Heat Transfer Coefficient Model Research Articles

Heat transfer parameter models and correlations for cooling applications

Cooling technology is widely used in a variety of engineering applications ranging from cooling of electronic devices to food cooling. It makes this industry play an important role in the economies. In practice there is an urgent need to design a cooling system with the optimum processing conditions and to provide energy saving along with the high quality products. In this respect, accurate determination of the heat transfer parameters for the cooling operation is essential. In this paper, recently developed models and correlations, e.g., thermal diffusivity and heat transfer coefficient models, and Nusselt–Reynolds and Fourier–Reynolds correlations to determine the cooling process and heat transfer parameters are presented with an illustrative example. Another important point is that the cooling parameters are incorporated into the heat transfer parameters and correlations. It is believed that these models and correlations are of great significance to refrigeration industry.

Analysis of a Load-Side Heat Exchanger for a Solar Domestic Hot Water Heating System

Testing is done of an unpressurized drainback system with a load-side heat exchanger. Analytical calculations for the heat exchanger effectiveness and three models for convective heat transfer coefficients from correlations are compared against the experimental data. TRNSYS simulations were performed using the average effectiveness of 0.78 (the calculated effectiveness varies from 0.68 to 0.95); the results compare favorably with experimental results, indicating that a constant effectiveness is an adequate model for the system.

Heat transfer during heat sterilization and cooling processes of canned products

In this paper, an analysis of transient heat transfer during heat sterilization and cooling processes of a cylindrical canned product is presented. In the analysis, most practical case including the boundary condition of third kind (i.e., convection boundary condition, leading to 0.1 ≤ Bi ≤ 100) was employed. A simple analytical model for determining effective heat transfer coefficients for such products is developed. For the heat sterilization process, heating coefficient is incorporated into heat transfer coefficient model. An experimental study was performed to measure the thermal center temperatures of the short-cylindrical canned products (i.e., Tuna fish) during heat sterilization at the retort medium temperatures of 115∘C and 121∘C, and during cooling process at 16∘C. The effective heat transfer coefficient model used the experimental temperature data. Using these effective heat transfer coefficients the center temperature distributions were calculated and compared with the experimental temperature distributions. Agreement was found considerably high. The results of the present study indicate that the heat-transfer analysis technique and heat-transfer coefficient model are reliable, and can provide accurate results for such problems.

Heat transfer and nonlinear thermal stress analysis of a convective surface mount package

Most prior heat transfer and thermal stress analyses of convective surface mount packages have relied on either an isothermal (constant temperature) model or a constant heat transfer coefficient model. This usually leads to a concern for the accurate estimation of the local temperature distributions and the induced stresses. To release this concern, this paper presents the use of the finite element analysis method in predicting the local temperature and stress distributions of a ceramic ball grid array (CBGA) package. The analysis has included a local heat transfer coefficient model with the thermal boundary condition that was obtained from a previous computational fluid dynamics (CFD) solution. The results are compared with that predicted by the isothermal model and the constant heat transfer coefficient model. Instances where the temperature dependent and elastic-plastic material behavior are significant to produce nonlinear stress response in some components of the modeled package are also examined.

Predictable Modelling of Heat Transfer Coefficient between Spraying Water and a Hot Surface above the Leidenfrost Temperature.

In order to evaluate the cooling intensity of water spray impacting on a hot metallic surface above the Leidenfrost temperature, the formulation of heat transfer coefficient in the forced convection boiling region has been made as a function of the droplet size, the impinging velocity and the number density of droplets whose parameters are independent of each other. So far, many works on the mist/spray cooling process have been made, in particular, from an experimental point of view. However, the general procedure capable of evaluating heat transfer rate between a hot metallic surface and water spray has not been established yet, because there are a large number of parameters affecting the spray cooling process. Then, we have experimentally derived a new formula consisting of the above three parameters to be dominant for heat transfer rate in the spray cooling process. The stainless steel surface heated to about 900°C has been cooled by water spray of ∼20°C and the time history of the surface temperature has been measured. We have selected some kinds of full cone nozzles whose characteristics such as the average droplet diameter, the velocity and the distribution of water flux have been different from each other, and performed the cooling tests using them. Finally, the formula capable of giving best-fit to the experimental results has been proposed. The effect of the spraying characteristics on the heat transfer rate has been discussed from an experimental point of view.

