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Abstract: In this work we present a mathematical model describing the coupled heat and moisture transport in paper. The model is solved numerically and the numerical solution is used to study the interdependency of the moisture and temperature distribution in paper. The results show that variation with temperature of the saturated water vapor concentration and the sorption isotherm parameters are both important for inducing moisture desorption. It is also found that for steep relative humidity ramps moisture sorption generates temperature increments that slow down the sorption process itself. The model is also used to study the moisture gradients in a paper sheet inside a printer from Océ Technologies, which contains a warm print surface. The results predict changes in moisture content of only 0.2%, which suggests that no deformations are induced on the printed sheet. [Copyright &y& Elsevier]

This paper describes an accurate model of the Electrical Power Subsystem (EPS) of the Thermal Analysis Support and Environment Characterization Laboratory (TASEC-Lab), a university experiment developed for using in high-altitude balloon missions to measure and analyze the convection heat transfer. A Li-ion battery and two high efficient DC–DC converters have been characterized through laboratory tests and fitting to the experimental results. The developed mathematical models described in this paper are used to carry out accurate EPS simulations and are validated by comparison with the experimental data. • Design and modeling of the electrical power subsystem of a stratospheric balloon experiment. • New Li-lion battery discharging model that describes the three main parts: initial decay, linear, and exponential decay. • Formulation of a new DC/DC converter efficiency model. • Simulation and model validation of the electrical power subsystem. [ABSTRACT FROM AUTHOR]

The present study investigates two models—two limiting cases—for the internal heat and mass transfer in a multicylinder dryer: the first model assumes that complete redistribution of heat and moisture in the thickness direction occurs instantaneously. The second model assumes that moisture transfer occurs only by vapor diffusion and that heat transfer takes place by conduction and condensation. The two models are written in dimensionless form, and applied for the same set of standard paper machine data. For basis weights below approximately 0.05 kg d.s./m2 the results are so close that the first, simple model is sufficient. A higher limiting basis weight—approximately 0.16 kg d.s./m2—was previously indicated by comparison of model predictions, assuming the simple model, to extensive sets of machine data from four different paper machines. [Copyright &y& Elsevier]

A mathematical model describing the heat and mass transfer in the dryer section of a paper machine has been applied to the production data from four paper machines. Model predictions for the machine speed are compared to actual machine speeds for a total of 163 data sets. The mathematical model assumes that the temperature and moisture content remain homogeneous in the thickness direction of the sheet. For three paper machines producing paper with basis weights ranging from 0.056 to 0.159 kg d.s./m2 the model predictions are adequate. For the paper machine producing the heaviest grades with basis weights ranging from 0.189 to 0.390 kg d.s./m2 the model predictions are flawed by a systematic error. For low machine velocities/high basis weights the machine velocity is over-predicted and for high machine velocities/low basis weights the machine velocity is under-predicted. This systematic error is caused by the assumption of homogeneous moisture content and temperature within the sheet being severely in error for thick sheets. [Copyright &y& Elsevier]

In order to make full use of the advantages of superheated steam (SHS), SHS injection in multi-point injection wells (MPIW) is proposed in this paper. Firstly, a mathematical model comprised of SHS flow model in inner tubing (IT) or long tubing (LT) and annulus, transient heat transfer model in oil layer is established. Secondly, type curves of SHS flow in MPIW is obtained by finite difference method on space and the iteration technique. Then, the effect of injection temperature on distributions of thermophysical properties of SHS in MPIW is discussed in detail. Results show that: (a) When the heat exchange between IT and annulus is taken into consideration. SHS temperature in IT has a decrease while SHS temperature in annulus has an increase. (b) With the help of MPIW, heating effect at both heel and toe points of the horizontal wellbores can be enhanced. (c) While the increase of SHS temperature certainly benefits the formation heating effect through the increase of both SHS temperature and superheat degree, the following decrease of SHS pressure in annulus will lead to the decrease of SHS absorption rate. This paper unravels some intrinsic flow characteristics of SHS in MPIW, which has a significant impact on the optimization of SHS injection parameters and analysis of heat transfer law in MPIW. [ABSTRACT FROM AUTHOR]

The numerical modelling of the internal heat generation in passenger vehicle tyres using finite element analysis is a well-known numerical approach. However, this application is rather uncommon for earthmover tyres. This paper describes the development of a finite element model of a 23.5R25 earthmover tyre for the numerical modelling of the temperature distribution in the tyre cross-section at steady-state heat transfer conditions using an uncoupled analysis procedure. Considering the non-linear behaviour of the rubber compounds used for the manufacturing of these tyres, as well as the complexity associated with the composite structural aspects of the tyre, the material properties used for the proposed numerical model were established experimentally. In the analyses completed, the tyre behaviour was studied by simulations at various inflation pressures, loads and rolling velocities. The numerical tyre defection was within an 8% deviation from the actual tyre behaviour. Thermal simulation results were used to derive an equation that can be used to predict the maximum temperature that would occur in the tyre’s cross-section as a function of its vertical deflection, its forward rolling velocity and the ambient temperature of the surroundings. The numerical models and simulations presented in this paper were completed using MSC.Marc/Mentat. [ABSTRACT FROM AUTHOR]

This paper presents a computational heat transfer model of a rotary kiln used for the production of rutile titanium dioxide by the calcination of paste-like hydrous titanium dioxide. The work details the modelling of several chemical reactions occurring in the solid bed region along with turbulent convection of gas, radiation heat exchange among hot gas, refractory wall and the solid surface, and conduction in the refractory wall. Finite-difference techniques are used and the steady state thermal conditions are assumed. The kiln is divided into axial segments of equal length. The solution is of marching type and proceeds from the solid inlet to the solid outlet. The direction of gas flow is opposite to that of the solids. Mass balance of each species in the solid charge, and mass and energy balances of the solid and gas in an axial segment are used to obtain solids and gas temperatures, and species concentration at the exit of that segment. The kiln length predicted by the present model is 45.75 m as compared to 45 m of an actual kiln reported by Ginsberg and Modigell (2011). The steady-state axial gas and solid temperature profiles have been also satisfactorily validated with the numerical results of the aforementioned paper. The output data consist of refractory wall temperature distribution, the axial solids and gas temperature profiles, axial solids composition profile, the length required for drying of the solid charge and the total kiln length required to achieve 98% conversion of anatase TiO 2 to rutile TiO 2 . A detailed parametric study with respect to the controlling parameters such as percent water content (with respect to dry solids), solids flow rate, gas flow rate, kiln inclination angle and kiln rotational speed lent a good physical insight into the rutile-TiO 2 production process in a rotary kiln. [ABSTRACT FROM AUTHOR]

