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Abstract: In this paper, a rigorous MILP formulation for grass-root design of heat exchanger networks is developed. The methodology does not rely on traditional supertargeting followed by network design steps typical of the Pinch Design Method, nor is a non-linear model based on superstructures, but rather gives cost-optimal solutions in one step. Unlike most models, it considers splitting, non-isothermal mixing and it counts shells/units. The model relies on transportation/transshipment concepts that are complemented with constraints that allow keeping track of flow rate consistency when splitting takes place and with mechanisms to count heat exchanger shells and units. Several examples from the literature were tested, finding that the model usually obtains better solutions. In some cases, the model produced unknown solutions that were not found using superstructure optimization methods, even when the same pattern of matches is used. [Copyright &y& Elsevier]

Abstract: A state-of-the-art review of horizontal-tube, falling film evaporation is presented; the review is critical, in an attempt to uncover strengths and weaknesses in prior research, with the overall purpose of clearly identifying gaps in our understanding. The review covers flow-pattern studies, and the experimental parameters that affect the heat transfer performance on plain single tubes, enhanced surfaces and tube bundles. In addition, this paper presents a comprehensive review of the significant efforts to develop mathematical models, and empirical correlations for the heat transfer coefficient. Emphasis is placed on studies that are related to refrigeration applications. [Copyright &y& Elsevier]

Knowledge of heat transfer in biological bodies has many therapeutic applications involving either raising or lowering of temperature, and often requires precise monitoring of the spatial distribution of thermal histories that are produced during a treatment protocol. Extremes of temperature into the freezing and burning ranges are useful in surgical procedures for selective killing and/or removal of target tissues. For example, the primary objective of hyperthermia is to raise the temperature of the diseased tissue to a therapeutic value, typically 41–44°C, and then thermally destroy it. The present paper therefore aims to develop a mathematical model for effective simulation of photo–thermal interactions between laser rays and biological tissues. In particular, damage of biological tissues when subjected to single point laser diathermy is numerically investigated using a unique enthalpy-based approach for modeling multiple phase change, (namely, melting of fat and vaporization of water content of the tissues) and the associated release/absorption of latent heat in conjunction with unsteady state heat conduction mechanisms. The governing equations of bio-heat transfer coupled with initial and boundary conditions are solved using a finite volume approach in conjunction with line by a line tri-diagonal matrix algorithm (TDMA) solver. Temperature responses of tissues subject to laser heating are quantitatively investigated in detail using the present model, and the resultant solutions are expected to be immensely useful in a variety of Bio-thermal practices in medicine and surgery. [Copyright &y& Elsevier]

Abstract: This paper presents a detailed analysis of the heat and mass transfer processes during the absorption of ammonia into water in a co-current vertical tubular absorber. The absorber configuration is of the shell and tubes type. The absorption process progresses as the vapour and liquid contact inside the tubes. Water is used as the absorber cooling medium. A differential mathematical model has been developed on the basis of mass and energy balances and heat and mass transfer equations, in order to provide further understanding of the absorber behaviour. The model takes into account separately for the churn, slug and bubbly flow patterns experimentally forecasted in this type of absorption processes inside vertical tubes and considers the simultaneous heat and mass transfer processes in both liquid and vapour phases, as well as heat transfer to the cooling medium. The model equations have been solved using the finite-difference method. Results obtained for specific data are depicted to show local values of the most important variables all along the absorber length. Parametric analyses have been performed to show the influence of design parameters and operating conditions on the absorber performance. The effect of the heat and mass transfer coefficients has also been evaluated. [Copyright &y& Elsevier]

In this paper a new mathematical model for calculating the indicator diagram of twin screw refrigeration compressor is presented firstly. The geometric parameters related to the rotation angle of male rotor are used in the model such as groove volume, suction and discharge port area, slide valve bypass port area, leakage area etc. The effects of internal leakage through five paths, oil injection, gas–oil heat transfer, refrigerant property and partial loading etc. are taken into account simultaneously and separately in the theoretical study. To verify the model and the calculated p–V indicator diagram, experimental recording of p–V indicator diagram of twin screw refrigeration compressor is carried out. Various indicator diagrams are recorded successfully by a small pressure sensor embedded in the bottom of female rotor at the discharge side. The results of theoretical calculation are in good agreement with the measured data, which lead to conclusion that the model can be used as a powerful tool for performance prediction and product development. [Copyright &y& Elsevier]

