Mathematical model of heat and mass transfer processes in evaporative condensers

This study presents a new mathematical model of heat and mass transfer processes in evaporative condensers. The model consists of four ordinary differential equations with their boundary conditions and some associated algebraic equations. The model was formulated for steady-state heat and mass transfer conditions. A simulation computer program based on the model was written. It was devised for heat calculations in condensers built from bare tubes. The quality of the model was calculated by comparing the results obtained by running the program with experimental results achieved by other authors. The computed results show a good degree of conformity with experimental results. The differences are less than 20% (but in one case, 30%). The computer program may be used to determine heat performance of evaporative condensers of horizontal in-line and staggered bundle systems (if S_q > 2d_z).     

A comprehensive design and rating study of evaporative coolers and condensers. Part II. Sensitivity analysis

Sensitivity analysis can be used to identify important model parameters, in particular, normalized sensitivity coefficients; by allowing a one-on-one comparison. Regarding design of evaporative coolers, the sensitivity analysis shows that all sensitivities are unaffected by varying the mass flow ratio and that outlet process fluid temperature is the most important factor. In rating evaporative coolers, effectiveness is found to be most sensitive to the process fluid flow rate. Also, the process fluid outlet temperature is most sensitive to the process fluid inlet temperature. For evaporative condensers, the normalized sensitivity coefficient values indicate that the condensing temperature is the most sensitive parameter and that these are not affected by the value of the mass flow ratio. For evaporative condenser design, it was seen that, for a 53% increase in the inlet relative humidity, the normalized sensitivity of the surface area increased 1.8 times in value and, for a 15 °C increase in the condenser temperature, the sensitivity increased by 3.5 times. The performance study of evaporative condensers show that, for a 72% increase in the inlet relative humidity, the normalized sensitivity coefficient for effectiveness increased 2.4 times and, for a 15 °C increase in the condenser temperature, it doubled in value.     

Experimental performance of a direct evaporative cooler operating during summer in a Brazilian city

This paper presents the basic principles of the evaporative cooling process for human thermal comfort, the principles of operation for the direct evaporative cooling system and the mathematical development of the equations of thermal exchanges, allowing the determination of the effectiveness of saturation. It also presents the results of experimental tests in a direct evaporative cooler that take place in the Air Conditioning Laboratory at the University of Taubaté Mechanical Engineering Department, and the experimental results are used to determinate the convective heat transfer co-efficient and to compare with the mathematical model.     

Optimization of evaporative fluid coolersOptimisation des refroidisseurs de liquide évaporatifs

In the paper the optimization of geometrical and operating parameters for evaporative fluid coolers has been presented. The algorithm of optimizational calculations contains:

• the mathematical model of heat and mass transfer in evaporative fluid coolers;

• model of operating costs based, among others, on the Zalewski–Gryglaszewski relations developed by the authors for evaluation of air pressure drops in the heat exchanger;

• model of evaporative heat exchangers production costs.

Optimization problem formulated for non-linear objective functions with inequality and equality constraints has been solved using Schittkowski's method based on quadratic programming. Two optimization problems have been considered. A solution to the first problem consists in the design of a heat exchanger with such geometrical parameters which ensure its maximum heat capacity at minimal total costs. A result to the second optimization problem are such thermal and flow parameters which will ensure minimum operating costs.The results of optimization calculations presented in the paper are accompanied by their experimental verification.     

A comprehensive design and performance evaluation study of counter flow wet cooling towers

Fouling of cooling tower fills is one of the most important factors affecting its thermal performance, which reduces cooling tower effectiveness and capability with time. In this paper, the fouling model presented in an earlier paper using the experimental data on fill fouling, is used to investigate the risk based thermal performance of the cooling tower. It is demonstrated that effectiveness of the cooling tower degrades significantly with time indicating that for a low risk level (p=0.01), there is about 6.0% decrease in effectiveness for the given fouling model. The sensitivity analysis of the cooling tower is investigated for both rating and design calculation for different values of mass flow rate ratios. The effect of atmospheric pressure on the thermal performance of the cooling tower is also demonstrated.     

