Non-uniform Heat Transfer Coefficient Research Articles

Some recent progress in reactor core thermal-hydraulics modelling

In the last more than ten years the research groups of the present authors have been working on some of the key phenomena or parameters widely used in sub-channel thermal-hydraulics (SCTH) codes, e.g. (a) transversal exchange between sub-channels, (b) circumferential non-uniform heat transfer in fuel assemblies with tight or semi-tight lattice (pitch-to-diameter ratio smaller than 1.25), (c) PDO heat transfer and rewetting and (d) CFD analysis of two-phase flow and heat transfer, incl. critical heat flux. Among others, three transversal exchange phenomena were studied, i.e. turbulent mixing coefficients, void drift and wire wrap induced sweeping flow. New models for various turbulent mixings, void drift and wire wrap induced cross flow were developed based on analytical analysis and CFD simulations. Importance of the non-uniform heat transfer behavior inside single sub-channel was identified in fuel assemblies with tight or semi-tight lattice. Correlations for predicting the non-uniform heat transfer coefficient were proposed, which were implemented into SCTH codes, to accurately determine the local hot spot on the fuel pin surface. A large experimental data base containing more than 60,000 data points of PDO heat transfer and rewetting was established. Based on the data base a new empirical correlation of PDO heat transfer was proposed. In addition, dynamic behavior of droplets (droplet size and velocity) and the thermal non-equilibrium were experimentally measured, which can be used for the validation and improvement of mechanistic models of PDO heat transfer and rewetting, also proposed by the research groups of the present authors. For the CFD prediction of CHF, a new and robust method for wall boiling heat transfer was developed to calculate the near wall void fraction and its connection to CHF.

Optimising integrated heat spreaders with distributed heat transfer coefficients: A case study for CPU cooling

Increasing power densities of modern CPUs has led to regions of high temperature on the semiconductor die which can lead to performance and reliability problems. In this case study, the effect of imposing a non-uniform heat transfer coefficient profile across the convective surface the CPU's integrated heat spreader was investigated as a potential enhanced cooling concept. A finite element model of a copper heat spreader of 40 × 40 mm2 area and 2.5 mm thickness with a centred 13 × 13 mm2 heat source at 100 W/cm2 heat flux was considered to approximate typical modern high-powered CPUs. Both uniform and Gaussian distributions of the heat transfer coefficient were then considered. For the latter, both single and multi-objective Genetic Algorithm optimisation were carried out for three source temperature objectives; average temperature, maximum temperature and maximum temperature difference. The analysis showed that the multi-objective optimisation strategy produced the best overall heat transfer coefficient distribution, with almost 5 K reduction in both the maximum temperature and temperature gradient across the heat source compared with a uniform heat transfer coefficient distribution.

The influence of nonuniform heat transfer coefficient distribution on the value of thermal deformations in mechanical gas dynamic seal rings

Currently, many different aircraft engine types exist. They have a wide range of operating conditions: the flight speed can vary from zero to hypersonic values, the flight altitude from near-earth conditions to space flights. During the flight, loads are not kept constant. Engines have significant dynamic overloads, temperature and pressure differences, can operate in conditions of high humidity or dust, as well as in various aggressive environments. The development of aviation and rocket engine building is associated with a continuous increase in the working thermodynamical cycle parameters.Further improvement of gas turbine engines (GTE) can be carried out in two directions. The first is using new advanced engine designs based on a modernized cycle, with a different fuel, original design, and power scheme. This direction also includes the application of new high-performance elements in the engine: bearings, seals, coatings, etc. The second direction is related to the improvement of existing structures, increasing their efficiency by more detailed working conditions forecasting based on the use of modern computing software systems. This article presents a study of the potential mechanical face gas dynamic seal (FGDS) in the support in an aircraft engine compressor. Aircraft engines are characterized by multi-mode operation and high temperature levels in the internal cavities. For a FGDS operating with a working gap of several microns the exact determination of the deformation value is a very important result of the design process. This article considers the influence of the convective heat transfer coefficients distribution on the value of sealing rings thermal deformations. To achieve this goal, two compaction models were created: the gas-dynamic model for determining the convective heat transfer coefficients in the ANSYS CFX software program; and the structural model for calculating the resulting deformations. Interaction between the models was performed based on a specially created methodology. The obtained results can be used in the design of a FGDS for the supports in the compressors of aircraft engines and power plants.