• Normal mode stability analysis performed on counjugate heat transfer (CHT) 1D problem. • Stability analysis reveals existence of lower stability bound for coupling coefficient in Robin-Dirichlet interface boundary conditions. • Validity of stability analysis results is verified empirically. • Stability analysis is extended to more general CHT problems. This paper aims to evaluate and validate a mathematical coupling model, based on a normal mode stability analysis, for steady conjugate heat transfer problems. In order to achieve this goal, an aerothermal computational code was designed specifically ex novo to meet the needs of the current study. A large number of numerical simulations were carried out within the framework of the Dirichlet-Robin fluid-solid interface procedure and with conditions strictly identical to those adopted in the mathematical model. These coupled computations have been synthesized in five representative cases. The computed results show that the stability limit and the numerical Biot number derived from the coupling model are very reliable parameters. Many other physical and numerical aspects, such as the splitting of the coupling period are also considered in this work from which some interesting and promising results are obtained. At the end of this paper, we assess the general potential, limits and constraints of the mathematical model and its extension to multidimensional cases is discussed. [ABSTRACT FROM AUTHOR]

Highlights • The optimal pitch ratio of the ribs mounted in a channel is provided based on inverse analysis. • The entransy dissipation was taken as the objective function in the inverse method. • Taking entransy dissipation as objective function leads to a fast and stable convergence process. Abstract The ribbed surface is a widely used convection heat transfer enhancement technology. The geometric parameters of the ribbed surface have great influences on its heat transfer performance. It is crucial to determine the optimum geometric parameters. In the present work, the optimal arrangement of ribs mounted in a rectangular channel is provided by solving the inverse optimization problem with the entransy dissipation as the objective function. The parameter analysis based on the direct solution is firstly carried out to get an approximate range near the optimal pitch ratio which can provide the initial value for the inverse optimization problem; afterwards, the inverse optimization problem is solved by a modified simplified conjugate gradient method, and the accurate optimal pitch ratio is obtained; finally the optimization results are discussed in detail. The results indicate that, (1) the inverse optimization analysis presented in this paper can provide an accurate optimal value of the pitch ratio; (2) taking the entransy dissipation as the objective function could lead to a faster converge process and give a more stable result than taking the temperature data as the objective function; (3) the optimal value under the fixed heat flux boundary condition is slightly larger than that under the fixed temperature boundary condition. [ABSTRACT FROM AUTHOR]

In numerical heat transfer, the model validation problem with respect to epistemic uncertainty, where only a small amount of experimental information is available, has been recognized as a challenging issue. To overcome the drawback of traditional probabilistic methods in dealing with limited data, this paper proposes a novel model validation approach by using evidence theory. First, the evidence variables are adopted to characterize the uncertain input parameters, where the focal elements are expressed as mutually connected intervals with basic probability assignment (BPA). In the subsequent process of predicting response focal elements, an interval collocation analysis method with small computational cost is presented. By combining the response BPAs in both experimental measurements and numerical predictions, a new parameter calibration method is then developed to further improve the accuracy of computational model. Meanwhile, an evidence-theory-based model validation metric is defined to test the model credibility. Eventually, the famous Sandia thermal challenge problem is utilized to verify the feasibility of presented model validation method in engineering application. [ABSTRACT FROM AUTHOR]

Heat losses from a building foundation are affected by both the surrounding conditions and the surrounding soil properties. These include many factors that complicate the analysis of heat loss, such as thermal storage, snow and soil freezing. The effect of snow and soil freezing was studied with a 3D simulation model in a subarctic climate. The heat losses from the most commonly used foundation types in Sweden were studied. This paper shows that it is possible to achieve a good thermal estimation of the air temperatures in a crawl space, with an average difference of 0.4 °C compared with the validation data over a year. Snow and soil freezing reduce the annual heat losses through the different foundation types by 7–10% and the maximum heat loss rate by 13–25%. In order to describe the heat transfer correctly, snow must be included in the calculations, while soil freezing has only a minor impact. The 3D model implemented in this study shows a significant impact on the soil temperatures when these parameters are included. For a subarctic climate, the commonly used calculation methods based on the European standard ISO 13370 are not thorough enough to calculate the heat transfer through a foundation accurately. [ABSTRACT FROM AUTHOR]

District Heating (DH) systems are commonly supplied using local heat sources. Nowadays, modern insulation materials allow for effective and economically viable heat transportation over long distances (over 20 km). The paper proposes a Decision Support System (DSS) for optimized selection of design and operating parameters of a long distance Heat Transportation System (HTS). The method allows for evaluation of feasibility and effectiveness of heat transportation from the considered heat sources to the given DH area. The optimized selection is formulated as the multicriteria decision-making problem. The constraints for this problem include a static HTS model, allowing considerations of the system life cycle, as well as time variability and spatial topology. Thereby, the variation of heat demand and ground temperature within the DH area, the insulation and pipe aging, as well as the terrain elevation profile are taken into account in the decision-making process. The HTS construction costs, the operating costs (pumping power), and the heat loss are considered as objective functions, while such parameters as: inner pipeline diameter, insulation thickness, temperature and pressure profiles, as well as pumping station locations are optimized during the decision-making process. Moreover, variants of pipe laying e.g. one pipeline with a larger diameter, or two parallel pipelines with smaller diameters might be considered during the optimization. The analyzed optimization problem is multicriteria, hybrid and nonlinear. The genetic solver has been proposed to solve it. [ABSTRACT FROM AUTHOR]

In this paper, a numerical model describing the heat transfer and air flow inside and outside the casing of the permanent magnet brushless direct current (PM BLDC) motor is presented. In the model, a conjugate heat transfer including the heat conduction with heat sources in windings, magnets, bearings, natural and forced convection and radiation phenomena within internal and external air domain were analysed. The complex geometrical model included windings, a magnet circuit, a rotor with neodymium magnets, a PCB electronic plate, plastic covers, internal air between solid parts as well as a portion of the external air. The validation process of the developed model was realised on the basis of the velocity and temperature fields. The experimental data were recorded by 7 constant temperature anemometers at 4 levels above the motor housing, Laser Doppler Anemometry sensors in two axes inside the rear portion of the motor and 25 thermocouples fixed inside and outside the motor. The experimental and numerical tests were performed for 4 motor loadings and 3 rotational speeds. The average temperature error for the internal point was of 9 K, while that of the external points was of 2 K. The velocity field was very well predicted close to the housing wall in terms of horizontal and vertical components. A slightly worse agreement was found for the vertical component, especially in the vicinity of the shaft. The results were consistent for all the considered motor loadings and rotational speeds. [ABSTRACT FROM AUTHOR]