Numerical simulation of dehumidifying fin-and-tube heat exchangers: Semi-analytical modelling and experimental comparison

The aim of this paper is to present a developed semi-analytical model for the simulation of dehumidifying air–liquid fin-and-tube heat exchangers. The simulation strategy and the mathematical methodology are described in detail. The model is based on -NTU method, and formulated in a compact way for dry and wet surface situations (temperature or enthalpy driven, respectively). Both rating and design procedures have been developed for fully dry, partially wet, or fully wet surface conditions. The model predictions are compared with experimental data obtained on a wavy and a plain finned heat exchanger, giving reasonably accurate results. The limitations of the empirical information used are clearly identified in the work. The aim of this model is to provide a fast but reliable rating and design numerical tool for air–liquid heat exchanger applications.     

CFD simulation of coupled heat and mass transfer through porous foods during vacuum cooling process

A numerical simulation by using a computational fluid dynamics (CFD) code is carried out to predict heat and mass transfer during vacuum cooling of porous foods on the basis of mathematical models of unsteady heat and mass transfer. The simulations allow the simultaneous prediction of temperature distribution, weight loss and moisture content of the meats at low saturation pressure throughout the chilling process. The simulations are also capable of accounting for the effects of the dependent variables such as pressure, temperature, density and water content, thermal shrinkage, and anisotropy of the food. The model is verified by vacuum cooling of cooked meats with cylindrical shape within an experimental vacuum cooler. A data file for pressure history was created from the experimental pressure values, which were applied in the simulations as the boundary condition of the surface temperature.     

A design method of thermoelectric coolerConception d'un refroidisseur thermoélectrique

A system design method of thermoelectric cooler is developed in the present study. The design calculation utilizes the performance curve of the thermoelectric module that is determined experimentally. An automatic test apparatus was designed and built to illustrate the testing. The performance test results of the module are used to determine the physical properties and derive an empirical relation for the performance of thermoelectric module. These results are then used in the system analysis of a thermoelectric cooler using a thermal network model. The thermal resistance of heat sink is chosen as one of the key parameters in the design of a thermoelectric cooler. The system simulation shows that there exists a cheapest heat sink for the design of a thermoelectric cooler. It is also shown that the system simulation coincides with experimental data of a thermoelectric cooler using an air-cooled heat sink with thermal resistance 0.2515°C/W. An optimal design of thermoelectric cooler at the conditions of optimal COP is also studied. The optimal design can be made either on the basis of the maximum value of the optimal cooling capacity, or on the basis of the best heat sink technology available.     

Assessment of boiling heat transfer correlations in the modelling of fin and tube heat exchangers

A new way to assess the performance of refrigeration system models is presented in this paper, based on the estimation of cycle parameters, such as the evaporation temperature which will determine the validity of the method. This paper is the first of a series which will also study the influence of the heat transfer coefficient models on the estimation of the refrigeration cycle parameters. It focuses on fin and tube evaporators and includes the dehumidification process of humid air. The flow through the heat exchanger is considered to be steady and the refrigerant flow inside the tubes is considered one-dimensional. The evaporator model is discretised in cells where 1D mass, momentum and energy conservation equations are solved by using an iterative procedure called SEWTLE. This procedure is based on decoupling the calculation of the fluid flows from each other assuming that the tube temperature field is known at each fluid iteration. Special attention is paid to the correlations utilised for the evaluation of heat transfer coefficients as well as the friction factor on the air and on the refrigerant side. A comparison between calculated values and measured results is made on the basis of the evaporation temperature. The experimental results used in this work correspond to an air-to-water heat pump and have been obtained by using R-22 and R-290 as refrigerants.     

