New correlations for heat transfer coefficients during direct cooling of products

An analytical method for determining the heat transfer coefficients of food products being cooled in water and in air flows is presented. Food products are idealized as geometrical solid objects of regular shapes. New correlations between heat transfer coefficients and cooling coefficients are developed in simple forms for practical use in the refrigeration industry. These correlations are then used to determine the heat transfer coefficient for a cylindrical carrot cooled in air flow as an illustrative example. In addition, evaluating the heat transfer coefficients for several products using the available experimental cooling coefficient values from the literature, two new correlations between the heat transfer coefficient and the cooling coefficient are also obtained for water and air cooling applications. The results show that the correlations presented in this article can determine the heat transfer coefficients of food products forced-convection cooling in a simple and accurate manner.     

Determination of heat transfer coefficients for cylindrical products exposed to forced-air cooling

An analytical model for estimation of transient heat transfer coefficients in forced-air precooling experiments of cylindrically shaped grapes, using a lumped capacitance approach were addressed and investigated. In order to determine transient heat transfer coefficients, the centre transient temperature measurements during forced-air precooling were used. Experiments involved cooling individual grapes in air flow without water losses. The individual grapes were instrumented with several interior thermocouples for measuring the centre transient temperature response during cooling. The transient values of the heat transfer coefficient history for five different air velocities were found to be about 21–40 W/m² K. These values were in good agreement with the values predicted using well-known Nusselt-Reynolds empirical correlation for forced convection. The present technique has the capability of determining transient heat transfer coefficients in a single transient experiment.     

Effective heat transfer coefficients for individual spherical products during hydrocooling

A correlation was developed that may be used to estimate the heat-transfer coefficients for the individual spherically shaped products in the batches containing 5, 10, 15, and 20 kg of product exposed to cooling at temperatures of 0.5, 1, and 1.5°C, respectively. Two different food commodities (tomatoes and pears) were evaluated using four different batch weights for each individual product. Temperatures at the centers of the individual products were measured in order to obtain the temperature distributions. A regression analysis was applied to these temperature distributions in the exponential form using the least-squares method in order to obtain the cooling process parameters, namely the cooling coefficients and the lag factors. Also, the thermal properties (thermal conductivity and thermal diffusivity) of the products were estimated. By combining the cooling coefficient and the thermal properties in the present model, the heat-transfer coefficients for the individual products were determined easily and accurately.     

Development of a new forced convection heat transfer correlation for CO2 in both heating and cooling modes at supercritical pressures

Experimental and numerical investigations on forced convection heat transfer of carbon dioxide at supercritical pressures in a prototypic printed circuit heat exchanger under both cooling and heating conditions have been performed in this present study. The experiment test section has nine semi-circular channels with a hydraulic diameter of 1.16 mm and a length of 0.5 m. Primary operational parameters include inlet pressure of 7.5–10 MPa, mass fluxes of 326 kg/m² s and 762 kg/m² s, inlet temperatures from 10 °C to 90 °C and the average heat flux was 30 kW/m². Beyond reproducing the regular experimental cases, numerical modeling also implemented higher heat fluxes of 60 kW/m² and 90 kW/m² in order to investigate the effect of heat flux. Good agreement was found between the experiments and FLUENT simulations using an SST k–w model with the near-wall region being completely resolved. The distinctive behavior of convection heat transfer at supercritical pressures between heating and cooling modes was systematically analyzed. A more physically reasonable property-averaging technique, Probability Density Function (PDF)-based time-averaged property, was developed to account for the effect of nonlinear dependency of properties on instantaneous local temperature. Furthermore, experimental and computational data were compared to empirical predictions by the Dittus–Boelter and Jackson correlations. The results showed that Dittus–Boelter correlation has better precision for the average value of the predicted heat transfer coefficient but cannot take account of the effect of heat flux. In contrast, the Jackson correlation, with property ratio correction terms to account for the distribution of the properties in the radial direction, could predict the distinction of heat transfer characteristics under heating and cooling conditions. However, it overestimates the average value of heat transfer coefficient in the whole range of the experiment conditions. Finally, a new correlation evaluated by PDF-based time-averaged properties for forced convection heat transfer of CO₂ in both heating and cooling mode at supercritical pressures was developed. Comparison of experimental and computational data with the prediction results by the new developed correlation reveals that it works quite well; i.e., more than 90% data in either heating or cooling mode with various heat fluxes are predicted within an accuracy of ±25%.     

