of a dusty fluid between two parallel plates with variable viscosity and electric conductivity. The fluid is driven by a constant pressure gradient and an external uniform magnetic field is applied perpendicular to the plates with a Navier slip boundary condition. The governing non-linear partial differential equations are solved numerically using a semi-implicit finite difference scheme. The effect of the wall slip parameter, viscosity and electric conductivity variation and the uniform magnetic field on the velocity and temperature fields for both the fluid and dust particles is discussed. [Copyright &y& Elsevier]

Abstract: In this paper we propose a novel bottom-up approach to generate a three-dimensional microtube surface with random roughness. This approach starts from four corner points with two defined coordinates and roughness height created by a Gaussian number generator, and then uses a bi-cubic Coons patch to form the curved surface. A computational fluid dynamics solver is used to isolate the roughness effect and solve the three-dimensional N–S equations for the water flow through the generated rough microtubes with diameter D =50μm and length L =100μm. No-slip, constant heat flux and periodic boundary conditions are applied to achieve the characteristics of fully developed flow. It is found that the wall roughness strongly affects the velocity near the wall and it almost has no effect on the flow at the center. When the mean diameter of a rough microtubes is used as the hydraulic diameter, the friction factor can still be predicted by the conventional flow theory. The temperature has large values at the peaks and small values at the valleys of the microtube surface. However, the roughness has almost no effect on the averaged Nusselt number because the effects of peaks and valleys counteract each other for the whole microtube. The local Nusselt numbers along the microtube randomly scatter from the theoretical value with a deviation less than 2%. The model has a potential to be used for direct simulations of three-dimensional surface roughness effect on the slip flow. [Copyright &y& Elsevier]

Abstract: The slip effect of gaseous flow in a micro-scale channel is dominant when the characteristic length is less than about 10μm under atmospheric conditions. The slip flow in a channel whose wall temperature is specified can be analyzed by solving the momentum and energy equations with taking into account the slip velocity and temperature jump. However, when there is slip, the shear work due to the slip at the wall should be included to calculate the heat flux from the wall. Unfortunately, the need of inclusion of the shear work in the heat balance equation has not been physically explained. In this paper, the physical reason of the inclusion of the shear work in the heat balance equation is physically explained from the point of view of both conservation law of energy and the kinetic theory of gases. [Copyright &y& Elsevier]

Abstract: In this paper, we consider an inverse problem of heat equation with Robin boundary condition for identifying heat transfer coefficient. Combining the method of fundamental solutions with discrepancy principle for the choice of the locations for source points, we give a method for solving the reconstruction problem. Since the resultant matrix is severe ill-conditioning, Tikhonov regularization with L-curve method is employed. Some numerical examples are given for verifying the efficiency and accuracy of the presented method. [Copyright &y& Elsevier]

Abstract: This paper reports an analytical and numerical study of natural convection in a shallow rectangular cavity filled with a micropolar fluid. Neumann boundary conditions for temperature are applied to the horizontal walls of the enclosure, while the two vertical ones are assumed insulated. The governing parameters for the problem are the thermal Rayleigh number, Ra, the Prandtl number, Pr, the aspect ratio of the cavity, A and various material parameter of the fluid. For convection in an infinite layer (), analytical solutions for the stream function temperature and angular velocity are obtained using a parallel flow approximation in the core region of the cavity and an integral form of the energy equation. The critical Rayleigh numbers for the onset of supercritical convection are predicted explicitly by the present model. Furthermore, a linear stability analysis is conducted yielding numerically the critical Rayleigh numbers for the onset of motion. Also, results are obtained from the analytical model for finite-amplitude convection for which the flow and heat transfer are presented in terms of the governing parameters of the problem. Numerical solutions of the full governing equations are obtained for a wide range of the governing parameters. A good agreement is observed between the analytical model and the numerical simulations. The influence of the material parameters on the flow and heat transfer is demonstrated to be significant. [Copyright &y& Elsevier]