The calorific losses through the sidewalls delay drying, particularly in the higher racks of the foodstuff dryers, which provide us information on total drying time. One notes a temperature gradient of the air during its circulation upwards, between the entry and the exit of the empty dryer. This gradient is more significant with the decrease of the air velocity.The heat transfer coefficient by forced convection between the air and the interior walls is often determined by using the average Nusselt number defined in flow of boundary layer on plane plate (laminar regime). In addition, the presence of the grills, on which slices of product are spread, causes turbulence which is not taken into account by this coefficient of Nusselt number. In this paper, we determine the heat transfer coefficient between the air and the sidewalls of a dryer experimentally. The latter contains grills on which thin layer slices of a dry material (wood) of the same geometry as the initial potato slices are spread. This leads us to determine an expression of the Nusselt number of the form Nu=aRebPr1/3, without mass transfer. Thereafter, this correlation of the Nusselt number is introduced into the mathematical model, already suggested in our former work, which predicts the performances, in forced convection, of the foodstuff dryers. In the end, the influence of these losses is presented by means of a comparative study between various models, those that take into account and those that ignore these losses between two beds of slices. The results thus obtained are compared with the experiment in an application on potato drying. [Copyright &y& Elsevier]

This paper presents a mathematical model for hydrogen storage in a metal hydride bed. For this purpose, a two-dimensional mathematical model which considers complex heat and mass transfer during the hydriding process is developed. The coupled differential equations are solved with a numerical method based on integrations of governing equation over finite control volumes. The driving force is considered to be pressure difference because of the temperature distribution in the system. The numerical results showed that the hydriding performance depends on the temperature distribution in the hydride bed. Fluid flow enhances the hydriding rate in the system by driving the hot fluid to the colder regions. The numerical results were found to agree satisfactorily with the experimental data available in the literature. [Copyright &y& Elsevier]

The aim of this paper is to describe a system for fouling monitoring of thermosiphon reboilers. This system is based on a static model of the fouling resistance. The latter has been constructed in three steps. First, a mathematical model of the fouling resistance based on the overall heat transfer coefficient and on the inside film heat transfer coefficient is developed. Then, the overall heat transfer coefficient is obtained from the mass and energy balances of the reboiler. In the last step, the inside film heat transfer coefficient is determined from correlations with some process variables. The resulting model is a function of measured quantities and of two unknown parameters. A procedure for identification of the unknown parameters from data selected so that hypotheses behind the model are fulfilled is presented. The effectiveness of the resulting monitoring system is illustrated by processing industrial data. [Copyright &y& Elsevier]

This paper presents a mathematical model with numerical simulations of the heat transfer across a simple glass window. The model is two-dimensional, transient based upon the energy equation with a source term to account for the solar radiation absorbed through the glass sheet. Variable incident solar radiation and external ambient temperature are considered in the numerical simulations. The governing equations and the associated boundary conditions are discretized by the finite difference approach and the ADI scheme. Numerical simulations are realized for the cases of clear and absorbing glass to show the effect of the glass thickness on the total heat gain, the solar heat gain and the shading coefficient. [Copyright &y& Elsevier]

A mathematical model for predicting thermal efficiency, heat gain, and outlet air temperature of a covered plate attic solar collector under steady conditions was developed. The model presented in this paper utilizes the basic principles and relationships of heat transfer to simulate the behavior of the solar air heaters under various conditions. The model was validated by comparing the predicted outlet air temperatures and collector efficiencies to those measured during drying operation of an attic solar collector. The effect of the air speed inside the collector and wind speed above the collector on the collector efficiency were investigated using the mathematical model. [Copyright &y& Elsevier]