The convection onset in a evaporation thermal model of a solute/solvent solution is numerically studied. The transient nature of the diffusion temperature profile requires to control the perturbations which will lead to the transition to a convective flow. Contrary to previous papers, we adopted here a perturbation mode, which is physical and experimentally reproducible, by accounting for a heat transfer at the lateral walls. Based on the Péclet number evaluated in the core flow field only, the critical viscosities and the corresponding times for the transition between a diffusion and convection regimes were calculated as a function of the fluid layer thickness, the aspect ratio and the convective heat transfer coefficient. The study of the spatio-temporal diagrams allowed us to characterize the way the convection propagates in the fluid domain as well as the evolution of the mean cell size and wavenumber. [ABSTRACT FROM AUTHOR]

The multi-term time-fractional diffusion equation is a useful tool in the modeling of complex systems. This paper aims to develop a high order numerical method for solving multi-term time-fractional diffusion equations. Based on the space-time spectral method, a high-order scheme is proposed in the present paper. In this method, the Legendre polynomials are adopted in temporal discretization and the Fourier-like basis functions are constructed for the spatial discretization. Such a space-time spectral method possesses high efficiency and exponential decay in both time and space directions. Rigorous proofs are given here for the stability and convergence of the scheme. Numerical results show good agreement with the theoretical analysis. [ABSTRACT FROM AUTHOR]

This paper numerically investigates the performance and heat and mass transfer processes that occur in counter-flow indirect evaporative air coolers. Different types of counter-flow air coolers were compared: a typical counter-flow unit, the same unit operating as a heat recovery exchanger, a regenerative unit and a novel modified exchanger, proposed by authors. Additionally the paper investigated impact of location of the perforated holes in the channel plate of regenerative air cooler. The numerical model is based on a one-dimensional heat and mass transfer analysis that was validated against existing experimental data. The results obtained from the simulation reveal the high effectiveness of the presented units. It was established that selected arrangements of the presented exchangers are characterized by the different efficiency in different air-conditioning applications. [ABSTRACT FROM AUTHOR]

In the present investigation, a non-linear mathematical model is developed for the analysis of Septuple effect flat falling film evaporator (SEFFFE) system used for concentrating black liquor in a nearby paper mill. This model is capable of simulating process of evaporation considering variations in boiling point rise (τ), overall heat transfer coefficient (U), heat loss (Q loss), flow sequences, liquor/steam splitting, feed, product and condensate flashing, vapor bleeding and physico-thermal properties of the liquor. Based on mass and energy balance around an effect a cubic polynomial is developed and solved repeatedly in a predetermined sequence using generalized cascade algorithm. For development of empirical correlations for τ, U and Q loss, plant data have been collected from SEFFFE system. These correlations compute τ, U and Q loss within average absolute errors of 2.4%, 10% and 33%, respectively, when their results are compared with the plant data. [Copyright &y& Elsevier]

• A mathematical model based on non-equilibrium formulation was established. • The simulation results show better accordance with the experimental results compared with the model based on equilibrium formulation. • The heat and mass transfer during the drying stage were analyzed. • The effects of different operating parameters on the drying time were investigated. Spray freeze drying has been expanding its influence in many fields. However, the long duration dramatically hinders its further development. A model established based on non-equilibrium formulation was established in this paper. The accuracy of the model proposed with that established based on equilibrium formulation was compared. And the history of temperature, vapor concentration and ice saturation were then investigated. Lastly, the effects of product thickness, particle diameter on the drying time were investigated. The simulation results reproduce well with the experimental data, and show a better agreement with the increase rate of experimentally measured temperature curve than that based on equilibrium formulation. In addition, the temperature increases from the bottom to the top region while the vapor concentration distribution presents the opposite trend. The ice saturation first obtains a slight increase and then decreases. Lastly, the drying time decreases as: (i) the product thickness decreases, (ii) the packing porosity increases and (iii) the chamber temperature increases. The mathematical model proposed in this paper could offer better understanding of the process and guide the design and optimization for the process. [ABSTRACT FROM AUTHOR]

In consideration of droplet flash evaporation and film flash evaporation, a comprehensive mathematical model of vacuum flash evaporation cooling (VFEC) was presented in this paper. Pure water was considered to be the working fluid. The droplet flash evaporation was modeled based on the diffusion-controlled evaporation model, while the film flash evaporation was modeled based on the film penetration theory. The droplet flash model coincided well with the experimental results reported in the literature and the comprehensive mathematical model was validated by experiment results in this paper. The droplet temperature and diameter after droplet flash evaporation were obtained numerically, and then analyzed. The effect of droplet flash evaporation on the surface temperature distribution, heat flux density, and heat transfer ratio of different mechanisms was studied based on the model. It can be concluded that the droplet flash evaporation, which can be expressed by the ratio of droplet-wall impaction heat transfer, had a great effect on vacuum flash evaporation cooling heat transfer. The droplet-wall impaction and film flash heat transfer were dominant in the vacuum flash evaporation cooling. The spray characteristics such as droplet diameter and temperature decreased a lot after droplet flash evaporation, compared to the initial parameters (measured by the PDA). After taking droplet flash into account, the surface temperature decreased and the heat flux increased. [ABSTRACT FROM AUTHOR]

This paper discusses the effect of temperature polarization in Vacuum Membrane Distillation (VMD). The main motivation for using VMD in this work is that this module configuration is much simpler and more suitable for this kind of investigation than the other MD configurations such as Direct Contact Membrane Distillation (DCMD). The coupling between heat and mass transfer mechanisms at the feed-membrane interface is presented from a theoretical point of view. In addition, a new simple graphical method and a mathematical model for determining VMD flux are presented. The two methods used in evaluating the extent of temperature polarization effect on water vapor flux (flux sensitivity factors and temperature polarization coefficient (TPC)) are also analyzed and compared. The effect of integrating a heat recovery system in a large scale module on the TPC coefficient has also been studied and presented in this paper. [ABSTRACT FROM AUTHOR]