Use of compound desiccant to develop high performance desiccant cooling system

The paper is aimed to develop a high performance rotary solid desiccant cooling system using a novel compound desiccant wheel (DW). The unique feature of the desiccant wheel is that it can work well under a lower regeneration temperature and have a higher dehumidification capacity due to the contribution of the new compound desiccant materials. Experimental results indicate that the novel desiccant wheel under practical operation can remove more moisture from the process air by about 20–40% over the desiccant wheel employing regular silica gel. A mathematical model that is used to predict the system performance has been validated with the test results. By integrating the desiccant wheel with evaporative cooling, heat recovery and heating for regeneration sections, a solid desiccant cooling system can be formed. Simulation results show that because of the use of the new compound desiccant, the desiccant cooling system can work under much lower regeneration temperature and have a relative high COP, thus low grade thermal energy resources, such as solar energy, waste heat, etc., can be efficiently utilized to drive such a cooling cycle.     

管式间接蒸发空气冷却器传热传质模型的建立及验证

回顾和分析现有间接蒸发冷却器的热工性能和数学模型,并在分析管式间接蒸发空气冷却器传热、传质过程及特点的基础上,建立针对管式间接蒸发空气冷却器热工计算模型。基于模型中管外二次空气侧空气与水膜之间的传热、传质系数是影响模型精度的重要因素,对管外二次空气侧空气与水膜之间的传热、传质系数进行深入分析,将模型用于水平单管外蒸发传热、传质系数的计算,并将计算结果与文献中的实验数据进行对比,证明所选模型的正确性,为下一步对管式间接蒸发空气冷却器整体热工性能的数值模拟奠定坚实的基础。     

Air-side thermal hydraulic performance of multi-louvered fin aluminum heat exchangers

An experimental study on the air-side heat transfer and pressure drop characteristics for multi-louvered fin and flat tube heat exchangers has been performed. For 45 heat exchangers with different louver angles (15–29°), fin pitches (1.0, 1.2, 1.4 mm) and flow depths (16, 20, 24 mm), a series of tests were conducted for the air-side Reynolds numbers of 100–600, at a constant tube-side water flow rate of 0.32 m³/h. The inlet temperatures of the air and water for heat exchangers were 21 and 45°C, respectively. The air-side thermal performance data were analyzed using effectiveness-NTU method for cross-flow heat exchanger with both fluid unmixed conditions. The heat transfer coefficient and pressure drop data for heat exchangers with different geometrical configurations were reported in terms of Colburn j-factor and Fanning friction factor f, as functions of Reynolds number based on louver pitch. The general correlations for j and f factors are developed and compared to other correlations. The f correlation indicates that the flow depth is one of the important parameters for the pressure drop.     

Modeling of frosting behavior on a cold plate

This paper proposes a mathematical model to predict the frost properties and heat and mass transfer within the frost layer formed on a cold plate. Laminar flow equations for moist air and empirical correlations for local frost properties are employed to predict the frost layer growth. Correlations for local frost density and effective thermal conductivity of the frost layer, derived from various experimental data, are expressed as a function of the various frosting parameters: the Reynolds number, frost surface temperature, absolute humidity and temperature of the moist air, cooling plate temperature, and frost density. The numerical results are compared with experimental data to validate the proposed model, and those agree well with the experimental data within a maximum error of 10%. Heat and mass transfer coefficients obtained from the numerical analyses are also presented. The results show that the model for the frost growth using the correlation of the heat transfer coefficient without considering the air flow has a limitation in its application.     

Operational performance of a cryogenic loop heat pipe with insufficient working fluid inventory

A cryogenic loop heat pipe (CLHP) has been developed for future aerospace applications at the Technical Institute of Physics and Chemistry (TIPC). It has been demonstrated that this CLHP, when placed horizontally, can operate in liquid-nitrogen temperature range and have a heat transfer capability of up to 12 W with proper working fluid inventory. This paper presents some particular characteristics of the CLHP when the compensation chamber is half-filled with liquid-phase working fluid before startup. The device has been tested at different orientations using nitrogen as the working fluid in order to compare its thermal behavior, specially related to the heat transfer capability, the operation temperature and the thermal resistance, as well as to investigate its operational characteristics under power level as low as 1 W. Tests were performed for the CLHP at horizontal position and with the liquid line 3.4 and 6.4 cm below the vapor line, respectively. The experimental results show the operationability of the CLHP tested at three orientations and tests with the liquid line 6.4 cm below the vapor line show lower operation temperatures and higher heat transfer capability.     