This paper presents the results of a mathematical and computer model used to predict building indoor wall heat fluxes. The model is based on an energy balance approach that uses conduction transfer functions (CTF) and simplified solar heat gain calculations via solar heat gain factors (SHGF). The model was implemented via computer programming. The purpose of the research was to produce an accurate model driven by only a time series set of measured outdoor and indoor air temperatures. In addition to the model, an experimental test set up was constructed and instrumented to gather data for verifying the model. It was found that the energy balance/CTF/SHGF enabled heat fluxes to be predicted with accepted degrees of accuracy, from which space cooling and heating loads as well as building energy could be estimated. [Copyright &y& Elsevier]

Wall-flow filters are worldwide recognized as the most efficient devices for the abatement of particulate emissions from automotive diesel engines. Mathematical models simulating the particulate thermal oxidation process in the filters are already applied for system optimization. This paper deals with the appropriateness of a specific assumption inherently used in all relevant published models, namely the temperature uniformity in the soot and wall layer. A new mathematical model is developed to predict the temperature gradients under various operating conditions. Based on the model results, it is shown that significant temperature gradients inside the soot layer may exist under some practical operating conditions. These conditions are associated with high flow rates and high soot loadings. In these cases, the uniform temperature assumption may lead to erroneous results for the prediction of the overall regeneration process. The error of this assumption is assessed as function of the soot porosity. [Copyright &y& Elsevier]

The paper presents the development of a complete analytical model of a thermoelectric generator (TEG). Based on data coming from a small number of easily obtainable measurements, the model makes it possible to determine basic parameters of the TEG. Owing to measurements performed in the steady state and immediately after a rapid change of the TEG electrical state, the following quantities can be established analytically: the Seebeck coefficient, thermal conductivity and thermal resistance between heat exchangers and the TEG. The applied rapid method is based on the large difference in inertia between the electric and the thermal field. A rapid change from the short-circuit to the open-circuit electrical state makes it possible to record the voltage for the system thermal state corresponding to the short circuit. Experimental tests were carried out on a commercially available thermoelectric generator and the results proved the developed model usefulness. The simulation results show that the thermal resistance of the contact layers between the heat exchangers and the thermoelectric generators caused a loss of the temperature difference of the junctions from 30% at the recommended mechanical load to even over 50% if the clamping force was too low. Due to that, the determined power ratio, being an indicator of the utilization of the theoretical power capacity of a system burdened with thermal resistance, reaches values lower than 40% for the required clamping force and is below 20% for improper contact conditions The impact of the accuracy of the measurements on the values of the system parameters obtained from the model is evaluated by means of sensitivity analysis. [ABSTRACT FROM AUTHOR]

• Multi-scale and multi-domain battery modelling framework is presented. • It enables more consistent virtual representation of the electrode topology. • Coupled treatment of main and side reactions as well as heat generation phenomena. • Main and side reaction driven heat transfer cross-talk between anode and cathode. • Modelling the entire chain of mechanisms leading to outbreak of the thermal runaway. Multi-scale and multi-domain mathematical models capable of modelling main electrochemical reactions, side reactions and heat generation can reduce the time and cost of lithium-ion battery development and deployment, since these processes decisively influence performance, durability and safety of batteries. Experimental evidences clearly indicate the importance of the interplay between electric and thermal boundary conditions, cell design and applied materials, side reactions as well as safety implications of batteries, which are not yet captured to a sufficient level by simulations models. As an answer to this challenge, the paper presents an advanced multi-scale battery modelling framework that can be seamlessly integrated into multi-domain models. The key hypothesis is that nanoscopic transport phenomena and resulting heat generation decisively influence the entire chain of mechanisms that can lead to the outbreak of the thermal runaway. This is confirmed by developing a multi-scale battery modelling framework that is based on the continuous modelling approach featuring more consistent virtual representation of the electrode topology and incorporating the coupled chain of models for heat generations and side reactions. As a result, the battery modelling framework intuitively yet insightfully elucidates the entire chain of phenomena from electric and thermal boundary conditions, over cell design and properties of applied materials to solid electrolyte interphase growth, its decomposition and subsequent side reactions at the anode, cathode and the electrolyte that lead to the thermal runaway. One of key results comprises multi-level main and side reaction driven heat transfer cross-talk between the anode and the cathode. Therefore, the presented advanced multi-scale battery modelling framework represents a contribution to the advanced virtual development of batteries thereby contributing to tailoring battery design to a specific application. [ABSTRACT FROM AUTHOR]