Abstract: Modeling subcooled flow boiling in vertical channels at low pressures requires not only the consideration of the dynamic behaviors of two-phase flow and bubbles undergoing coalescence, breakup and condensation in the bulk subcooled liquid but also the characterization of the single-phase and local boiling heat transfer phenomena in the near-wall region. The focus of this paper is the assessment of the heat flux partitioning model in handling the latter physics of subcooled flow boiling. In order to achieve closure to the model, the current prevailing approach has always been the utilization of empirical correlations particularly for the active nucleation site density, bubble departure diameter and bubble departure frequency. A comprehensive survey of existing empirical correlations is presented in the first part of this paper to assess the performance of these empirical models. Selected combinations of empirical correlations are compared and validated against axial and local radial experiments encompassing a wide range of different mass and wall heat fluxes and inlet subcooling temperatures for subcooled flow boiling at low pressures. Based on the comparisons made against the axial and local distributions of void fraction and bubble Sauter diameter, not one single combination of empirical correlations has shown the propensity of providing satisfactory predictions covering the entire axial and local conditions. For the modeling of subcooled flow boiling at low pressures to become an effective predictive tool, it must therefore be complemented with further consideration of first principal models of the underlying physical phenomena. [Copyright &y& Elsevier]

Despite the fact that the conventional one-dimensional model for counter-flow spray separation tower is advanced in reasonable accuracy as well as time and computational resources saving, it fails to describe the physical processes in details. In this paper, the concept of supersaturated state of the moist air was introduced, then a new sectional one-dimensional model was developed with a detailed derivation. A prototypic apparatus was set up and the reliability of the model was validated by the experimental study. When predicting the outlet solution temperature and outlet moist air wet bulb temperature, the relative errors would be more pronounced with a bigger heat and mass transfer driving potential, but they would not exceed 3.59% and 9.54% respectively under the experimental conditions. The simplifying assumptions, the ignored heat and mass transfer at cyclone region and the measuring errors are mainly blamed for the predicted errors. An in-depth heat and mass transfer investigation was conducted with the help of the validated model by studying the profiles of humidity ratio and moist air dry bulb temperature. The proposed model succeeded in capturing the state transformation of the air flow along the axis of the tower and the effects of the operating parameters on the process profiles are discussed. [ABSTRACT FROM AUTHOR]

Large eddy simulations (LES) of combustion instabilities are often performed with simplified thermal wall boundary conditions, typically adiabatic walls. However, wall temperatures directly affect the gas temperatures and therefore the sound speed field. They also control the flame itself, its stabilization characteristics and its response to acoustic waves, changing the flame transfer functions (FTFs) of many combustion chambers. This paper presents an example of LES of turbulent flames fully coupled to a heat conduction solver providing the temperature in the combustor walls. LES results obtained with the fully coupled approach are compared to experimental data and to LES performed with adiabatic walls for a swirled turbulent methane/air burner installed at Engler-Bunte-Institute, Karlsruhe Institute of Technology and German Aerospace Center (DLR) in Stuttgart. Results show that the fully coupled approach provides reasonable wall temperature estimations and that heat conduction in the combustor walls strongly affects both the mean state and the unstable modes of the combustor. The unstable thermoacoustic mode observed experimentally at 750 Hz is captured accurately by the coupled simulation but not by the adiabatic one, suggesting that coupling LES with heat conduction solvers within combustor walls may be necessary in other configurations in order to capture flame dynamics. [ABSTRACT FROM AUTHOR]

This paper examines the dynamics of the flame leading edge in a laminar premixed CH 4 /air flame stabilized on a bluff body in a channel. Harmonic fluctuations and step velocity change are used to simulate the flame response to acoustic oscillations, which are of primary importance in the study of thermo-acoustic instabilities. We use a fully resolved unsteady two-dimensional code with detailed chemistry and species transport, with coupled heat transfer to the bluff body. Calculations were conducted with different equivalence ratios, body materials, and steady state inlet velocity with step or harmonic perturbations. Results reveal that the flame leading edge dynamics displays a peak response around St = 0.5 suggesting that the leading edge motion is mainly due to the advection of appropriate ignition conditions as a result of the excitement of the wake recirculating flow. There is considerable augmentation of the flame wrinkles generated by the flame leading edge motion as result of the flow–flame interaction. Additionally, we show that a flame that anchors on average further upstream leads to stronger damping of the shear layer vortices and thus weaker vortex-flame interaction and heat release fluctuations. Hence, we identify two different mechanisms by which the flame leading edge location and oscillation amplitude impact heat release fluctuations. The study suggests a stronger dependence of the overall flame wrinkling and heat release fluctuations on the flame leading edge dynamics than recognized previously and the potential role it plays in combustion dynamics. [ABSTRACT FROM AUTHOR]

An analytical estimate of the effective thermal conductivity of a pebble bed with mono-sized pebbles in the presence of a stagnant gas is presented. The Discrete Element Method (DEM) is used to simulate granular assemblies under uniaxial compression and Resistor Network (R-N) model is applied for estimating the effective thermal conductivity numerically. In this paper, two heat transfer paths, i.e., conduction through pebble–pebble contact and pebble–gas–pebble interface are considered. The effect of the cutoff range for gap and the strain on the effective conductivity is studied. The validity of the analytical model is verified with the results from the R-N Model for different solid-to-gas thermal conductivity ratios and for different packing fractions. The analytical and numerical models show a good agreement with the experimental results of the effective thermal conductivity for lithium orthosilicate pebble beds in the presence of helium and air at different temperatures. [ABSTRACT FROM AUTHOR]

In order to investigate the effects of the buoyancy and finite size particles on the heat transfer process in the turbulent thermal boundary layer, we have carried out three simulations in the present paper, a single-phase neutral boundary layer, an unstable boundary layer with buoyancy effect, and a multi-phase boundary layer with thousands of finite size particles. This is the first time that particle-resolved direct numerical simulation (PR-DNS) is used in the study of thermal boundary layer. The DNS results show the turbulent statistics as well as the thermal structures. It turns out that both the buoyancy and the finite size particles will dramatically affect the turbulent statistics of the boundary layer. Detailed comparisons between the three simulations reveal that the buoyancy effect reshapes the coherent structures in the boundary layer, while finite size particles mainly induce additional disturbance all over the computational domain. Specifically, the Reynolds shear stress and the wall normal turbulent heat flux are remarkably enhanced in the log region by the effect of buoyancy. On the other hand, the finite size particles cause remarkable increment of velocity fluctuations all over the boundary layer, while have the effect of stabilizing temperature fluctuation near the wall. [ABSTRACT FROM AUTHOR]