Abstract: This paper formulates an edge-based smoothed point interpolation method (ES-PIM) for analyzing 2D and 3D transient heat transfer problems with mixed boundary conditions and complicated geometries. In the ES-PIM, shape functions are constructed using the polynomial PIM with the Delta function property for easy treatment of essential boundary conditions. A generalized smoothing technique is used to reconstruct the temperature gradient field within the edge-based smoothing domains. The generalized smoothed Galerkin weak form is then used to establish the discretized system equations. Our results show that the ES-PIM can provide more close-to-exact stiffness compared with the “overly-stiff” finite element method (FEM) and the “overly-soft” node-based smoothed point interpolation method (NS-PIM). Owing to this important property, the present ES-PIM provides more accurate solutions than standard FEM using the same mesh. As an example, a practical cooling system of the rapid direct plasma deposition dieless manufacturing is studied in detail using the present ES-PIM, and a set of “optional” processing parameters of fluid velocity and temperature are found. [Copyright &y& Elsevier]

Abstract: Three-dimensional unsteady natural convections in an inclined porous cavity with time oscillating boundary conditions are numerically studied in this paper. The Darcy–Forchheimer–Brinkman model is adopted to model the fluid flow in the porous medium and the combination effects of inclination angles (α 1, α 2) and temperature oscillation frequency (f) on the convection characteristics with different Rayleigh numbers (Ra =106 and 107) are carefully investigated, especially when the porous cavity is seriously inclined (). It is revealed that, when the porous cavity is moderately inclined (), the natural convections inside are stable and quasi two-dimensional. However, if the cavity is seriously inclined (), the flow patterns inside are much more complicated and the three-dimensional multiple roll-cells with different intercrossing angles are established. It is also found that, when the porous cavity is inclined with three-dimensional method (α 1 >0°, α 2 >0°), the natural convections become quite different and a series of three-dimensional screw type flexural roll-cells appears. Furthermore, it is suggested that, with proper selection of inclination angles and oscillation frequency, the natural convection heat transfer will be significantly improved and the maximal heat fluxes are finally obtained at the optimal combinations of f =35π, α 1 =50°, α 2 =45° when Ra =106 and f =40π, α 1 =45°, α 2 =45° when Ra =107. [Copyright &y& Elsevier]

Abstract: This paper reports the results of a numerical study of the Nusselt number for the H1 and T boundary conditions in laminar, fully-developed flows of pseudoplastic and dilatant fluids in rectangular ducts. Equations for the apparent viscosity that span the entire shear rate range were utilized and the Nusselt numbers were calculated as a function of a shear rate parameter that determines the flow regime where the duct is operating. Numerical results for the Nusselt number in all flow regimes are included along with correlation equations. Finally, errors associated with applying power law solutions are discussed. [Copyright &y& Elsevier]

Abstract: This paper deals with analytical solution of steady-state heat transfer for laminar, two-dimensional and rarefied gas flow in an infinite microtube subjected to mixed boundary conditions. To account for the slip-flow characteristics of microscale heat transfer, temperature jump condition at the wall has been incorporated in the model while the fluid velocity is assumed to be constant (slug flow). The energy equation in the thermal entrance region has been solved by the method of separation of variables. The solution yields closed form expressions for bulk-mean temperature and Nusselt number in terms of Knudsen number and Peclet number. [Copyright &y& Elsevier]

Abstract: In this paper, a theoretical study of laminar forced convection inside ducts, subjected to periodically varying inlet temperature is presented. A thermal diffusion in the duct walls and a boundary condition which accounts for external convection are considered. In the first part, this problem is solved by applying a Generalized Integral Transform Technique (GITT). The complex eigenvalues and coefficients results are listed and compared with the literature. In the second part, the Quasi-steady Approach (QSA) which employs a constant heat transfer coefficient at liquid–solid interface is also investigated and compared with the GITT solution. The bulk temperature, Nusselt number, the damping and phase lag coefficients as function of the inlet temperature frequency are plotted. [Copyright &y& Elsevier]