• Inverse method used to improve original T-history method equations to determine PCMs latent heat. • The method shown to be suitable method to calculate latent heat of low thermal conductivity bulk PCMs. • New transient modelling is more suitable for calculating latent heat with cooling rates than using original equations. High temperature phase change materials (PCMs) are being proposed as thermal energy storage media in concentrated solar power plants. The thermophysical properties of PCMs, such as the latent heat of fusion/solidification need to be defined to enable system design and evaluate system performance and cost analysis. Several methods have been used to measure the latent heat of fusion/solidification of PCMs including the T-history method. The original assumption of the T-history method is the Biot number should be less than 0.1 where the lumped capacitance method is applicable. However, when the Biot number is more than 0.1 then the original equations are not applicable to estimate the latent heat of PCM. This paper demonstrates how a one-dimensional heat transfer mathematical model can be used by applying an inverse method to overcome the limitation of the lumped capacitance method in the original T-history method to determine the latent heat of PCMs. The mathematical model demonstrates that variation of the temperature distributions inside the samples for the discharge curves. Furthermore, this model shows the errors in the latent heat values if the T-history method is used. It is evident from the discharge curves of low thermal conductivity PCMs that the original simplified equations used for interpreting the T-history test results are not applicable for calculating the latent heat at different ambient temperature. [ABSTRACT FROM AUTHOR]

• The mathematical model of the multi-panel RHR was established. • Investigation of the refrigerant flow distribution of the multi-panel RHR. • The mathematical model was validated with the experimental data. • The ratio of radiation to convection of the multi-panel RHR is 10.2%. • Analysis on thermal potentials of the RHR with the limited and critical flow rates. The refrigerant-heated radiator (RHR) is an efficient and feasible heating terminal for space heating. In order to improve the efficiency of RHR, a multi-panel RHR was proposed in this paper. To investigate the thermal potentials of the multi-panel RHR, a heat transfer and pressure drop model of the multi-panel RHR was established. To predict the refrigerant flow distribution of the multi-panel RHR effectively, a hydraulic model was established. Combining the hydraulic model with the heat transfer and pressure drop model, a comprehensive mathematical model of the multi-panel RHR was set up. The feasibility and effectiveness of the mathematical model were validated with experimental data. The thermal potential of the multi-panel RHR was investigated with the mathematical model. The results indicated that the ratio of radiation to convection of the multi-panel RHR is 10.2%. Meanwhile, the refrigerant flow rate that makes the outlet refrigerants of all panels in the supercooled region is limited. Once the refrigerant flow rate reaches the limit value, the pressure drop of the RHR will increase rather than the heating capacity. Therefore, the predictions of the limited flow rate of RHR under different condensation temperatures are conducted, and relevant regressions can be extended to the RHR with more panels. [ABSTRACT FROM AUTHOR]

• Integrated mathematical models for counter-flow heat and mass transfer process are built. • Thermodynamic balancing of simultaneous heat and mass transfer process is accomplished by water mass injection/extraction. • The total entropy generation can be minimized at the balance conditions of HCR = 1. • A minimum value of NEG = 0.0054 is obtained at the inlet relative humidity of 0.85. • Adjusting the injection height shows significant potential in reducing the total entropy generation, although the HCR is always 1. In this paper, a specific procedure is considered to reveal how the simultaneous heat and mass transfer process achieves thermodynamic balancing such that the total entropy generation can be minimized, in combination with the unsaturated state of inlet humid air. In view of the simultaneous heat and mass exchange with zero and single water mass injection/extraction, integrated mathematical models based on mass and energy conservation are established using the finite difference method. The novel proposed driving force criterions, heat transfer temperature difference (HTTD) and mass transfer pressure difference (MTPD), are balanced at off-design conditions, while the relevant influences from the critical parameters are investigated and analyzed. The simulation results demonstrate that the total normalized entropy generation (NEG) can be minimized at the balance condition of HCR = 1, meanwhile, the energy efficiency has a minimum value. It is found that single mass injection can better decrease the entropy generation at its minimum point and along the variation curve, compared to zero and single mass extraction. Specific injection ratio is given at the balance condition with fixed inlet liquid-gas ratio. Moreover, it is valuably observed that varying the injection height shows significant potential in reducing entropy generation, although the HCR keeps a constant value of one. Furthermore, a minimum value of NEG = 0.0054 is emerged at φ i = 0.85, as raising the relative humidity of inlet humid air can effectively reduce the total entropy generation and elevate the energy efficiency, simultaneously. Image, graphical abstract [ABSTRACT FROM AUTHOR]