Numerical Simulation of Coupling Thermal and Mechanical Influence on Submerged Nozzle in Solid Rocket Motor

The coupling thermal and mechanical effect on submerged nozzles is important in the design of modern rockets upon thermal loading and aerodynamic pressure. In this paper, a simulation with the subroutine of nonuniform pressure and nonuniform heat transfer coefficient was conducted to study the thermo-structural response of a submerged nozzle at the pressure 6 MPa and stagnation temperature 3200 K. Both the aerodynamic parameters and heat coefficients were obtained through analyzing the flow field. It was found that the thermal loading had an important influence on the stress of throat insert for the solid rocket motor (SRM). The hoop stress increases at first and then decreases with the increase of time for the throat insert. The ground hot firing test of SRM with a submerged nozzle was carried out. The experimental results showed that the structural integrity of the submerged nozzle is very normal during SRM operation. The present method is reasonable, which can be applied to study the thermo-structural response of submerged nozzle for SRM.

Residual Stress Distribution of Non-Uniform Quenching in Al-Zn-Mg-Cu Aluminum Alloy Thick Plate

Effect of multi-section linear non-uniform heat transfer coefficient on quenching residual stress distribution in 27mm-thick Al-Zn-Mg-Cu aluminum alloy plate was simulation studied by using the finite element method, and the surface quenching residual stress distribution was measured by the X-ray diffraction method and hole-drilling method. The results show that the surface quenching residual stress represents the same distribution with non-uniform heat transfer coefficient in the transverse direction and the stress level maintains initial stress level of the heat transfer coefficient at each location. The distribution of the quenching residual stress in the center of the plate is approximately uniform and the stress level is approximately equal to average of maximum and minimum initial stress level. The measured surface quenching residual stress shows a wavy distribution in the transverse direction, which is similar to the simulated surface stress distribution without considering the stress level. The measurement results can be explained by the multi-section linear non-uniform quenching model.

Thermal Resistance of a Three-Dimensional Flux Channel with Two-Dimensional Variable Convection

In the microelectronics industry, heat sinks are used for cooling microelectronic devices by transferring the heat generated by the device into an ambient fluid. In most applications, the heat convection along the sink plane is not uniform due to a nonuniform heat transfer coefficient that might be present according to a nonuniform distribution of the sink extended surfaces (fins or bins) or because of the nonuniform nature of a moving ambient fluid over the sink region. This can be observed when considering a jet impingement or transverse fans as cooling techniques. In this paper, analytical approximate solutions of the temperature field and the thermal resistance of a three-dimensional flux channel with eccentric heat source(s) and a variable heat transfer coefficient that varies in the two horizontal dimensions are developed. The method of the separation of variables combined with the method of least squares is used to develop these solutions. Different parametric studies are conducted to study the effect of two different variable heat transfer coefficient distributions on the dimensionless total thermal resistance of the channel and the temperature distribution along the source plane in comparison with using a uniform heat transfer coefficient. For verification reasons, the analytical results are compared with numerical solution results obtained based on the finite element method using the ANSYS commercial software package.

Study of coupling thermal and mechanical effect on submerged nozzle in solid rocket motor

The thermo-structural response of submerged nozzles is widely investigated in the design of modern rockets upon thermal loading and aerodynamic pressure. In this paper, by means of commercial finite element software with the subroutine of non-uniform pressure and non-uniform heat transfer coefficients, the simulation was performed to study the thermo-structural response of a submerged nozzle at the pressure 6MPa and stagnation temperature 3200K. By means of fluid software, the steady flow field with hot gas was determined. The aerodynamic parameters and heat coefficients were obtained. It was found that the thermal loading has an important influence on stress of throat insert for the solid rocket motor (SRM). Secondly, the hoop stress increases at first and then decreases with the increase of time for the throat insert. Finally, the ground hot firing test of SRM with submerged nozzle was carried out. The structural integrity of the submerged nozzle is very perfect during SRM operation. The present method is reasonable, which can be applied to study the thermo-structural response of submerged nozzle for SRM.