Abstract: Firstly, a brief review of the MPCL system design and work principle is presented and a proposed experimental system is described. Special attention was paid to the system start-up and dynamic working characteristics under different conditions such as heat load variation, mass flow rate or sinusoidal temperature variation of boundary condition. According to the experimental findings, the transient liquid transfer between the main loop and accumulator was analyzed to explain the transient phenomena during the experiments. From the experiments, it was demonstrated that the system presents a good performance and has more stable characteristics for start-up processes and normal operation than the heat pipe, CPL or LHP system. The paper presents MPCL system has self-adjusting ability. Because the accumulator, which is just like the “brain” of the system, determines stable capability, and each action of the vapor–liquid interface in it could cause the temperature or pressure change of the evaporator. [Copyright &y& Elsevier]

Abstract: For purposes of an accurate mathematical modeling, it is essential to establish trustworthy boundary conditions. The heat transfer that occurs at the casting/mold interface is one of these important conditions, which is a fundamental task during unsteady solidification in permanent mold casting processes. This paper presents an overview of the inverse analysis technique (IHCP) applied to the determination of interfacial heat transfer coefficients, hi , for a number of alloy solidification situations. A search algorithm is used to find the transient metal/mold interface coefficient during solidification which is reported either as a function of the casting surface temperature or time. Factors affecting hi such as the direction of gravity in relation to the growth interface, the initial melt temperature profile, the wettability of the liquid layer in contact with the mold inner surface, were individually analyzed and experimental laws for hi have been established. [Copyright &y& Elsevier]

Abstract: A numerical model is presented to determine the thermal shielding performance of an exterior wall (e.g., building envelope) containing layers of PCMs. The model is exploited to perform a parametric study to assess the influence of the position and melting temperature of one PCM layer. Results showed that benefits are to be expected when the interior and exterior temperatures are close. Then, the wall composition has been optimized with a genetic algorithm based on a yearly analysis with the possibility of including several PCM layers. Idealized weather conditions and measured weather conditions (including solar radiation) have been considered. Results showed that for Québec City, optimal south-facing wall includes one PCM layer when real weather data are considered. Its effect is to shield the heat transfer in the summer. This paper provides a fundamental understanding of multilayer walls with PCMs. [Copyright &y& Elsevier]

Abstract: This paper concerns the physical process of heat transfer from hot wires located in the proximity of walls consisting of different thermal conductivities. It points out that it is common practice to calibrate hot wires in a free stream of constant and known velocity, but when utilized for near-wall measurements additional heat losses occur owing to the presence of the wall, resulting in erroneous velocity readings. Therefore, a combined experimental and numerical methodology for heat transfer from a heated wire in a flow field is proposed, taking the effects of wire diameter, overheat ratio, wall thermal conductivity, wall distance, wall thickness and shear rate on the measured velocity into account. The present investigations indicated that the flow under the plate, i.e., the corresponding shear rate at the wall opposite the location of the wire where velocity measurements were taken, changes the thermal boundary conditions around the hot wire. It was also observed that heat diffusivity is dominant in the wall region and plays the major role in heat transfer from the wire rather than convection, especially for highly heat-conducting materials. For highly heat-conducting walls, a universal correction law for the wall influence was given by Durst et al. [F. Durst, E.-S. Zanoun, M. Pashtrapanska, In situ calibration of hot wires close to highly heat-conducting walls, Exp. Fluids 31 (2001) 103–110]. However, for poorly heat-conducting walls, the correction law depends on the wall thickness and the heat transfer from the surface opposite the wall where the hot-wire measurements were performed. [Copyright &y& Elsevier]