Natural Convective Heat and Mass Transfer of Water with Corrosion Products at Super—Critical Pressures under Cooling COnditions

A numerical study is reported of laminar natural convective heat and mass transfer on a vertical cooled plate for water containing metal corrosion products at super-critical pressures. The influence of variable properties at super-critical pressures on natural convection has been analyzed. The difference between heat and mass transfer under cooling or heating conditions is also discussed and some correlations for heat and mass transfer under cooling conditions are recommended.     

A simple model for heat and mass transfer in absorption cooling systems (ACSs)

The article presents a simple technique for the purpose of heat and mass transfer analysis in an ACS. The LiBr/water ACS was selected as an example. based on optimum operation conditions (i.e., the maximum cooling temperature delivered by the ACS), simple but effective expression were derived in terms of the mass flow rate of absorbent—the most important parameter for practical design calculations. The results show that the proposed technique provides, for practical application purposes, a useful tool for a general analysis of the ACS as well as for the system design purpose.     

Development of a new number (the Dincer number) for forced-convection heat transfer in heating and cooling applications

In this article, a new number is developed for the use of forced-convection transient heat transfer to take place during heating and cooling of any solid object. This is called the ‘Dincer number’ which indicates the effect of the flow velocity of the surrounding fluid on the heating coefficient or cooling coefficient. It indicates that there is a strong relation between the Nusselt number and the Dincer number. For this reason, an application of this number was made and a new Nusselt-Dincer correlation, namely Nu = (2·2893 × 10 ⁻⁴ Di^1·0047) was developed for food products exposed to forced-air cooling using the experimental data sets. It is therefore possible to determine the heat transfer coefficient from the Nusselt number after estimating the Dincer number. It can be concluded that the Dincer number brings a new approach to heating and cooling problems. Owing to their simplicity and effectiveness, development of the Nusselt-Dincer correlations will be beneficial to scientists and industries concerned with heating and cooling applications.     

Flow and heat transfer studies of multijet impingement cooling for different configurations: A review

Increasing the gas turbine engine's turbine intake temperature has long been a potential strategy for increasing the specific work output of the engine. However, the melting temperature of the turbine blades and vane material limits the maximum intake temperature. As a result, internal and external cooling techniques are commonly used to maintain the vane material in a safe condition. This study provided an overview of internal impingement cooling to highlight the significance of geometrical variations, such as flat plate, curve plate, and actual vanes. It was observed that flat and curved plate impingement heat transfer studies were reported extensively, whereas limited studies were found on the conjugate effects on airfoil surfaces. The importance of conjugate heat transfer studies and their impact has recently been described in the literature. In most of the literature, a wide range of instruments, such as Laser Doppler Velocimeter, Particle Image Velocimeter, liquid crystal sheets, and so forth, were used for experimental investigations. According to most studies, the local value of internal surface temperature and heat transfer coefficient are vital factors of local flow behavior. Jet-to-jet spacing, jet-to-plate spacing, jet hole diameter, and jet Reynolds numbers played a crucial role in both numerical and experimental analyses. Different geometric variations strongly influence flow behavior. Therefore, the usual method for determining interior temperature distributions and heat transfer coefficients by considering generalized geometries like the flat and curved plate may not produce accurate conjugate solutions. Most of the computational studies on the flat and curved plate indicate the usage of κ−ω shear stress transport and κ–ε realizable model to predict the heat transfer coefficient.     

A simple solution for transient heat transfer during heating of a slab product

A theoretical and experimental study of transient heat transfer in the heating of an individual slab product, subjected to an air flow at a temperature of 50°C and a velocity of 1 m/s, is presented. Experimental temperature measurements at the centre of the slab product were made, and the experimental heat-transfer rates were derived from the temperature data. A simplified analytical technique, using the boundary condition of the third kind in transient heat transfer, was used to predict the theoretical heat transfer rates for two cases, the first considering that the heat transfer coefficient is a convective heat transfer coefficient, and the second considering that heat transfer coefficient is the sum of the convective and radiative heat transfer coefficients. The experimental heat-transfer rates were compared with the predictions for two cases, and a very good agreement was obtained.     