Flow resistance and enhanced heat transfer characteristics of TiO 2 -water nanofluids in a stainless-steel corrugated tube and a circular tube are investigated by experimental and numerical methods respectively. The flow and heat transfer characteristics of TiO 2 -water nanofluids and deionized water in test tubes are compared in this paper. In addition, effects of Reynolds number ( Re ) and nanoparticle mass fraction ( ω ) on flow and heat transfer performances are discussed respectively, and Nusselt number ( Nu ) and resistance coefficient ( f ) are studied respectively. Finally, comprehensive performance of flow resistance and heat transfer enhancement is evaluated. It can be obtained that adding nanoparticle into deionized water doesn’t cause a large additional resistance loss in some degree, while the combination of corrugated tube and TiO 2 -water nanofluids shows an excellent heat transfer enhancement, which can enhance the heat transfer by 53.95% at maximum extent. In addition, the corrugated tube has a strong sustainability in enhancing heat transfer. The enhanced heat transfer rising part (6000 ≤ Re ≤ 10,000) has a large rising slope (about 7.90E−5), and the descending slope (about 7.16E−6) of enhanced heat transfer part (10,000 ≤ Re ≤ 12,000) is small. [ABSTRACT FROM AUTHOR]

Existence of magnetic field causes heat transfer to reduce in free convection but in several engineering uses for example: electronic application; enhancing heat transfer is a purpose. Thus, nanofluid should be selected as working fluid. Nanofluid is dispersion of very small metal particles in the base fluid. Two phase and single phase are two ways for estimating the behavior of nanofluid. At first model, nanofluid suppose as homogenous fluid without any slip mechanism. But in second method, slip velocities are included. Brownian motion and Thermophoresis impacts are taken into consideration in second approach. In this paper, previous publications about nanofluid hydrothermal treatment in existence of magnetic field are reviewed. Rely of variable and constant magnetic fields, Ferrohydrodynamic (FHD) and Magnetohydrodynamic (MHD) can take role in simulations. Numerical and analytical methods are considered by authors. Results proved that temperature gradient augments with augment of solid particle concentration and buoyancy forces, while it decreases with augment of magnetic field. [ABSTRACT FROM AUTHOR]

This paper reports the effect of changing the aspect ratio on the heat transfer and flow quantities over in-line tube banks. Two types of in-line arrangements were employed; square and non-square configurations. The models that were examined are a standard k-ε model, SST k-ω model, v2-f model, EB k-ε model and EB-RSM model. The closer results to the experimental data and LES were obtained by the EB k-ε and v2-f models. For the square pitch ratios, the solution has faced a gradual change from a strong asymmetric to asymmetric and then to a perfect symmetry. The strong asymmetric solution was found by the very narrow aspect ratio of 1.2. However, the behaviour of cases of 1.5 and 1.6 became less strong than that predicted in the case of 1.2. In the larger aspect ratio of 1.75, the flow behaviour is seen to be absolutely symmetric for all variables under consideration except Nusselt number. For the very large pitch ratio of 5, the flow has recorded maximum distributions for all parameters on the windward side of the central tube with a perfect symmetric solution around the angle of 180° while the vortex shedding frequency has recorded minimum value and the Strouhal number; therefore, has given the smallest value. However, for the non-square pitch ratio of constant transverse distance, the solution is still asymmetric for all parameters with merely one stagnation at the angle of 52° at the case of the 1.5 × 1.75 while by increasing the longitudinal distance to 2 and 5, the solution provided a comprehensive symmetry for all variables with two vortices are fully developed mirrored in shape on the leeward side of the central tube. On the contrary, for the non-square pitch ratio of constant longitudinal distance, the flow of the case of 1.75 × 1.5 provided two stagnation locations at around 52° and 308° with a very similar solution to the case square ratio of 1.75 for all variables whereas by increasing the transverse distance to 2 and 5, the solution recorded was not perfectly symmetric resulting in two different vortices and one stagnation position located at the leading edge of the cylinder provided by the case of 5 × 1.5. In terms of vortex shedding effect, the reduction in the Strouhal number at a constant transverse pitch is less steep than those at a constant longitudinal pitch. [ABSTRACT FROM AUTHOR]

In this paper, a numerical study of heat and mass transfer in counter-flow indirect evaporative air coolers is presented using an approach proposed by previous work. The mathematical model equations of continuity, momentum, energy and concentration are solved by the finite volume method to obtain the value of primary outlet dimensionless temperature. This mathematical model developed is validated against published data acquired from literature. The key target of presented analysis is to develop a performance correlation based on five dimensionless factors: ratio of channel length to half width of secondary air channel, ratio of water to secondary air mass flow rate, primary air inlet Reynolds number, secondary air inlet dimensionless temperature and water film inlet dimensionless temperature. Numerical simulations are performed by changing the value of each dimensionless factor under a constant value for other parameters. The simulation results are regressed to obtain the empirical constants of the correlation. The value of outlet dimensionless temperature is varied from 0.47 to 0.92. The developed correlation can predict the performance of the counter-flow indirect evaporative air coolers within a discrepancy of 12.6%. The correlation would be helpful to provide a simpler equation to improve the calculation speed within the engineering allowable accuracy range. [ABSTRACT FROM AUTHOR]

The plate-fin structure with high efficiency of heat transfer is a type of periodic pore material. The equivalent homogenization method has been proposed to design the strength of plate-fin structure, and it is essential to calculate homogenized elastic constants of the pore structure. This paper proposed an analytical model to calculate homogenized elastic constants of the plate-fin structure including the elastic modulus, shear modulus and Poisson's ratio. These proposed equivalent formulas have considered the effects of geometrical parameters. The finite element method and experimental study have also been performed to verify the analytical method. In addition, the effects of geometrical parameters on homogenized elastic constants have been fully studied. The results show that homogenized elastic constants by the proposed analytical model show a good agreement with results by FEM and experimental. It has been proved that the stretching deformation is the dominating deformation mechanism of the fin in Z -direction and only the fin paralleled to Y -direction can influence the tensile deformation in Y -direction. The homogenized elastic constants are strongly dependent on the geometrical parameters. This work provides theory formulas to calculate basic mechanical constants for conducting the full-scale design of plate-fin structure by equivalent homogenization method. [ABSTRACT FROM AUTHOR]

This paper presents a mathematical model to determine the minimum energy targets for a batch process with flexible schedule. Techniques developed for flexible-schedule batch processes typically result in nonlinear formulations. The proposed model was formulated as a mixed integer linear programming model (MILP). The model is developed based on the source-demand classification of process streams instead of the typical classification of hot and cold streams. In such classification, each stream is simultaneously treated as a source at its shifted supply temperature, and as a demand at its shifted target temperature. Such classification eliminates the model's non-linearity and reduces its complexity as well as the solution time. The mathematical model can be used to calculate the utility targets for a flexible-schedule batch process. Application of the proposed mathematical formulation demonstrates significant energy saving potential. The first illustrative example predicted a potential reduction of 11% cold utility and 14% hot utility. In the second illustrative example, up to 35% hot utility reduction and 62% cold utility reduction could be achieved. [ABSTRACT FROM AUTHOR]