Abstract: In this paper the flow of a power-law fluid due to a linearly stretching sheet and heat transfer characteristics using variable thermal conductivity is studied in the presence of a non-uniform heat source/sink. The thermal conductivity is assumed to vary as a linear function of temperature. The similarity transformation is used to convert the governing partial differential equations of flow and heat transfer into a set of non-linear ordinary differential equations. The Keller box method is used to find the solution of the boundary value problem. The effect of power-law index, Chandrasekhar number, Prandtl number, non-uniform heat source/sink parameters and variable thermal conductivity parameter on the dynamics is analyzed. The skin friction and heat transfer coefficients are tabulated for a range of values of said parameters. [Copyright &y& Elsevier]

Abstract: This paper examines the three-dimensional problem of finding thermal stresses due to an insulated rigid sheet-like inclusion (anticrack) in an elastic space under a uniform perpendicular heat flow. By using appropriate harmonic potentials, a general method of solving this problem is presented. The resulting boundary-value problems are reduced to classical mixed problems of potential theory. For the purpose of illustration, a complete solution in terms of elementary functions for a rigid circularly shaped inclusion is given and discussed from the point of view of material failure. [Copyright &y& Elsevier]

Abstract: In this paper, a numerical investigation of two-dimensional heat and mass transfer during absorption of hydrogen in a cylindrical metal hydride bed containing MmNi6.4Al0.4 is presented. By considering the variation in cooling fluid temperature along the axial direction (variable wall temperature), the changes in hydrogen concentration, hydride equilibrium pressure, and average hydride bed temperature at different axial locations are presented. The average bed temperature profiles and hydrogen storage capacities at different supply pressures showed good agreement with the experimental data reported in the literature. As the absorption progresses, the change in cooling fluid temperature along the axial direction is found to decrease and becomes unchanged at the end of the absorption process. The effect of variable wall temperature on hydrogen absorption rate for different supply pressures and hydride bed thicknesses are presented. The effect of variable wall temperature on absorption time is found to be significant for the hydride beds of thickness of above 7.5mm. For a supply pressure of 20bar, the maximum difference in absorption time between variable wall temperature and constant wall temperature boundary conditions is about 300s for 17.5mm bed thickness. [Copyright &y& Elsevier]

Abstract: The paper presents results of an experimental study of heat transfer and friction in a rectangular section duct with fully perforated baffles (open area ratio of 46.8%) or half perforated baffles (open area ratio of 26%) at relative roughness pitch of 7.2–28.8 affixed to one of the broader walls. The Reynolds number of the study ranges from 2700 to 11,150. The baffled wall of the duct is uniformly heated while the remaining three walls are insulated. These boundary conditions correspond closely to those found in solar air heaters. The study shows an enhancement of 79–169% in Nusselt number over the smooth duct for the fully perforated baffles and 133–274% for the half perforated baffles while the friction factor for the fully perforated baffles is 2.98–8.02 times of that for the smooth duct and is 4.42–17.5 times for the half perforated baffles. In general, the half perforated baffles are thermo-hydraulically better to the fully perforated baffles at the same pitch. Of all the configurations studied, the half perforated baffles at a relative roughness pitch of 7.2 give the greatest performance advantage of 51.6–75% over a smooth duct at equal pumping power. [Copyright &y& Elsevier]

Abstract: This paper addresses the problem of heat transfer in the near-wall region of a turbulent channel flow. We investigate the role of coherent eddy structures on the thermal exchange between the solid and fluid materials. In the present approach, the instantaneous velocity field is modelled by means of a low-order dynamical system based on proper orthogonal decomposition (POD) modes while the temperature field is accounted for by using a stochastic filtered density function (FDF) method. A good comparison of results with reference DNS data on mean temperature and on temperature r.m.s. at various Prandtl numbers and for different wall boundary conditions (isotemperature, isoflux, and conjugate heat transfer) is achieved. [Copyright &y& Elsevier]

