Erratum to “Validation of the use of heat transfer models in liquid/solid fluidized beds for ice slurry generation” [International Journal of Heat and Mass Transfer 46 (2003) 3683-3695]

In the concerned paper, tube dimensions have been taken from the experimental set-up drawings. Recently, during Wilson plot calibration tests, after extension of the operating range of the set-up, came to light that the tube sizes used were slightly different from what was stated in the drawings. Consequently, published experimental fluidized bed heat transfer coefficients are up to 40% too low and some conclusions had to be adapted. The new, correct experimental heat transfer results show a much better agreement with heat transfer models in literature. The authors of the subjected paper deeply regret the errors. Corrected versions of Sections 4 and 5 of the paper are presented here.     

New design equations for liquid/solid fluidized bed heat exchangers

Liquid/solid fluidized bed heat exchangers have originally been developed for desalination plants. However, due to their substantial benefits with respect to significantly improved heat transfer and fouling reduction, successful applications also exist in areas such as petrochemical, minerals and food processing as well as in the paper and power industries. The excellent performance of fluidized bed heat exchangers is related to the interaction between particles and heat transfer surface and to mixing effects in the viscous sublayer. In this paper, the results of experimental investigations on heat transfer for a wide range of Newtonian and non-Newtonian fluids are presented. New design equations have been developed for the prediction of bed voidage and heat transfer coefficients. The predictions of these correlations and of numerous correlations recommended by other authors are compared with a large database compiled from the literature.     

Heat transfer characteristics of microencapsulated phase change material slurry in laminar flow under constant heat flux

Due to its large apparent specific heat during the phase change period, microencapsulated phase change material slurry (MPCMS) has been suggested as a medium for heat transfer. In this paper, the convective heat transfer characteristics of MPCMS flowing in a circular tube were experimentally and numerically investigated. The enhanced convective heat transfer mechanism of MPCMS, especially in the thermal fully developed range, was analyzed by using the enthalpy model. Three kinds of fluid–pure water, micro-particle slurry and MPCMS were numerically investigated. The results show that in the phase change heat transfer region the Ste number and the Mr number are the most important parameters influencing the Nusselt number fluctuation profile and the dimensionless wall temperature. Re_b, d_p and c also influence the Nusselt number profile and the dimensionless wall temperature, but they are independent of phase change process.     

An experimental study of the effect of pin fins on heat transfer in circulating fluidized beds

An experimental investigation was conducted to study the effect of pin fins on heat transfer in circulating fluidized beds. Experiments were conducted in a 100 mm i.d., 5.15 m tall CFB unit, initially with no fins and then with 16-pin and 32-pin fins. Each pin was 6.35 mm in diameter and 15 mm long. It was observed that, although the heat transfer coefficient decreases with the use of fins, the total heat transfer increases owing to the increase in surface area which the fins provide. The results of heat transfer for unfinned surface were compared with those of other workers and found to be in good agreement.     

Effect of probe size on heat transfer at the wall in circulating fluidized beds

An experimental investigation was made to study the effect of vertical probe height on heat transfer at the wall in circulating fluidized beds. Experiments were conducted in a 100 mm internal diameter, 5.15 m tall circulating fluidized bed. Four probes having 85, 127.5, 170 and 255 mm heights were tested. Heat transfer measurements covered a range of superficial velocity from 7.2 to 12.5 m/s and a range of suspension density from 25 to 68 kg/m³. The results were compared with those of other investigators. An empirical correlation incorporating the dimensionless probe height and the particle Nusselt number and Reynolds number has been suggested.     

Numerical heat transfer studies of the fatty acids for different heat exchanger materials on the performance of a latent heat storage system

Theoretical investigations of fatty acids as a phase change material (PCM) for energy storage system have been conducted in this study. The selected fatty acids were capric acid, lauric acid, myristic acid, palmitic acid and stearic acid. For the two-dimensional simulation model based on the enthalpy approach, calculations have been made for the melt fraction with conduction only. Glass, stainless steel, tin, aluminium mixed, aluminium and copper were used as heat exchanger materials in the numerical calculations. Theoretical results show that capric acid was found good compatibility with latent heat storage system. The large value of thermal conductivity of heat exchanger materials did not make significant contribution on the melt fraction.     