Numerical model using an implicit finite difference algorithm for stability simulation of a cable-in-conduit superconductor

A new numerical model and calculation method for stability simulation of a cable-in conduit conductor (CICC) has been developed. In this model, the governing equations are a one-dimensional fluid dynamics equation and heat conduction equations for strands and a conduit. Precise modelling of transient heat transfer from the strands to the coolant is the key to accurate simulation of stability. Modelling of the transient heat transfer coefficient is carried out more accurately than the conventional model by taking into account the variation in the heat flux and the temperature around the strands. The governing equations are made discrete by an implicit time-dependent finite different scheme to avoid any limitation from the CFL (Courant-Friedrichs-Lewy) condition. The finite different equation for the fluid is linearized according to a certain procedure used by Beam and Warming, resulting in a tridiagonal system. Therefore, no iteration is necessary to solve the fluid dynamics equation, in spite of the use of the implicit scheme. As a result, a large amount of CPU time could be saved. The simulated and experimental results of stability for a small CICC was compared for verification of the code. The results were in good agreement, resulting in a completion of the verification of the code.

Convective Heat Transfer Coefficient Model for Spherical Products Subject to Hydrocooling

An analytical model was developed to determine the convective heat transfer coefficients of spherical products being cooled in any medium. In order to verify the present model, the experimental center temperature measurements of the individual spherical products (i.e., plums, peaches, tomatoes, pears) were determined in batches containing 5 and 20 kg of product. It was found that the convective heat transfer coefficient of an individual product varied with the batch weight. This study shows that the present model is a simple and effective tool to determine such coefficients and could be a benefit to the refrigeration industry.

An analytical model for local heat transfer coefficients for forced convective condensation inside smooth horizontal tubes

An analytical model based on annular flow is proposed for predicting the local heat transfer coefficient for forced convective condensation inside smooth horizontal tubes. The Prandtl mixing length theory, Van-Dreist's hypothesis and Reynolds analogy are used for the analysis. Experiments are conducted by condensing R-22 inside an 8.001 mm (0.315 in.) i.d. copper tube for a wide range of mass flux rates and condensing temperatures. The analytical results, compared with the experimental data and four other correlations reported in the literature indicate that 80% of the predictions are within ±25% of the experimental data, with a mean deviation of 15.3%.

Effect of interior heat transfer coefficients on thermal dynamics and energy consumption

A thermal analysis program of buildings, called TASE, has been verified in cooperation with the International Energy Agency (IEA) and used to study the effects of interior heat transfer coefficient models on the thermal dynamics of a test cell and on the energy consumption and peak loads of an office building module. Measured and calculated interior air and surface temperatures and values of the wall heat flux have been compared. The correlation equations of ASHRAE, Alamdari and Hammond and Khalifa and Marshall have been used in the calculations. Both constant heat transfer coefficients, i.e., average values for the whole calculation period, and variable heat transfer coefficients, i.e., those calculated for each time point iteratively using the air-surface temperature differences, have been used in the calculations. The principles for modelling a radiator heating system have also been presented.

A measurement technique and a new model for the wall heat transfer coefficient of a packed bed of (reactive) powder without gas flow

An experimental technique, designed for investigating altogether the effective thermal conductivity and the wall heat transfer coefficient in a packed bed of hydride powder, and the coupling of heat transfer with the hydriding reaction, is presented. It consists of measuring transient temperature evolution in a reactor with only geometrical symmetry and of fitting to the experimental data the numerical solution of the heat equation in the two-dimensional domain including the whole reactor. This method requires only a relatively small powder volume (30 cm 3). As a first step, results on non-reactive packed beds (500 μm glass beads with argon and 20 μm iron powder with hydrogen) validate the experimental technique. A new model for the wall heat transfer coefficient is developed for packed beds without gas flow. This model attempts to unify the current differing approaches of modeling this quantity. It predicts high values for small grain size and large variations in the Knudsen transition domain: this is qualitatively confirmed by experiments, with coefficients at around 3000 W m 2 K 1 being measured for 20 μm iron powder in hydrogen. Experimental results show that the pressure-dependent thermal resistances on wall and grain surfaces are not negligible.