Abstract: The glass pressing process involves heat transfer between the glass gob and the forming tool which are among the most important parameters influencing the thermo-mechanical stresses in the moulds. The present paper presents the development of the instrumentation of a mould for the measurement of temperatures during the production cycle. These measurements are exploited with an inverse method to evaluate the heat flux densities at the working surface of the mould. The influence of each process stage and of the location at the surface of the mould on the thermal loadings are described. The evaluated heat flux densities are used as boundary conditions in a finite element calculation. The validity of these results are discussed taking into account the differences between experiment and calculation, the hypothesis of the inverse method and the time response of the thermocouples. [Copyright &y& Elsevier]

Abstract: The promising performance of microchannels has given rise to intensive research on pressure drop and heat transfer characteristics of flows at the small scale. To check the classical models and to validate new ones, experiments need to be conducted, which are particularly difficult given the characteristic dimensions involved and the magnitude of the fluxes to be measured. Although more care has been devoted lately to the design of experiments in terms of control of the geometry and of the boundary conditions, the uncertainties which inevitably affect each measurement do not seem to have been given the proper consideration. Correctly calculating uncertainties not only allows a correct assessment of the experimental data obtained, but can also be used to decide which measurements need to have the highest precision to achieve a certain accuracy, thus saving money on the others. In this paper, a quantitative criterion is given to assess the accuracy achievable in the determination of the friction factor in the laminar regime for the flow of a fluid in a circular microtube. The influence of the six quantities (pressure drop, outlet pressure, temperature, length, diameter and volume flow rate) measured to determine f in the laminar regime are studied separately and when combined. It is found that at low Reynolds numbers flow rate and pressure drop measurements are determinant for the final value of the uncertainty, while at larger Reynolds numbers the influence of the accuracy in measuring the hydraulic diameter prevails and also limits the minimum value that the total uncertainty can take. [Copyright &y& Elsevier]

Abstract: A Direct Numerical Simulation (DNS) method has been developed to solve the heat transfer equations for the computation of thermal convection in particulate flows. This numerical method makes use of a finite difference method in combination with the Immersed Boundary (IB) method for treating the particulate phase. A regular Eulerian grid is used to solve the modified momentum and energy equations for the entire flow region simultaneously. In the region that is occupied by the solid particles, a second particle-based Lagrangian grid is used, which tracks particles, and a force density function or an energy density function is introduced to represent the momentum interaction or thermal interaction between particle and fluid. The numerical methods developed in this paper have been validated extensively by comparing the present simulation results with those obtained by others. [Copyright &y& Elsevier]

Abstract: In this paper, we discuss the physical nature of the jump parameters that generally appear in the expression for the jump conditions at a fluid/porous interface. These jump parameters are generally thought of as intrinsic interfacial properties, just like surface tension in the case of fluid/fluid interfaces. Based on a two-step up-scaling analysis, we show that jump parameters can be interpreted as surface-excess quantities. The value of a surface-excess quantity is shown to depend linearly on the position of the discontinuous interface and is therefore not an intrinsic property. We propose a theoretical approach that allows to introduce genuine intrinsic interfacial properties and to propose a best choice for the position of the discontinuous interface. We show that these properties are tightly related to the definition of the interfacial zone. This theoretical approach is successfully assessed on three important cases: a laminar flow parallel to a fluid/porous interface, a turbulent flow perpendicular to a porous/fluid interface and heat transfer perpendicular to a fluid/porous interface. It is believed that this approach is general enough to be applied to any interfacial transport phenomenon. [Copyright &y& Elsevier]