Experimental assessment of heat storage properties and heat transfer characteristics of a phase change material slurry for air conditioning applications

A new microencapsulated phase change material slurry based on microencapsulated Rubitherm RT6 at high concentration (45% w/w) was tested. Some heat storage properties and heat transfer characteristics have been experimentally investigated in order to assess its suitability for the integration into a low temperature heat storage system for solar air conditioning applications. DSC tests were conducted to evaluate the cold storage capacity and phase change temperature range. A phase change interval of approximately 3 °C and a hysteresis behaviour of the enthalpy were identified. An experimental set-up was built in order to quantify the natural convection heat transfer occurring from a vertical helically coiled tube immersed in the phase change material slurry. First, tests were carried out using water in order to obtain natural convection heat transfer correlations. Then a comparison was conducted with the results obtained for the phase change material slurry. It was found that the values of the heat transfer coefficient for the phase change material slurry were higher than for water, under identical temperature conditions inside the phase change interval.     

Study on boiling heat transfer in liquid saturated particle bed and fluidized bed

An investigation on the effects of solid particles on boiling heat transfer enhancement is performed. The range of particle diameter is from millimeter to nanometer. The experimental results show that boiling heat transfer can be enhanced greatly by adding the solid particle into the liquid whether in fixed particle bed or in fluidized particle bed. The boiling enhancement is closely related to the particle size, the initial bed depth and the heat flux applied. The experiments show that boiling characteristics are greatly changed when a particle layer is put on the heated surface. The major effects of fixed particle bed on nucleate pool boiling heat transfer are the nucleation, bubble moving and thermal conductivity effect. A boiling heat transfer correlation is obtained to predict the boiling heat transfer coefficients in a liquid saturated porous bed. A volumetric convection mechanism of boiling heat transfer enhancement by fluidized particles is proposed. The calculated results from the model suggested in this paper agree reasonably with the experimental values.     

Modelling heat transfer in a circulating fluidized bed

A model for the bed-to-wall heat transfer under low temperature condition in a circulating fluidized bed (CFB) was developed based upon a simplified cluster renewal concept. The age of clusters in contact with the wall at different locations along the height of the CFB was estimated as the weighted average age considering their formation and disintegration. One set of experimental data on heat transfer in a 4.5-metre high, 0.15-metre diameter CFB under low temperature condition (67–77°C) was chosen for comparison with prediction of local heat transfer coefficient. The experimental observation and prediction have shown a qualitative agreement.     

A study of heat transfer in a circulating fluidized bed

An experimental investigation was carried out to study the effects of operating parameters on the local bed-to-wall heat transfer coefficient in a 4.5 m tall, 0.150 m diameter circulating fluidized bed with a bed temperature in the range of 65°C to 80°C, riser flow rate varying from 1400 litres/min to 2000 litres/min, bed inventory in the range of 15 kg to 25 kg of sand, and average sand sizes of 200 μm, 400 μm and 500 μm. A heat flux probe was attached to the riser wall at five different vertical locations for measuring the heat flux from the bed to the wall surface. From the present work, the heat transfer coefficient in the dilute phase was found to be in the range of 62 to 83 W/m²K, 51 to 74 W/m²K, and 50 to 59 W/m² K for sand sizes of 200 μm, 400 μm and 500 μm, respectively. Relevant mathematical correlations were developed to predict local heat transfer coefficient based on the results of the practical work.     