Reverse computation of forced convection heat transfer for optimal control of thermal boundary conditions

A reverse computation based on adjoint formulation of forced convection heat transfer is proposed to obtain the optimal thermal boundary conditions for heat transfer characteristics; for example, a total heat transfer rate or a temperature at a specific location. In the reverse analysis via adjoint formulation, the heat flow is reversed in both time and space. Thus, using the numerical solution of the adjoint problem, we can inversely predict the boundary condition effects on the heat transfer characteristics. As a result, we can obtain the optimal thermal boundary conditions in both time and space to control the heat transfer at any given time. © 2004 Wiley Periodicals, Inc. Heat Trans Asian Res, 33(3): 161–174, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20002     

Overall heat transfer coefficient in the presence of the axial dispersion coefficient for a forced draught cooling tower

An overall heat transfer coefficient was calculated for a forced draught counterflow cooling tower by using the pulse response technique. The presence of an axial dispersion coefficient for both gas and liquid was considered. Results indicate that, on neglecting the axial mixing and assuming a plug flow, the overall heat transfer coefficient is overestimated and can lead to errors in design applications.     

Simplified solution for temperature distributions of spherical and cylindrical products during rapid air cooling

The transient heat transfer between individual spherical and cylindrical products and the air medium during cooling was analyzed and modeled, and therefore, the center temperature distributions of the spherical and cylindrical products were computed in a simple manner. These computed temperature distributions were compared with experimental measurements, and very good agreement was found between the computed and measured temperature values.     

大型轴类工件喷气冷却流动和传热特性的数值模拟

以某喷气冷却装置为参考,对缝隙喷气冷却大型轴类工件展开研究.通过数值模拟研究了具有两相对缝隙的大型轴类工件(直径D=1 000～3 000 mm)喷气冷却装置内的漉动传热特性,对比数值计算结果与实验数据验证了模型预测的准确性,探讨了大型喷气冷却装置内部气体的流动特点,分析了双缝隙喷气冷却轴类工件的传热规律,获得了轴类工...     

Development of a finite element based heat transfer model for conduction mode laser spot welding process using an adaptive volumetric heat source

Numerically computed results of weld pool dimensions in conduction mode laser welding are sensitive to the estimated value of the actual beam energy absorbed by the substrate. In a conduction based heat transfer analysis, the incorporation of the laser beam induced energy as a surface only heat flux fails to realize enhanced heat transfer in weld pool as molten material attains higher temperature and convective transport of heat becomes predominant. An alternate is to include fluid flow analysis considering phenomenological laws of conservation of mass and momentum that greatly increases the complexity in modeling. Uncertainty of material properties such as effective thermal conductivity and viscosity in the weld pool also impedes such extensive fluid flow analysis. A simpler and tractable approach can be to consider a volumetric heat source within weld pool in a conduction based heat transfer analysis. Earlier efforts to accommodate volumetric heat source such as double-ellipsoidal form remained unpopular since the size of the final weld pool shapes is required to be known to begin with the calculation. The present work describes an improved approach where a volumetric heat source is defined adaptively as the size of the weld pool grows in size within the framework of a conduction based heat transfer analysis. The numerically computed results of weld pool dimensions following this approach have shown fair agreement with the corresponding measured values for laser spot weld samples.     

Influence of conjugate heat transfer on the minimization of entropy generation for forced convective flow through parallel plate channel filled with porous material

A fluid–solid conjugate heat transfer model is developed to analyze the characteristics of entropy generation for forced convective steady hydrodynamically fully developed laminar flow of a Newtonian fluid through a parallel plate channel filled with porous material by modulating the following parameters: substrate thickness, the ratio of thermal conductivity of wall to fluid, Biot number, the axial temperature gradient in the fluid, and Peclet number. The exteriors of both the walls are subjected to the thermal boundary conditions of the third kind. The mass and Brinkman momentum conservation equations in the fluidic domain and the coupled energy conservation in both the solid and fluidic domain are solved analytically using the local thermodynamic equilibrium model, so as to derive closed-form expressions for the velocity in the fluid and the temperature both in the fluid and solid walls in terms of relevant parameters. Suitable combinations of influencing factors, namely the geometric parameters of the system, fluid, flow, and substrate properties are identified for which global entropy generation rate is minimized. The findings may be helpful in the design of thermal systems frequently used in diverse engineering applications having heat transfer in the solid wall being a crucial parameter.     