Abstract: In the paper, numerical and experimental analyses of heat and mass transfer during frost formation on a fin-and-tube heat exchanger have been presented. Modelling of the frost formation on cold surfaces placed in a humid air stream, requires a complex mathematical approach. A transient two-dimensional mathematical model of frost formation has been developed. The applied mathematical model has been defined using governing equations for the boundary layer that include air and frost sub-domains as well as a boundary condition on the air–frost interface. The mathematical model with initial and boundary conditions has been discretised according to the finite volume method and solved numerically using the SIMPLER algorithm for the velocity–pressure coupling. Results have shown that the frost layer formation significantly influences the heat transfer between air and fins. As a result of numerical calculations, time-wise frost thickness variations for different air humidities, temperatures and velocities have been presented. Using the developed mathematical model, the algorithm and the computer code, which have been experimentally validated, it is possible to predict a decrease of exchanged heat flux in the heat exchanger under frost growth conditions. [Copyright &y& Elsevier]

Abstract: This paper describes the restoration of boundary conditions in one-dimensional transient inverse heat conduction problems (IHCP). In the formulation, convective boundary conditions are represented by linear relations between the temperature and the heat flux, together with an initial condition as a function of space. The temperature inside the solution domain together with the space-dependent ambient temperature or heat transfer coefficient are found from additional boundary temperature or average boundary temperature measurements. The determination of the spacewise dependent ambient temperature is a linear IHCP, whilst the determination of the spacewise dependent heat transfer coefficient is a nonlinear IHCP. For both problems uniqueness theorems are available. Numerical results obtained using the boundary element method are presented and discussed. [Copyright &y& Elsevier]

Abstract: The paper discusses heat transfer enhancement and deterioration phenomena observed in experimental data for fluids at supercritical pressure. The results obtained by the application of various CFD turbulence models in the prediction of experimental data for water and carbon dioxide flowing in circular tubes are firstly described. On this basis, the capabilities of the addressed models in predicting the observed phenomena are shortly discussed. Then, the analysis focuses on further results obtained by a low-Reynolds number k – ε model addressing one of the considered experimental apparatuses by changing the operating conditions. In particular, the usual imposed heat flux boundary condition is changed to assigned wall temperature, in order to highlight effects otherwise impossible to point out. The obtained results, supported by considerations drawn from experimental information, allow comparing the trends observed for heat transfer deterioration at supercritical pressure with those typical of the thermal crisis in boiling systems, clarifying old concepts of similarity among them. [Copyright &y& Elsevier]

Abstract: The main objective of this paper is to extend to two-dimensional (2-D) medium the ray tracing-node analyzing method, which has already been successfully used to solve one-dimensional (1-D) problem of coupled heat transfer in a semitransparent medium. For simplicity, an infinitely long rectangular semitransparent medium with four black opaque surfaces is chosen as our studying object. A control volume method in the implicit scheme is adopted for discretizing the partial transient energy equation. In combination with spectral band model, the radiative heat source term is calculated using the radiative transfer coefficients (RTCs), which are deduced by the ray tracing method. The Partankar''s linearization method is used to linearize the radiative source term and the opaque boundary condition, and the linearized equations are solved by the ADI method. Effects of absorption coefficient, refractive index and conductivity on transient cooling process in the 2-D gray rectangular medium are investigated under the condition that the radiation and convection processes cool one side of the rectangular medium while heat the remaining three sides. [Copyright &y& Elsevier]

Abstract: Due to the complexity of the flow and the difficulty of measuring heat transfer directly in gas turbines or even in turbine cascade, heat transfer coefficients have been extracted from data obtained in mass transfer measurements using the heat/mass transfer analogy. The present paper shows the validity of the heat/mass transfer analogy from separate heat transfer and mass transfer measurements on simulated turbine blades with equivalent experimental and geometric conditions. The Nusselt numbers from heat transfer experiments employing a constant temperature boundary condition are compared to the Sherwood number from mass transfer experiments employing a constant concentration boundary condition. [Copyright &y& Elsevier]