Analogy between pressure drop and heat transfer in liquid–solid circulating fluidized beds

An analogy was found between the frictional pressure drop and the heat transfer in liquid–solid circulating fluidized beds. This investigation is based on the predicting correlations for the particle holdup, the heat transfer coefficient, and the pressure drop, which were all developed by the authors. When the heat transfer coefficients were expressed in terms of the modified j‐factor, then a close mutual relationship was observed between the modified j‐factor and the friction factor of the pressure drop due to liquid and particle flow. A correlation to express this mutual relationship was derived, which consists of the density ratio of particle to liquid and the non‐dimensional riser diameter. The heat transfer coefficient predicted from the derived correlation agreed well with the experimental data by the authors, and with existing data. © 2009 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20246     

Method to improve geometry for heat transfer enhancement in PCM composite heat sinks

Use of composite heat sinks (CHS), constructed using a vertical array of ‘fins’ (or elemental composite heat sink, ECHS), made of large latent heat capacity phase change materials (PCM) and highly conductive base material (BM) is a much sought cooling method for portable electronic devices, which are to be kept below a set point temperature (SPT). This paper presents a thermal design procedure for proper sizing of such CHS, for maximizing the energy storage and the time of operation until all of the latent heat storage is exhausted.For a given range of heat flux, q″, and height, A, of the CHS, using a scaling analysis of the governing two dimensional unsteady energy equations, a relation between the critical dimension for the ECHS and the amount of PCM used (?) is determined. For a ?, when the dimensions of the ECHS are less than this critical dimension, all of the PCM completely melts when the CHS reaches the SPT. The results are further validated using appropriate numerical method solutions. A proposed correlation for chosen material properties yields predictions of the critical dimensions within 10% average deviation. However, the thermal design procedure detailed in this paper is valid, in general, for similar finned-CHS configurations, composed of any high latent heat storage PCM and high conductive BM combination.     

Finite element analysis of the flow and heat transfer of solid particles in moving beds

A numerical analysis for the flow and heat transfer of solid particles in moving beds of heat exchangers is presented. The solid particles pass through a bundle of heat source tubes as the result of the gravitational force. Heat energy is transferred through direct contact of particles with the heat source tubes. A viscous-plastic fluid model and a convective heat transfer model are employed in the analysis. The flow field dominantly determines the total heat transfer in the heat exchanger. As the velocities of solid particles around the heat source tubes increase, the heat transfer from the tubes also increases. Examples are presented to show the performance of the numerical model. The effect of flow on heat transfer has also been studied. © 1998 John Wiley & Sons, Ltd.     

Experimental study of natural convection heat transfer in a microencapsulated phase change material slurry

A new microencapsulated PCM (Phase Change Material) slurry (MEPCS) at high concentration (45% w/w) was developed based on microencapsulated Rubitherm RT6. Its heat storage and heat transfer characteristics have been experimentally investigated in order to assess its suitability for integration into a low temperature heat storage system for solar air conditioning applications. Differential scanning calorimetry tests have been conducted to evaluate the cold storage capacity and phase change temperature range. An experimental setup was built in order to quantify the natural convection heat transfer occurring from a vertical helically coiled tube immersed in the MEPCS. First, tests were carried out using water in order to obtain natural convection heat transfer correlations and then a comparison was made with the results obtained for the MEPCS. It was found that inside the phase change interval the values of the heat transfer coefficient for the MEPCS were significantly higher than for water, under identical temperature conditions.     

Solving heat transfer problems with phase change via smoothed effective heat capacity and element-free Galerkin methods

This paper presents a smoothed effective heat capacity model that is combined with element-free Galerkin (EFG) method, to solve heat transfer problems with phase change. The Sigmoid function is employed to build a continuous and smooth effective heat capacity function, so as to avoid possible error caused by the step-jump. The proposed numerical model is verified via numerical examples, and the effects of arrangement of EFG nodes and parameters relevant with Sigmoid function on the solutions are investigated. Satisfactory results are achieved in comparison with analytical solutions.     

Analysis of particle motion and heat transfer in circulating fluidized beds

In this study, the forces affecting the motion of particle clusters near the wall of a CFB were theoretically analysed. The motion trajectory and the contact time of clusters were determined from the proposed model for two cases, steel ball having density of 6980 kg m^?3 and sand having density of 2500 kg m^?3. Computational results showed that the construction and operational parameters such as the bed equivalent diameter, the gas velocity and the bed temperature have great influence on the contact time of clusters. Based on analysis of the contact time of clusters, a theoretical model was developed for predicting the particle–gas convection heat transfer coefficient. The results were compared with experiments and were a quite agreement with the measured data in the open literature which suggests that the theoretical analysis conducted in this work can very well describe the convection heat transfer in a CFB. Copyright © 2004 John Wiley & Sons, Ltd.     