Mechanism analysis of the buoyancy effects on heat transfer of supercritical nitrogen in horizontal serpentine tube

In this paper, the buoyancy effects on heat transfer performance of cryogenic supercritical fluid in the submerged combustion vaporizer (SCV) are studied experimentally and numerically. Supercritical nitrogen is selected to substitute LNG for the safety reason. A three-dimensional model is established to calculate the flow and heat transfer of supercritical nitrogen, and the maximum relative error between the simulation and experiment is 2.78%. Based on the simulation results, a non-uniform circumferential heat transfer coefficient distribution is found in the pseudo-critical region, and the mechanism of the non-uniformity is analyzed. The reason for the phenomenon that the top and bottom generatrices reach the peak value of the heat transfer coefficient at different positions is further revealed by analyzing the average thermo-physical properties in different regions of the boundary layer. The results showed that the secondary flow caused by buoyancy leads to a non-uniform distribution of the thermal boundary layer thickness on the radial section. Under the influence of buoyancy, the temperature of the buffer layer near the top and bottom generatrices reach the large specific heat region successively, leading the peak position of the heat transfer coefficient of them not appear synchronously. Overall, comparing to the no-buoyancy condition, the whole heat transfer coefficient increased, with the heat transfer enhancement at the bottom and side generatrices but deterioration at the top generatrix.

Spreading Resistance in Flux Tubes With Variable Heat Flux and Nonuniform Convection

cylindrical-shaped flux tubes with variable heat flux distributions and nonuniform heat transfer coefficients are obtained. The solutions are presented based on the method of separation of variables combined with the method of least squares in the cylindrical coordinate system. In the source region, a variable heat flux modeling function is considered. The modeling function depends on a distribution parameter, where different distributions can be defined by changing the value of this parameter. Along the sink region, a nonuniform heat transfer coefficient with a distribution parameter is considered. The sink distribution parameter can define a wide variety of different conductance distributions, from intense conductance under the source area to a uniform conductance along the entire sink plane. The developed solutions are used to evaluate the nondimensional total thermal resistance for different nondimensional parameters, represented by the heat-source aspect ratio, thickness aspect ratio, Biot numbers, flux distribution parameter, and conductance distribution parameter. The solutions are used to examine the effects of different conductance distributions on the nondimensional total thermal resistance for three different heat flux distributions. Furthermore, numerical results based on the finite-element method are obtained for some of the conducted studies to verify the analytical results, where very good agreement has been observed.

Thermal spreading resistance of heat sources on rectangular flux channel under non-uniform convective cooling

A general solution, based on the method of separation of variables, for the temperature distribution of an orthotropic rectangular substrate heated by heat sources on one side and cooled with a non-uniform heat transfer coefficient on the opposite side is presented. A system of infinitely many algebraic equations obtained by taking advantage of the orthogonality property is encountered and must be solved for the solution coefficients. An iteration method is proposed to overcome this difficulty. Such an analytical solution provides an easy and efficient way to explore the influence of relevant parameters. A fitting curve to the analytical predictions against interested parameters can be next obtained, if desired, to replace the troublesome infinite-series solution and employed in the resistor-capacitor thermal models for predicting the heat dissipation power of electronic packaging designs.

Multi-Pass Serpentine Cooling Designs for Negating Coriolis Force Effect on Heat Transfer: Smooth Channels

The combined action of Coriolis and centrifugal buoyancy forces results in nonuniform heat transfer coefficient on pressure and suction side internal walls, hence leading to nonuniform metal temperatures and increased thermal stresses. The present study addresses the problem of nonuniform heat transfer distribution due to rotation effect and proposes novel designs for serpentine cooling passages, which are arranged along the chord of the blade. The two configurations were four-passage and six-passage serpentine smooth channels. Detailed heat transfer coefficients were measured using transient liquid crystal thermography under stationary and rotating conditions. Heat transfer experiments were carried out for Reynolds numbers ranging from 12,294 to 85,000 under stationary conditions. Rotation experiments were carried out for the Rotation numbers of 0.05 and 0.11. Heat transfer enhancement levels of approximately two times the Dittus–Boelter correlation (for developed flow in smooth tubes) were obtained under stationary conditions. Under rotating conditions, we found that the four-passage configuration had slightly lower heat transfer compared with the stationary case, and the six-passage configuration had higher heat transfer on both the leading and trailing sides compared with the stationary case. The leading and trailing side heat transfer characteristics were near-similar to each other for both the configurations, and the rotating heat transfer was near-similar to the stationary condition heat transfer.