Abstract: This paper presents experimental validation of a numerical model of coupled processes within a three-phase medium-power dry-type electrical transformer. The analysis carried out employed a multi-disciplinary approach involving heat, fluid flow and electromagnetics. The thermal and fluid flow analysis was coupled with an electromagnetic model in order to examine the specific power losses within the coils and the core. The thermal boundary conditions, i.e. the local and temperature-dependent heat fluxes, were computed by considering a numerical model of the surrounding internal and external air. Moreover, separate numerical and analytical models were considered in order to obtain the anisotropic thermal conductivities for different types of coils and also for laminated cores. To validate the numerical model, experimental transformer temperature tests in the short-circuit, open-circuit, and under nominal parameters according to the current European Standards for dry-type transformers were performed. During the tests, temperatures were measured at selected points on elements of the transformer using thermocouples and thermometers, while on the external tank walls an infrared thermography was employed. The obtained numerical results showed that the prediction of the temperature distribution within the analyzed transformers and their surroundings was very accurate. [Copyright &y& Elsevier]

Abstract: This paper reports the results of a numerical investigation of transient turbulent natural convection heat transfer from a volumetric energy generating source placed inside a cylindrical enclosure filled with low Prandtl number fluid (liquid sodium, Pr =0.005). Two-dimensional conservation equations of mass, momentum and energy, coupled with the Boussinesq approximation, are solved using a finite volume based discretisation method employing the SIMPLE algorithm for the pressure velocity coupling. Turbulence is modeled using the k–ε model with physical boundary conditions. The study presents the transient features of confined turbulent natural convection, due to time varying generation of heat in the volumetric source. The intensity of heat source exponentially decays with time and the source is placed over circular plates with a central opening. Results obtained from the numerical model compare favorably with those reported in the literature for steady state natural convection. Numerical simulations are carried out to display the sequential evolution of flow and thermal fields and the maximum temperature reached in the source. The advantages of distributing the heat source on multi trays have been quantified. [Copyright &y& Elsevier]

Abstract: This paper describes the reconstruction of the heat transfer coefficient (space, Problem I, or time dependent, Problem II) in one-dimensional transient inverse heat conduction problems from surface temperature or average temperature measurements. Since the inverse problem posed does not involve internal temperature measurements, this means that non-destructive testing of materials can be performed. In the formulation, convective boundary conditions relate the boundary temperature to the heat flux. Numerical results obtained using the boundary element method are presented and discussed. [Copyright &y& Elsevier]

Abstract: In this paper we will conduct an analytic comparative study between the powerful Adomian method and the traditional separation of variables method. This is achieved by handling homogeneous and non-homogeneous boundary value problem for one-dimensional heat equation. The study shows the reliability and efficiency of Adomian method. Adomian method provides the solution in a rapidly convergent series through evaluating elegantly computable components. [Copyright &y& Elsevier]

Abstract: In this paper, a mixed finite element (FE) and differential quadrature (DQ) method as a simple, accurate and computationally efficient numerical tool for two dimensional transient heat transfer analysis of functionally graded materials (FGMs) is developed. The method benefits from the high accuracy, fast convergence behavior and low computational efforts of the DQ in conjunction with the advantages of the FE method in general geometry, loading and systematic boundary treatment. Also, the boundary conditions at the top and bottom surfaces of the domain can be implemented more precisely and in strong form. The temporal derivatives are discretized using an incremental DQ method (IDQM), whose numerical stability is not sensitive to time step size. The effects of non-uniform convective–radiative conditions on the boundaries are investigated. The accuracy of the proposed method is demonstrated by comparing its results with those available in the literature. It is shown that using few grid points, highly accurate results can be obtained. [Copyright &y& Elsevier]

Abstract: This paper presents multi-element stochastic reduced basis methods (ME-SRBMs) for solving linear stochastic partial differential equations. In ME-SRBMs, the domain of definition of the random inputs is decomposed into smaller subdomains or random elements. Stochastic reduced basis methods (SRBMs) are employed in each random element to evaluate the response statistics. These elemental statistics are assimilated to compute the overall statistics. The effectiveness of the method is demonstrated by solving the stochastic steady-state heat transfer equation on two geometries involving different types of boundary conditions. Numerical studies are conducted to investigate the h-convergence rates of global and local preconditioning strategies. [Copyright &y& Elsevier]