Momentum, heat and mass transfer in turbulent pipe flow: The extended random surface renewal model

A model is presented for a quantitative prediction of the transfer coefficients of momentum, heat and mass, and the radial profiles of the axial velocity, the temperature, and the concentration in the near-wall fluid of a turbulent pipe flow. In this model, the tube wall is assumed to be covered by a mosaic of fluid elements of random age and laminar flow with unsteady profiles of velocity, temperature, or concentration. This model, which is an extension of the RSR model developed by Fortuin and Klijn, is the extended random surface renewal model, and is referred to as the ERSR model. The distribution and the mean value of the ages of the fluid elements at the tube wall govern the local time-averaged transfer coefficients and radial profiles in the wall region. The mean age of the fluid elements is derived from the friction factor and the Reynolds number using the ERSR model. Both the distribution and the mean ages of the fluid elements at the tube wall agree quantitatively with the experimental results obtained from velocity signals measured with a laser-Doppler anemometer in turbulent pipe flow at thirteen Reynolds numbers between 5 × 10 3 and 43 × 10 3. The equations derived from the ERSR model for the local time-averaged heat and mass transfer coefficients in turbulent pipe flow, and the radial profiles of the axial velocity, the temperature and the concentration in the wall region, agree with correlations or experimental data presented in literature. The analogy between momentum, heat and mass transfer in turbulent pipe flow is elucidated by introducing a dimensionless number for momentum transfer. This so-called Fanning number for momentum transfer ( Fa = k m d/v), is comparable with the Nusselt number for heat transfer and the Sherwood number for mass transfer. Furthermore, the ERSR model provides a basis for both explaining the Chilton-Colburn analogy and the relationship between transfer rates and measured mean ages of fluid elements at the wall in turbulent pipe flow.

Heat transfer and gas holdup in a two-phase bubble column: Air-water system — Review and new data

Hydrodynamic and heat transfer investigations on an air-water system in a bubble column are reported and discussed. Gas holdup data (total and local) and the heat transfer coefficient between a 19 mm outer diameter heat transfer probe and an air-water dispersion are measured in continous and semibatch mode. In addition to new data, earlier data of Saxena et al and those available in the literature are discussed and employed to assess the available correlations and models for gas-phase holdup and heat transfer coefficient. Simple approaches based on general theoretical considerations are proposed to correlate gas holdup and heat transfer data. A few interesting conclusions follow from this study.

Modelling the cooling phase of heat sterilization processes, using heat transfer coefficients

SummaryA mathematical model based on finite differences was presented, which improved the accuracy of current modelling techniques during the cooling period for conduction heating foods undergoing thermal processing. The surface heat transfer coefficient between can and cooling fluid was incorporated into the finite difference equations, with a value of 600 W m−2 K−1 chosen from literature and confirmed by calculations from surface temperature measurements and a correlation of the form Nu = f(GrxPr)n.Experimental results were obtained for a cylinder of Sylgard 184 elastomer (length 62mm, diameter 57mm) and a polypropylene block (26x91x141 mm). At the end of cooling the heat transfer coefficient model predicted a centre temperature just 2.5°C above the measured value for polypropylene, and for Sylgard 184 this difference was 2.7°C.This model will improve both real‐time process control via the ‘derived‐value’ technique, and the use of controlled pressure cooling with less damage to containers. Optimization of quality factors will also be improved with increased knowledge of in‐container temperatures.

Forced Convection Heat Transfer from a Shrouded Fin Array with and without Tip Clearance

An analysis is made of the laminar heat transfer characteristics of an array of longitudinal fins with an adiabatic shroud situated adjacent to the fin tips. The analysis involves the solution of the velocity field in the inter-fin space and in the shroud clearance gap beyond the tips, after which the governing energy equations for the fluid and the fins are solved simultaneously. Solutions are obtained for representative values of dimensionless parameters which describe the system geometry and the fin conductance. For the fin, the results show that the heat loss is a minimum adjacent to the base and increases along the fin in the direction of the tip. The maximum fin heat loss occurs either at the tip or intermediate between the base and the tip, depending on whether or not there is clearance between the fin tips and the shroud. The calculated heat transfer coefficients vary along the fin and, in some cases, take on negative values. Heat loss variations are also encountered along the base surface, the extent of which depends on the fin conductance, the inter-fin spacing, and the extent of the clearance gap. With regard to the overall heat loss, the fin is, on a unit area basis, a more efficient transfer surface than is the base. The results demonstrate that the conventional uniform heat transfer coefficient model is inapplicable to shrouded fin arrays.