Analysis of a combined power and cooling cycle for low‐grade heat sources

This paper presents a parametric analysis of a combined power/cooling cycle, which combines the Rankine and absorption refrigeration cycles, uses ammonia–water mixture as the working fluid and produces power and refrigeration, while power is the primary goal. This cycle, also known as the Goswami Cycle, can be used as a bottoming cycle using waste heat from a conventional power cycle or as an independent cycle using low‐temperature sources such as geothermal and solar energy. Optimum operating conditions were found for a range of ammonia concentration in the basic solution, isentropic turbine efficiency and boiler pressure. It is shown that the cycle can be optimized for net work, cooling output, effective first law and exergy efficiencies. The effect of rectification cooling source (external and internal) on the cycle output was investigated, and it was found that an internal rectification cooling source always produces higher efficiencies. When ammonia vapor is superheated after the rectification process, cycle efficiencies increase but cooling output decreases. Copyright © 2010 John Wiley & Sons, Ltd.     

Unsteady free convection of second‐grade nanofluid with a new time‐space fractional heat conduction

The Caputo and Caputo–Fabrizio derivative are applied to study a second‐grade nanofluid over a vertical plate. A comparative analysis is presented to study the unsteady free convection of a second‐grade nanofluid with a new time–space fractional heat conduction. The governing equations with mixed time–space fractional derivatives are non‐dimensionalized and solved numerically, and a comparison between the Caputo and the Caputo–Fabrizio models is made. It is found that the temperature is higher for the Caputo–Fabrizio fractional model than the Caputo model, but the higher velocity only exists near the vertical plate for the Caputo–Fabrizio model than the Caputo model. Moreover, the velocity for the Caputo model will exceed the Caputo–Fabrizio model as y evolves.     

Experimental and numerical study of convection heat transfer of CO2 at super-critical pressures during cooling in small vertical tube

Convection heat transfer of CO₂ at super-critical pressures during cooling in a vertical small tube with inner diameter of 2.00 mm was investigated experimentally and numerically. The local heat transfer coefficients were determined through a combination of experimental measurements and numerical simulations. This study investigated the effects of pressure, cooling water mass flow rate, CO₂ mass flow rate, CO₂ inlet temperature, flow direction, properties variation and buoyancy on convection heat transfer in small tube. The results show that the local heat transfer coefficients vary significantly along the tube when the CO₂ bulk temperatures are in the near-critical region. The increase of specific heat and turbulence kinetic energy due to the density variation leads to the increase of the local heat transfer coefficients for upward flow. The buoyancy effect induced by density variation leads to a different variation trend of the local heat transfer coefficients along the tube for upward and downward flows. The numerical simulations were conducted using several k–ε turbulence models including the RNG k–ε model with a two-layer near wall treatment and three low-Reynolds number eddy viscosity turbulence models. The simulations using the low-Reynolds number k–ε model due to Yang–Shih has been found to be able to reproduce the general features exhibited in the experiments, although with a relatively large overestimation of measured wall temperatures. A better understanding of the mechanism of properties variation and buoyancy effects on convection heat transfer of CO₂ at super-critical pressures in a vertical small tube during cooling has been developed based on the information generated by the simulation on the detailed flow and turbulence fields.     

Characteristics of heat transfer inside a tube during sodium‐water reaction in a FBR steam generator

Sodium reacts chemically with water in the case of an unexpected tube failure of a steam generator (SG) in a fast breeder reactor (FBR). In order to predict the event with high accuracy, it is very important to understand the characteristics of heat transfer inside the tube in detail during the tube failure due to the sodium–water reaction. Experiments were performed by using purified water under the following conditions: initial pressure of 11.2–13.4 MPa, initial water temperature of 200 °C, and water mass flux of 45.7 to 3630 kg/(m²s). The test tube was heated rapidly by high‐frequency induction current. The time averaged heat flux was estimated by using an inverse solution from the measured temperatures at two points on three different locations along the tube. It was confirmed that the derived values agreed with the measured heat fluxes on the outer surface within 20% accuracy. It was found that the characteristics of the heat transfer strongly depend on the flow rate. The heat transfer on the wall changed from nucleate boiling to transient‐film boiling during increasing the heat flux and returned to the nucleate boiling during decreasing the heat flux. A counterclockwise cycle always appeared in the transition boiling region, where the nucleate and film boiling coexisted and the area ratio of these varied with time. The adequacy of heat transfer correlations to evaluate tube overheating was confirmed. © 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/htj.20320