Computational examination of two-phase microchannel heat transfer correlations with conjugate heat spreading

Microchannel flow boiling is an attractive thermal management strategy for ever-growing volumetric heat dissipation demands associated with electronic systems. Due to difficulties related to measurement at the microscales, the majority of researchers have chosen to study relatively simple situations with uniform heat flux. However, many applications involve local hotspots which give rise to highly non-uniform heat flux and temperature gradients due to heat spreading. This necessitates the consideration of conjugate heat transfer for accurate analysis.The current work is aimed at investigating conjugate heat transfer in a two-phase microchannel array. Experimental data was collected on R134a flow boiling heat transfer for very small hydraulic diameter (<100 µm) silicon microchannels with very high heat fluxes (>1 kW cm−2) applied via platinum strip heaters with a footprint size of 1 cm × 1 mm. The collected experimental data was then combined with detailed computational modeling utilizing finite element modeling with COMSOL Multiphysics and MATLAB to examine the applicability of five published heat transfer correlations for use in determining local heat transfer coefficients. A two-phase correlation from Agostini and Bontemps, developed for markedly different test parameters, provided the best computational agreement with an RMS temperature difference from experiment of 3.3 °C and a predicted peak perimeter-averaged heat transfer coefficient of 116 MW m−2 K−1. Modeling confirms the presence of highly non-uniform local heat flux and correspondingly non-uniform local heat transfer coefficient. The results of this study make clear the need for better micro-scale two-phase correlations developed to predict local heat transfer coefficients at these small scales and high local heat fluxes.

Thermal optimization of tapered pin fin exposed to nonuniform surface heat transfer coefficient

Thermal optimization of tapered pin fin exposed to nonuniform surface heat transfer coefficient

Thermal Resistance of a 3-D Flux Channel With Nonuniform Heat Convection in the Sink Plane

Heat sinks are designed in different types and shapes depending on temperature distribution along the sink plane, where sometimes intense cooling is only required in the high-temperature regions. Thus, a nonuniform heat transfer coefficient might be present along the sink plane. In this paper, the temperature distribution and thermal resistance of a 3-D flux channel with a nonuniform heat transfer coefficient along the sink plane is modeled and analyzed by solving the problem analytically. A single concentric heat source is considered in the source plane, while the conductance along the sink plane is modeled by a symmetric conductance function. This function is used to define different conductance distributions along the sink plane from the most intense conductance in the central area to a uniform conductance along the sink plane. Furthermore, a convective cooling condition with uniform conductance is assumed along the lateral edges of the channel, which can be turned into adiabatic edges by assuming a very small heat transfer coefficient along the edges. The problem is solved analytically using the method of separation of variables combined with the method of least squares. A dimensionless total thermal resistance is then introduced to study the effect of different aspect ratios between the heat-source dimensions, cross-sectional dimensions, and channel thickness for different Biot numbers and different conductance distributions along the sink plane. For validation of the presented solution, the analytical results were compared with numerical solution results obtained by solving the problem with the finite-element method using the ANSYS commercial software package.

Heat and moisture transfer in a counter flow regenerative evaporative cooler made of plastic film/paper composite

In this study, a new Regenerative evaporative cooler (REC) sample was made, and heat and moisture transfer characteristics were investigated. Heat and moisture transfer model was developed, which incorporated salient features of REC, for example air leakage between channels, entrance region, non-uniform overall heat transfer coefficient, etc. Comparison of the model with limited experimental data revealed favorable results. There existed optimum extraction ratio, which maximizes the cooling capacity. On the other hand, dew point efficiency increased as extraction ratio increased. Parametric study revealed that dew point efficiency increased as dry channel inlet temperature or hmidity increased. However, cooling capacity decreased as humidity increased.

Modeling of Heat and Moisture Transfer in an Indirect Evaporative Cooler Made of Plastic Film/Paper

In this study, a thermal model of indirect evaporative cooler (IEC) was constructed. An IEC made of plastic film/paper composite was tested, and the results were compared with predictions of the model. In adddition, parametric study was conducted using the model. The model was based on [Formula: see text]-NTU analysis of wet surface heat and mass transfer. Especially, the model considered air leakage, nonuniform overall heat transfer coefficient and entrance region. Comparison of the predictions of the model with limited experimental data showed favorable results. Parametric study using the model showed that increase of the dry and wet channel inlet temperature resulted in increase of the indirect evaporation efficiency. The increase of the wet channel inlet humidity also increases the efficiency. The dry channel inlet humidity, however, was independent of the efficiency. The indirect evaporation efficiency and the pressure drop increased as the IEC size increased. However, they decreased as the channel height increased.