Dynamic force reduction and heat transfer improvement for horizontal tubes in large-particle gas-fluidized beds

The effects of tube bank configuration on forces and heat transfer were investigated for both two-dimensional and three-dimensional gas fluidized beds. Effective dynamic forces and heat transfer coefficients were measured for several tube bank configurations, and it was found that the average forces are smaller than for a single tube. The heat transfer coefficient can be increased by providing sufficient space for particles to descend around both sides of the tube bank. The results provide useful guidelines for optimizing the configuration of tube banks to achieve high heat transfer coefficients while reducing tube erosion due to dynamic forces.     

Study of heat transfer between an over-bed oil burner flame and a fluidized bed during start-up: Determination of the flame to bed convection coefficient

A study of the heat transfer processes between an over-bed burner flame and a fluidized bed during start-up as been conducted. Owing to the difficulty of estimating the flame to bed convection coefficient in an industrial boiler, convection coefficients were determined using a laboratory bench scale unit. Such convection heat transfer coefficients are obtained for 3 kg, 4 kg and 5.5 kg initial bed inventories by combining measured temperatures and flow rates with a mathematical model representing the complex energy exchange in the system. Results show that the height of the fluidized bed and its distance to the flame are an important factor in the overall heat transfer process, both by convection and radiation. For 5.5 kg, 4 kg and 3 kg initial bed inventories, the convection coefficients obtained, at the end of start-up, are 180 ± 30 W/m² K, 150 ± 20 W/m² K and 95 ± 10 W/m² K respectively. The determined convection coefficients can be utilized in the future as guides in the design of start-up systems for BFB boilers. The energy analysis performed also identified the major sources of heat losses in the bubbling fluidized bed.     

Melting heat transfer characteristics of a horizontal ice cylinder immersed in an immiscible liquid

The melting characteristics of a horizontal ice cylinder immersed in an immiscible liquid were investigated both experimentally and analytically. A clear cylindrical ice layer formed around a horizontal cooling tube with a coaxial outer heated tube was melted in oil as the test immiscible liquid in the annulus between the ice and outer tube. Both the melting behavior of ice and the flow patterns of the immiscible liquid were observed under a variety of outer wall temperature conditions. In the analysis, two boundary layers were introduced for both the melt water film and ambient liquid, respectively. It was found from the experiments that the tendency of the mean Nusselt number changes clearly at Ra = 10⁶, which corresponds to the temperature condition T0 = 12.0 °C. This analysis might be used to estimate the melting characteristics of such a system during the initial stage of low temperature conditions. © 1998 Scripta Technica, Heat Trans Jpn Res, 27(5): 336–352, 1998     

Heat transfer characteristics of liquid–solid circulating fluidized beds

An experiment was conducted to obtain heat transfer data in liquid–solid circulating fluidized beds. In the experiment, two kinds of risers were provided, their inner diameter being 24 mm and 12 mm, respectively. Tested particles were of glass and ceramics, having a diameter range from 2.10 to 4.95 mm. Water at ambient conditions was used as the fluidizing liquid. The experimental data showed a trend where the heat transfer coefficient increases gradually with increasing liquid velocity approaching that for a liquid single‐phase flow (“heat transfer enhanced region”), and finally coincides with that for a liquid single‐phase flow (“liquid single‐phase heat transfer region”). The heat transfer coefficient in the heat transfer enhanced region was found to be a function of the slip velocity between liquid and particles. Based on the experimental data, a correlation was proposed for predicting the heat transfer coefficient in the entire region from the heat transfer enhanced region to the liquid single‐phase heat transfer region, which could reproduce the experimental data with an accuracy of ±15%. The proposed correlation agreed well with existing data. © 2008 Wiley Periodicals, Inc. Heat Trans Asian Res, 37(3): 127–137, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20200