The paper deals with the development of convective flows in a complex system of thin liquid layers occurring under the effect of thermal load. To study this process a mathematical model which is based on the decomposition of complex problem into unitary elements (modules) with some set of rules allowing their linkage with each other was constructed. Each module represents a monotypic local model. The fluid flow and heat transfer in each of these modules are described by the Navier-Stokes and thermal conductivity equations. The boundary conditions required to solve these systems of equations are represented explicitly and written in the form of conservation laws. The numerical analysis of effect of thermal load on the characteristics of the liquid layers movement depending on the Marangoni number is carried out. It is shown that physical and thermophysical properties of liquid layers play the decisive role. It is exactly they control the convective flows in layers and determine the position and shape of interfaces. The results of model problem solutions are presented. [ABSTRACT FROM AUTHOR]

The present paper presents fluid flow and mixed convective heat transfer characteristics past a semi-circular cylinder at incidence with a tandem square cylinder in cross flow. Using air ( Pr = 0.71 ) as an operating medium, numerical simulations are performed for the range of Reynolds numbers, 10 ≤ Re ≤ 45 and incidence angles, 0 0 ≤ α ≤ 180 0 . The effect of thermal buoyancy is brought about by varying the Richardson number in the range 0 ≤ R i ≤ 2 . The mathematical model is firstly validated with the experimental and numerical results from the literature and found to be in good agreement. The steady separated flow is observed to become unsteady periodic under the superimposed thermal buoyancy. Furthermore, apart from thermal buoyancy effect, angle of incidence is found to play a pivotal role in bringing hydrodynamic instabilities and thereby vortex shedding for such steady mixed convective flows. Functional dependence of drag ( C D ) , lift ( C L ) , and moment ( C M ) coefficients on the combined influence of α and R i , is explored and analysed in detail. Additionally, other global quantities, such as local and average Nusselt number distribution, Strouhal number ( S t ) are determined with respect to the various ranges of parameters considered in the present investigation. [ABSTRACT FROM AUTHOR]

• Molecular distillation processes and equipment have been revised. • Molecular distillation models and the corresponding equations governing the mass, energy and momentum phenomena have been reviewed. • Thermodynamic and transport properties estimation methods of natural-based mixtures were reviewed. • Several molecular distillation applications on different mixtures have been presented and summarized including operation conditions. Molecular distillation is a separation technique used to separate thermosensible compounds. This process is often used to obtain concentrates of value-added products. For this reason, the research in this field has grown steadily during the past years. However, many efforts to simulate the transport phenomena occurring in this process and the thermodynamic properties of the molecules to be separated have fallen flat. Achieving a simulation that resembles what occurs in this process requires a thorough understanding of the molecular behavior of various substances under different conditions. This paper reviews several recently proposed methodologies to predict this behavior during the molecular distillation process. Thus, group contribution models and empirical correlations are used to estimate the value of some properties and coefficients which, in turn, determine the specific ways in which heat, mass, and momentum vary in a Molecular Distillation separation system. The transfer equations are discussed in mathematical models. Thin film, vapor phase, molecule collision, and mean free path are also important topics in molecular distillation, so they are also discussed in this review. Finally, some applications are summarized and a new case for the cannabis industry is supported. [Display omitted] [ABSTRACT FROM AUTHOR]

Abstract: This paper proposes a new frequency domain method to model the heat transfer between the injected/extracted heat and the temperature of the fluid exiting a borehole heat exchanger. The method is based on in situ measurements and focuses particularly on the short-term borehole heat transfer. It uses a rational function of the Warburg variable in the Laplace domain to model the borehole heat transfer. The rational model is transformed to a time domain model using inverse Laplace transformation. This time domain model makes it possible to calculate the temperature response on a random heat variation signal. The paper also demonstrates a new way to perform the classical thermal response test. Instead of injecting a constant amount of heat, the experiments have been performed using multiple short-duration heat injections. In this way, the obtained rational heat transfer model contains information about both the short- and the long-term heat transfer. The results obtained using the proposed modeling method are compared with those obtained from a state-of-the-art analytical method. The time domain model can be used to design a controller to optimize the performance of a Ground Source Heat Pump system, the efficiency of which depends strongly on the temperature of the fluid exiting the borehole. [Copyright &y& Elsevier]

Abstract: Along with the developments of lattice-Boltzmann method in simulation of fluid flow, its thermal features should be also improved. An important problem which is encountered in many cases is the conjugate heat transfer or heat transfer at the fluid–solid interface. In this case, a strict technique is required to calculate the heat exchange between fluid and solid. Only a few works have been published regarding this phenomenon. In this paper, we have presented a model for analysis of the conjugate heat transfer. The model has been validated by two benchmarks: (I) Fluid flow and heat transfer in a backward-facing step channel with heated thick wall, and (II) Fluid flow and heat transfer in a channel with infinite number of heated obstacles mounted on the wall. The numerical tips concerned in the simulation of these problems by lattice-Boltzmann method have been also represented in the paper. [Copyright &y& Elsevier]

Abstract: In this paper, a transient numerical model for a liquid-to-air membrane energy exchanger (LAMEE) is developed and the results are compared to the experimental data. The data for the sensible, latent and total effectiveness are compared with transient and steady-state simulations for various values of NTU and operating parameters (Cr∗, inlet temperature and humidity) while the exchanger undergoes a step change in inlet conditions and reaches a new steady-state. The transient and steady-state performances are shown to be a function of the design and operating parameters. The paper also shows that buoyancy forces become important and affect the LAMEE performance under certain operating conditions. The verified numerical model is used to investigate the impact of outdoor air conditions on the LAMEE performance. [Copyright &y& Elsevier]