Modeling and performance analyses of evaporators in frozen-food supermarket display cabinets at low temperatures

This paper presents modeling and experimental analyses of evaporators in “in situ” frozen-food display cabinets at low temperatures in the supermarket industry. Extensive experiments were conducted to measure store and display cabinet relative humidities and temperatures, and pressures, temperatures and mass flow rates of the refrigerant. The mathematical model adopts various empirical correlations of heat transfer coefficients and frost properties in a fin-tube heat exchanger in order to investigate the influence of indoor conditions on the performance of the display cabinets. The model is validated with the experimental data of “in situ” cabinets. The model would be a good guide tool to the design engineers to evaluate the performance of supermarket display cabinet heat exchangers under various store conditions.     

Optimal shape of the multi-passage branching system in a single-phase parallel-flow heat exchanger

A numerical simulation is performed to examine the heat and fluid flow characteristics of the branching system in a single-phase parallel-flow heat exchanger (PFHE) and to obtain its optimal shape. The relative importance of the design parameters [injection angle of the working fluid (Θ), inlet shape and location (Y_c), and height of the protruding flat tube (Y_b)] is determined to decide the optimization sequence. The optimal geometric parameters are obtained as follows: Θ=−21°, Type A, Y_c=0 and Y_b=0. The heat transfer rate of the optimum model compared to that of the reference model is increased by about 55%. The optimal values of the parameters can be applicable to the Reynolds number ranging from 5000 to 20,000.     

Evaluation of heat and mass transfer coefficients for falling-films on tubular absorbers

A coupled heat and mass transfer model is developed to extract the transfer coefficients for falling-films from the measurements on a tubular absorber. The mass transfer coefficients obtained from the coupled model and the log-mean-difference approach agree within about 10%. For the heat transfer coefficient, the values given by the two models can differ quite significantly. The cooling water temperature distribution predicted by the coupled model agrees well with measurements. The transfer coefficients obtained from experimental measurements using the various methods reported in the literature show wide variations.     

Modelling of the heat exchangers of a small capacity, hot water driven, air-cooled H2O–LiBr absorption cooling machine

General models for the design of the heat exchangers (absorber, generator, condenser and evaporator) of a prototype of an air-cooled absorption chiller of 2 kW for air-conditioning using the pair H₂O–LiBr have been developed. An absorption machine of such characteristics has been constructed to be used as a test facility for validating the results obtained from the mathematical models developed. The discrepancies considering the heat exchanged between numerical results and experimental data are under 15% in most cases for all these components except the condenser, where the discrepancies are higher. The conclusions reported will lead to: (i) future improvements of the mathematical simulation models and (ii) improvements in the experimental infrastructure.     

Predicting local surface heat transfer coefficients by different turbulent k-ε models to simulate heat and moisture transfer during air-blast chilling

A numerical investigation using a computational fluid dynamics (CFD) code is carried out to predict the turbulent flow field, and heat and moisture transfer in a three-dimensional air-blast chiller with cooked meats of cylindrical and elliptical shapes. Three turbulent models [standard, low Reynolds number (LRN) and RNG k-ε model] have been used in these simulations. Based on local heat transfer coefficients on the surface of the meat calculated by CFD code, the unsteady heat and mass transfer were simulated which took into account of the effects of conduction within the meat, forced and natural convection, radiation and moisture evaporation on the surface of the cooked meat joint. The model allowed the simultaneous CFD prediction of both temperature distribution and weight loss of the meat throughout the chilling process. Good agreement with experimental results was obtained. The effect of using different models on the accuracy of the simulation of local heat transfer coefficient is presented.