Abstract: The extremely small length scale of the electric double layer (EDL) of electro-osmotic flows (EOF) in a microchannel makes it difficult to simulate such flows and associated thermal behaviors. A feasible solution to this problem is to neglect the details in the thin EDL and replace its effects on the bulk flow and heat transfer with effective velocity-slip and temperature-jump boundary conditions outside the EDL. In this paper, by carrying out a scale analysis on the fluid flow and heat transfer in the thin EDL, we analytically obtain the velocity and the temperature at the interface between the EDL and the bulk flow region. The Navier–Stokes equations and the conservation equation of energy, along with the interfacial velocity and temperature as the velocity-slip and temperature-jump boundary conditions, form a simple model for the electro-osmotic flows with thermal effects in a microchannel with a thin EDL. We use the double distribution function lattice Boltzmann algorithm to solve this model and found that numerical results are in good agreement with those by the conventional complete model with inclusion of the EDL, particularly for the cases when channel size is about 400 times larger than the Debye length. Moreover, we found that the present model can substantially reduce the computational time by four to five times of that using the conventional complete model. Therefore, the simplified model proposed in this work is an efficient tool for simulating electro-osmosis-based microfluidic systems. [Copyright &y& Elsevier]

Abstract: The paper describes the results of an experimental study of natural convection in a closed half-scale model of a building comprising two floors connected by a stairway, and a horizontal opening between the two floors. The driving force for the flow is a heat source in the lower floor. The results indicate a complex three-dimensional flow within the model. The rate of heat losses from each wall, wall temperatures, air speed and temperature in the horizontal opening for a range of heat inputs are presented and discussed. The results are then used to suggest boundary conditions for numerical simulation of the flow. [Copyright &y& Elsevier]

Abstract: In this paper, meshless element free Galerkin (EFG) method has been extended to obtain the numerical solution of nonlinear, unsteady heat transfer problems with temperature dependent material properties. The thermal conductivity, specific heat and density of the material are assumed to vary linearly with the temperature. Quasi-linearization scheme has been used to obtain the nonlinear solution whereas backward difference method is used for the time integration. The essential boundary conditions have been enforced by Lagrange multiplier technique. The meshless formulation has been presented for a nonlinear 3-D heat transfer problem. In 1-D, the results obtained by EFG method are compared with those obtained by finite element and analytical methods whereas in 2-D and 3-D, the results are compared with those obtained by finite element method. [Copyright &y& Elsevier]

Abstract: This paper presents a linear stability analysis for the buoyant convection in a vertical cylinder with isothermal top and bottom walls at the same temperature and with an axisymmetric heat transfer into the liquid from the vertical cylindrical wall. Results are presented for Prandtl numbers between 0.0 and 0.1 and for two different thermal boundary conditions at the vertical wall: a prescribed parabolic temperature variation or a prescribed parabolic radial heat flux variation. The results are radically different for the two thermal boundary conditions. [Copyright &y& Elsevier]

Abstract: This paper presents a physically based model coupling water and heat transport in a soil–mulch–plant–atmosphere continuum (SMPAC) system, in which a transparent polyethylene mulch is applied to a winter wheat crop. The purpose of the study is to simulate profiles of soil water content and temperature for different stages of wheat growth. The mass and energy balance equations are constructed to determine upper boundary conditions of governing equations. Energy parameters are empirically formulated and calibrated from three-month field observed data. Resistance parameters in the SMPAC system are calculated. The mass and energy equations are solved by an iterative Newton–Raphson technique and a finite difference method is used to solve the governing equations. Water-consuming experiments are performed within the growing period of wheat. The results show that the model is quite satisfactory, particularly for high soil water content, in simulating the water and temperature profiles during the growth of the winter wheat. [Copyright &y& Elsevier]