The ammonothermal crystal growth technique is one of the most effective methods used for growing Gallium Nitride (GaN) crystals in terms of the final product quality and manufacturing efficiency. Popular applications of GaN crystals include light emitting diodes (LEDs) and high-frequency electronic devices. A laterally-heated cylindrical enclosure with a top to bottom temperature gradient is considered in this study to investigate the fluid mechanics and heat transfer in an ammonothermal crystal growth reactor. Three-dimensional (3D) large eddy simulations (LES) results of natural convection in a laterally heated cylindrical reactor, using the commercial computational fluid dynamics (CFD) software, ANSYS FLUENT, are presented in this paper for a Rayleigh number ( R a ) of 8.8 × 10 6 . The R a is defined based on a length scale that is equal to the ratio of volume to the lateral area of the cylinder ( R / 2 ). In addition, an experiment of a geometrically- and dynamically-similar geometry is developed, and particle image velocimetry (PIV)-based flow visualizations are carried out for the purpose of validating the numerical model. Comparisons between experiments and numerical simulations showed that flow patterns were qualitatively similar, and Fourier transforms of velocity magnitudes at selected points in the domain matched reasonably well. An added interesting observation in the simulation was the existence of temperature inversion, which has potential implications on the choice of mineralizer (acidic/basic). [ABSTRACT FROM AUTHOR]

In this paper, a novel model is presented for predicting thermophysical properties of superheated steam (SHS) in offshore superheated steam injection wells (OSSIW). Firstly, a mathematical model comprised of mass, energy and momentum balance equations is proposed for OSSIW. Secondly, the distribution of temperature, pressure and superheat degree along the wellbores are obtained by finite difference method on space and solved by using the iteration technique. Then, model validation and sensitivity analysis are conducted. The results show that (1). The superheat degree increases at first but then turns to decrease with the increase of injection rate. (3). The superheat degree increases with the increase of injection temperature. (4). The superheat degree at well bottom increases at first but then turns to decrease with the increase of injection pressure. (5). The superheat degree in the wellbore has a drop when seawater starts to flow. [ABSTRACT FROM AUTHOR]

In this paper, mixed convection of non-Newtonian nanofluid, using the Buongiorno’s mathematical model in a cavity has been analyzed by Finite Difference Lattice Boltzmann method (FDLBM). The cavity is filled with nanofluid which the mixture shows shear-thinning behavior. The Prandtl number is fixed at Pr = 1. This study has been performed for the certain pertinent parameters of Richardson number ( Ri = 0.001, 0.01, and 1), buoyancy ratio number ( Nr = 0.1, 1, and 20), power-law index ( n = 0.2–1), Lewis number ( Le = 1, 5, and 10), Thermophoresis parameter ( Nt = 0.1, 0.5, 1), and Brownian motion parameter ( Nb = 0.1, 1, 5). Results indicate that the augmentation of the power-law index causes heat and mass transfer to drop at Ri = 0.001 and 0.01. The drop of Richardson number from Ri = 1 to 0.001 enhances heat and mass transfer for various power-law indexes. The increase in the Lewis number augments mass transfer while it causes heat transfer to drop. The rise of the Thermophoresis and Brownian motion parameters ameliorates mass transfer and declines heat transfer significantly. The augmentation of buoyancy ratio number enhances heat and mass transfer. [ABSTRACT FROM AUTHOR]

This paper aims to investigate the coupling influences of thermal loading and surface effects on pull-in instability of electrically actuated circular nanoplate based on Eringen's nonlocal elasticity theory, where the electrostatic force and thermally corrected Casimir force are considered. By utilizing the Kirchhoff plate theory, the nonlinear equilibrium equation of axisymmetric circular nanoplate with variable coefficients and clamped boundary conditions is derived and analytically solved. The results describe the influences of surface effect and thermal loading on pull-in displacements and pull-in voltages of nanoplate under thermal corrected Casimir force. It is seen that the surface effect becomes significant at the pull-in state with the decrease of nanoplate thicknesses, and the residual surface tension exerts a greater influence on the pull-in behavior compared to the surface elastic modulus. In addition, it is found that temperature change plays a great role in the pull-in phenomenon; when the temperature change grows, the circular nanoplate without applied voltage is also led to collapse. [ABSTRACT FROM AUTHOR]

Crystallization is generally considered as the most destructive factor of porous material, but few studies have reported the coupling effects among fluid flow, heat transfer, crystallization and deformation in porous media. In this paper, the driving forces of phase transition were studied initially and then the crystallization kinetics models were established. Moreover, constitutive relations related to saline frozen soil were discussed, and the expression of unfrozen water content in non-equilibrium state was improved. Finally, a thermo-hydro-salt-mechanical coupled model for fully saturated saline frozen soil with phase change was proposed. Validation of the model is illustrated by comparisons between the simulation and experimental results. The predicted values of frost heave, temperature and moisture distribution are consistent with the experimental data, and it is demonstrated that the presented crystallization kinetics approach is valid for studying heat and mass transfer coupled problem with phase change in porous media. [ABSTRACT FROM AUTHOR]

Abstract: The inlet fog cooling scheme has been considered as an economic and effective means to augment gas turbine output power on hot or dry days. A previous paper developed a stage-by-stage wet-compression theory for overspray and interstage fogging using the equilibrium droplet evaporation model with given compressor and blade configurations. This paper extends the previous work by including the non-equilibrium droplet heat transfer model. The equilibrium model assumes that water evaporates to saturation according to psychrometry at each stage without considering water evaporation rates, whereas the non-equilibrium model considers water evaporation rates according to heat and mass transfer of droplets. The non-equilibrium model can predict the different evaporation from different droplet sizes, but equilibrium model can''t. An 8-stage, 2-D compressor airfoil geometry and stage settings at the mean radii are employed. Eight different cases including saturated fogging, overspray with different droplet sizes with both equilibrium and non-equilibrium heat transfer models have been investigated and compared. The results show saturated fogging increases the pressure ratio and reduces the compressor power consumption; however, overspray actually increases both the specific and total compressor power consumption. For small droplet size of 10 μm, the droplet evaporation rate is fast, so the non-equilibrium method predicts results close to the equilibrium method. Larger droplets lead to slower evaporation, reduction of pressure ratio, and less effective compressor performance than the smaller droplets. The equilibrium method predicts that wet compression increases axial velocity, blade inlet velocity, incidence angle, and tangential component of velocity. The non-equilibrium methods predict a similar trend except with lesser increments as the droplet size increases. In the present study, the equilibrium method predicts that all the water droplets evaporate completely at the end of stage 3, while the non-equilibrium approach predicts that the completion of evaporation delays, but all droplets completely evaporate in the compressor except the biggest droplets (30 μm). Saturated fogging increases air density; however, both equilibrium and non-equilibrium methods predict that overspray wet compression actually reduces air density in the earlier 70% of the compressor. The non-equilibrium model predicts that small droplets relax the load in the earlier stages but increase the load in the later stages. Larger droplets show less load changes. Detailed stage-to-stage performance and property value changes are analyzed and discussed in this study. [Copyright &y& Elsevier]