Heat transfer and erosion mechanisms of an immersed tube in a bubbling fluidized bed: A LES–DEM approach

Particle-scale modeling of the gas–solid motion in a bubbling fluidized bed is conducted to explore the heat transfer and erosion mechanisms of an immersed tube. Heat transfer and erosion quantities around the tube are obtained to analyze the critical factors affecting their distributions. The results indicate that vigorous particle stream washes against the top and bottom of the tube, resulting in the formation of a halo and a stagnated cap in these two regions, respectively. Instantaneous heat transfer coefficient oscillates in a complex way with the solid velocity and concentration near the tube surface. The non-uniform time-averaged heat transfer coefficient around immersed tube is a combined effect of local solid velocity and concentration. Total heat transfer flux is mainly occupied by the convective heat flux. Moreover, erosion distribution can be identified from the circumferential distribution of solid flux. Increasing the superficial velocity enlarges the local heat transfer coefficient and the erosion quantity.

Investigation of heat transfer characteristics in plate-fin heat sink

The present study applies the inverse method in conjunction with the experimental temperature data to investigate the accuracy of the heat transfer coefficient on the fin in the plate-fin heat sink for various fin spacings. The commercial software is applied to solve the governing differential equations with the RNG k–ɛ model in order to obtain the heat transfer and fluid flow characteristics. Under the assumption of the non-uniform heat transfer coefficient, the entire fin is divided into several sub-fin regions before performing the inverse scheme. The average heat transfer coefficient in each sub-fin region is assumed to be unknown. Later, the present inverse scheme in conjunction with the experimental temperature data is applied to determine the heat transfer coefficient and fin efficiency. In order to determine a more reliable heat transfer coefficient, a comparison between the present inverse and numerical results and those obtained from the existing correlations will be made. The numerical fin temperatures will also be compared with the experimental data.

Theoretical prediction of longitudinal heat conduction effect in cross-corrugated heat exchanger

In the elementary heat exchanger design theory, the longitudinal heat conduction through the heat transfer plate separating hot and cold fluid streams is neglected, and only the transverse heat conduction is taken into account for the conjugate heat transfer problem. In the cross-corrugated heat exchanger, the corrugated primary surface naturally leads to the highly non-uniform convective heat transfer coefficient distribution on opposite sides of the plate. In such a case, the longitudinal heat conduction may play a significant role in the thermal coupling between high heat transfer regions located on opposite sides of the plate. In the present study CFD is used to perform a quantitative assessment of the thermal performance of a cross-corrugated heat exchanger including the longitudinal heat conduction effect for various design options such as different plate thickness and corrugation geometry for a typical operating condition. The longitudinal heat conduction effect is then predicted by the theoretical method using the ‘network-of-resistance’ in the wide range of the heat exchanger design space.

Heat transfer analysis of cheese cooling incorporating uncertainty in temperature measurement locations: Application to the industrial process

A cylindrical cheese product with an irregular cross sectional geometry is cooled by partial immersion in brine. It is essential to calculate the temperature–time history of the product during this cooling phase to ensure its microbiological safety. The heat transfer analysis is complicated by both the non-standard product geometry and the non-uniform surface heat transfer coefficients that prevail. The flotation behaviour of the cheese at the air/brine interface is analysed to determine the heat transfer areas exposed to each cooling fluid. A finite element model is developed to predict temperature histories at various points in the product and to determine the slowest cooling region in the product. The cooling performance of the cheese is also studied experimentally. Comparison of the theoretical and experimental temperature histories is complicated by uncertainty in the location of the thermocouples in the product. By statistically quantifying the imprecision in thermocouple position, the expected temperatures in each region of interest can be found from the thermal model by Monte Carlo sampling. With the model, the top region of the cheese stick has been shown to determine cooling time because the existence of the non-uniform boundary condition is significant in determining the evolution of temperature.