• Mathematical models can describe the industrial anaerobic solid-state fermentation. • The models describe product concentrations and predict temperature. • The models predict overheating in large fermenters and at higher soil temperatures. • Our findings can be useful to improve traditional anaerobic solid-state fermentations. Traditional solid-state fermentation processes can give fluctuating product quality and quantity due to difficulties in control and scale up. This paper describes an engineering study of an industrial-scale anaerobic solid-state fermentation process for Chinese liquor (Baijiu) production, aimed at better understanding of the traditional process, as an initial step for future optimization. This mixed-culture fermentation is done in 0.44-m3 vessels embedded in the soil. At this scale, the fermentation is limited by product inhibition. We developed mathematical models based on the Han-Levenspiel equation for product inhibition, with parameters derived from measured data. The models accurately predicted the concentrations of starch and dry matter. A model with radial conduction into a small soil volume around the fermenter and consecutive vertical conduction into the underlying soil accurately predicted the pit temperature in the heating and cooling phases. This model is very sensitive to the values used for the enthalpies of combustion, meaning that direct measurement of the heat production rate would be preferable. In the industry practice, the fermenter volume can be from around 0.20 to 15.00 m3. The model predicts that overheating will occur not only in larger fermenters, but also in the 0.44-m3 fermenters when the soil temperature is high in summer. Our model predictions are consistent with observed behavior in the industry. Our findings can be used to improve this traditional process, as well as similar systems. [ABSTRACT FROM AUTHOR]

Abstract: Our 1985 paper (JQSRT 1985; 33: 533–549) reported the result of the research we conducted back then to better understand heat transfer processes in large-scale combustion chambers, especially in pulverized coal-fired furnaces. It was one of the first works exploring radiative transfer in three-dimensional enclosures where absorption and scattering coefficients due to combustion particles and gases were allowed to vary within the medium. This flexibility of the mathematical model made it useful for applications to realistic furnaces and different types of high-temperature systems. This note briefly discusses the motivation behind the paper and the immediate extension of the idea to different systems. [Copyright &y& Elsevier]

Abstract: The current study outlines a general approach to construct a one-dimensional pyrolysis model based on milligram-scale and bench-scale test data collected systematically to isolate a specific process in each test. This approach is demonstrated by developing a model of burning for corrugated cardboard. Thermogravimetric analysis and differential scanning calorimetry were conducted on pulverized cardboard to determine the thermal degradation mechanism, the enthalpy of decomposition reactions, and the heat capacities of apparent species. Data collected in pyrolysis-combustion flow calorimetry tests were analyzed to assign a heat of combustion to the volatiles evolved from each reaction. Bench-scale tests were conducted with a cone calorimeter on samples in a horizontal orientation to observe the flaming combustion of this material at external heat fluxes ranging from 20 to 80kWm−2. Condensed phase temperature data was collected in these tests to measure and infer thermal transport properties and to characterize property changes associated with thermal degradation through an iterative inverse analysis. All the parameters determined through analysis of the milligram-scale and bench-scale tests were used to construct a one-dimensional pyrolysis model that predicted the average mass loss and heat release rates from cone calorimeter tests to within, on average, 17% and the times to ignition to within 2s. [Copyright &y& Elsevier]