Abstract: This paper introduced the concept, potential application and benefits relating to a novel solar photovoltaic/loop-heat-pipe (PV/LHP) heat pump system for hot water generation. On this basis, the paper reported the process and results of characterizing the performance of such a system, which was undertaken through dedicated thermo-fluid and energy balance analyses, computer model development and operation, and experimental verification and modification. The fundamental heat transfer, fluid flow and photovoltaic governing equations were applied to characterize the energy conversion and transfer processes occurring in each part and whole system layout; while the energy balance approach was utilized to enable inter-connection and resolution of the grouped equations. As a result, a dedicated computer model was developed and used to calculate the operational parameters, optimise the geometrical configurations and sizes, and recommend the appropriate operational condition relating to the system. Further, an experimental rig was constructed and utilized to acquire the relevant measurement data that thus enabled the parallel comparison between the simulation and experiment. It is concluded that the testing and modelling results are in good agreement, indicating that the model has the reasonable accuracy in predicting the system’s performance. Under the given experimental conditions, the electrical, thermal and overall efficiency of the PV/LHP module were around 10%, 40% and 50% respectively; whilst the system’s overall performance coefficient (COPPV/T ) was 8.7. Impact of the operational parameters (i.e. solar radiation, air temperature, air velocity, heat-pump’s evaporation temperature, glazing covers, and number of the absorbing heat pipes) to the performance of the system (in terms of efficiencies of the PV/LHP module and the system’s overall performance coefficient COPPV/T ) was investigated individually. The results indicated that lower solar radiation, lower air temperature, higher air velocity and smaller cover number led to enhanced electrical efficiency but reduced thermal efficiency of the module; whereas lower heat-pump’s evaporation temperature and larger number of heat absorbing pipes gave rise to both thermal and electrical efficiencies of the module. The research results would assist in developing a high efficient solar (space or hot water) heating system and thus contribute to realisation of the energy saving and associated carbon emission targets set for buildings globally. [Copyright &y& Elsevier]

Abstract: This paper discusses results of simulations conducted for non-contacting face seals showing the influence of the operational parameters on the distributions of temperature in the structural elements and the fluid film separating the sealing rings. The mathematical model developed for noncontacting face seals consists of cross-coupled differential equations with partial derivatives. We solved it analytically, taking into account various boundary conditions. The heat equations were solved using the method of separation of variables. The derived relationships were based on Bessel functions of the first and second kinds. By defining the relationships describing the distributions of temperature in the sealing rings and the fluid film separating them, we could determine the effect of the operational parameters on the variability of temperature fields. Confirmation of the simulation results with experimental data is essential to better recognize the phenomena taking place in the sealing assembly and improve the design of non-contacting seals so that they can be used in various industrial applications. In this paper, we also describe a specially designed test stand for compensation of the misalignment of the flexibly mounted ring and automatic control of the radial clearance height. The test stand can also be used to verify the results of analytical studies. [Copyright &y& Elsevier]

This study numerically examines three-dimensional natural convection of air induced by temperature difference between a cold outer cubic enclosure and a hot inner cylinder. Simulations have been carried out for Rayleigh numbers ranging from 10 3 to 10 7 and a titled angle of the enclosure varying from 0° to 90°. The developed mathematical model is governed by the coupled equations of continuity, momentum and energy and is solved by finite volume method. The effects of cylinder inclination and Rayleigh number on fluid flow and heat transfer are presented. The distribution of isocontours of temperature, components of velocity and streamtraces eventually reaches a steady state for Rayleigh numbers ranging from 10 3 to 10 7 for titled inclination of 90°. However, for the remaining inclinations, Rayleigh numbers must be in the range 10 3 –10 6 to avoid unsteady state which is manifested by the subdivision of the area, containing the maximum local heat transfer rate, into three parts for a Rayleigh number equal to 10 7 and an inclination of 90°. We mention that instability study is not included in the present paper which is solely devoted to three dimensional calculations. Results indicate also that optimal average heat transfer rate is obtained for Rayleigh number set to 10 6 and an inclination of 90° for both cases of the inner cylinder and lateral walls of cubical enclosure. [ABSTRACT FROM AUTHOR]

In this paper, a numerical investigation is presented to study Buongiorno's mathematical model for hydromagnetic free convection flow in an isosceles triangular cavity filled with nanofluid. The inclined walls of the cavity are maintained at constant cold temperature whereas various combinations of the thermal boundary conditions at the bottom heated wall are considered. The cavity is permeated by an inclined uniform magnetic field and the effects of Brownian motion and thermophoresis are incorporated into the nanofluid model. The Galerkin weighted residual finite element method has been employed to solve the governing partial differential equations after converting them into a non-dimensional form using a suitable transformation of variables. In the numerical simulations, alumina-water based nanofluid has been taken into account. Comparisons with previously published work are performed and excellent agreement is obtained. The effects of various parameters such as Hartmann number, Rayleigh number and inclined magnetic field angle on streamlines, isotherms and isoconcentrations have been displayed graphically. The heat transfer augmentation for various combination of model parameters as well as various thermal boundary conditions have been done in light of the average Nusselt number from the bottom heated wall. The results show that the heat transfer rate can be decreased with the increasing values of the Hartmann number and inclination angle of the magnetic field but it can be increased by increasing the Rayleigh number and by reducing the diameter of the nanoparticles. The obtained numerical results also indicate that the variable thermal boundary conditions have significant effects on the flow and thermal fields. [ABSTRACT FROM AUTHOR]

A numerical model for heat and mass transfer in vacuum membrane distillation (VMD) under laminar flow was developed using Computational Fluid Dynamics (CFD). Three-dimensional (3D) simulations of temperature and concentration polarization in single and multiple fibre VMD modules were used to estimate permeate flux (kg m −2 h −1 ) over a range of temperatures (30–70 °C), vacuum pressures (10–100 mmHg), crossflow velocities (0.0072–0.72 m/s), and feed concentrations (0–0.4 kg/L NaCl). Simulated flux differed by less than 7% from experimental data for a module with comparable dimensions. Simulations indicate that a 56% increase in fibre packing density resulted in a 24% flux decline at high operating temperature (70 °C), and more than 50% flux decline at low crossflow velocity (0.0072 m/s). The effect of vacuum pressure on flux was found to be independent to the module packing density, while the effect of salt concentration was found to be 28% lower than estimates based on Raoult's law, due to lower spatial variations in membrane surface temperatures at higher salt concentrations. The approach developed in this paper may be used to evaluate performance of alternative configurations for VMD models to aid module design, scale-up and process optimization. [ABSTRACT FROM AUTHOR]