Uniform Heat Transfer Coefficient Research Articles

Coupled fluid-thermal-structural analysis during the air cooling for glass tempering

The tempering process of plate glass involves rapidly cooling the high-temperature glass using an array of impinging air jets, inducing desired stress during cooling. Consequently, the formation of tempering stress results from the coupled interaction among flow, heat transfer, and stress. However, most previous studies have commonly neglected the influence of the flow field by assuming a uniform and constant distribution of heat transfer coefficients at different positions on the glass plate, which deviates from actual situations. This study employed a fluid-thermal-structural coupled simulation approach to predict the non-uniform residual stress distribution in tempered glass and investigate the interaction mechanisms among flow, heat transfer, and stress. Simultaneously, to validate the reliability of the method and model, this study experimentally investigated the single-nozzle jet impingement cooling for glass tempering. The study concluded that the simulation results were consistent with the experiment. Subsequently, a comparative analysis was performed between the fluid-thermal-structural coupled simulation results based on real boundary conditions and the thermal-structural coupled simulation results based on ideal uniform heat transfer coefficient boundary conditions. The results revealed non-uniform distributions of both heat transfer coefficient and temperature due to varying localized flow characteristics. Consequently, the ratio of surface compressive stress to internal tensile stress along the width direction of the glass was not a fixed value but ranged from 1.63 to 2.38. Furthermore, significant differences were observed in the stress distribution under the simulations of fluid-thermal-structural coupling and thermal-structural coupling. Therefore, it is recommended to employ the fluid-thermal-structural coupling method when predicting localized stress distribution.

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.

Supercritical carbon dioxide in an array of micro impinging jets

Heat transfer of micro multi-jet with supercritical carbon dioxide is experimentally studied. A thermal micro specimen chip constituting of a concentric distribution of three resistance temperature detectors (RTDs) on a serpentine heater, which was mechanically supported by a 500 µm thick fused silica substrate, was microfabricated and used to obtain the heat transfer coefficient under a range of operating conditions. The jets issued from a concentric array of thirteen micro jets with an interject spacing (S/d) of ∼ 1.5, each measuring ∅205 µm, which were perpendicularly positioned over the temperature sensors with a relative standoff, L/d, of 7.3. The effect of radial position, heat flux, mass flux and inlet pressure on the heat transfer were studied at an inlet temperature of 21.7 °C.Results showed a uniform heat transfer coefficient over the heater with optimum values recorded mostly around the pseudocritical condition. In addition, the heat transfer coefficient increased with pressure above the critical condition, which was tied to a corresponding increase in the pseudocritical temperature. Furthermore, the observed heat transfer characteristics of the micro jet impingement cooling using multi-jet were compared to single jet under the same working conditions. This comparison showed that although the multi-jet ensued a more uniform temperature distribution over the heater, the single jet performed better due to an undermined heat transfer process in the multi-jet — a consequence of the jet-to-jet interaction.

Dual Entropy Regime in Channel Flow Subjected to Temperature Dependent Convection Mechanism

The central stimuli of this brief note is to underscore the effect of the temperature dependent convection coefficient that give rise to a dual temperature regime facilitating dual entropy distribution. In order to avoid unwarranted complexities, a simple geometry of shear flow in a channel is considered. The energy equation amenable to an analytic solution is simulated to extract the desired numerical findings in as much as for what parameters’ values, the temperature has dual distribution /does not yield temperature distribution at all. In fact, a range of parameter values have been worked out for which dual temperature regime exists or not. The plots of entropy generation number Ns also show the dual regime. The findings reveal a qualitative and quantitative difference in dual systems of temperature and entropy. It further underlines that the thermal systems with the idealized uniform heat transfer coefficient may be far distinct from actual behaviour and even weak temperature dependence of convection coefficient need due attention while designing a system.

Temperature Regulation of Photovoltaic Cells using Phase Change Material Heat Sinks Integrated with Metal Foam

This article investigates the cooling performance of Phase Change Material “PCM”-heat sinks integrated with porous metal that are attached to PV cells. Numerical simulations were carried out for a 2-dimensional configuration of a PCM-based heat sink subjected to uniform heat flux of 900W/m2 on the upper side and heat convection takes place at all other sides with a uniform convective heat transfer coefficient of 10 W/m2.°C. Two different PCMs were considered (n-Eicosane and RT44HC) and three values of metal foam porosity “e” were chosen as well (ε = 1.00, 0.97 and 0.90, where ε = 1.00 refers to no-metal foam case). Results showed that addition of metal foam enhances the cooling performance of PCM-based heat sinks. In the n-Eicosane based heat sinks, the PV-surface temperature was reduced by 6.31 °C and 7.00 °C for the 97% and 90% porosities respectively when compared to the no-metal foam case (100% porosity). On the other hand, in the RT44HC based heat sinks the PV-surface temperature was reduced by 5.50 °C and 6.15 °C for the 97% and 90% porosities respectively when compared to the no-metal foam case (100% porosity).

Achieving uniform heat transfer coefficient in coaxial pulsating jet

The main aim of the present paper is to investigate the inverse design of uniform distribution of heat transfer coefficient on the target plate by employing coaxial jet in the steady and pulsating state. The objective function is defined as the root-mean-square of the deviation of the local Nusselt number on the target plate in computational fluid dynamics simulation from the desired Nusselt number. The heat transfer search method minimizes the objective function. The geometric and fluid parameters are taken into account as design variables. Firstly, optimization in the steady state for the target Nusselt numbers 7, 10 and 13 is carried out and the values of the objective function in the optimal state are found to be 0.51, 0.18 and 0.314, respectively. The range of design variables in the steady and pulsating state is similar, while the heat transfer rate of the pulsating state is higher than that of the steady state. The variations of velocity in the inner and outer nozzles with time are considered to have a sine–sine, cosine–sine and constant–sine behavior. Optimization is carried out in the pulsating state for the Nusselt numbers 33, 44, 55 and 57. The objective function for these numbers in the optimal state is less than 0.02. By employing the conjugate gradient method with adjoint equation and the optimal value of design variables, the distribution of Nusselt number on the target plate in the steady and pulsating state for the constant–sine velocity case is experimentally estimated. The difference between experimental results and the value of the target Nusselt number is about 4–14%, indicating a good agreement between the two approaches.

Experimental Verification of an Analytical Mathematical Model of a Round or Oval Tube Two-Row Car Radiator

The paper presents an analytical mathematical model of a car radiator, which takes into account various heat transfer coefficients (HTCs) on each row of pipes. The air-side HTCs in a specific row of pipes in the first and second passes were calculated using equations for the Nusselt number, which were determined by CFD simulation by the ANSYS program (Version 19.1, Ansys Inc., Canonsburg, PA, USA). The liquid flow in the pipes can be laminar, transition, or turbulent. When changing the flow form from laminar to transition and from transition to turbulent, the HTC continuity is maintained. Mathematical models of two radiators were developed, one of which was made of round tubes and the other of oval tubes. The model allows for the calculation of the thermal output of every row of pipes in both passes of the heat exchangers. Small relative differences between the total heat flow transferred in the heat exchanger from hot water to cool air exist for different and uniform HTCs. However, the heat flow rate in the first row is much higher than the heat flow in the second row if the air-side HTCs are different for each row compared to a situation where the HTC is constant throughout the heat exchanger. The thermal capacities of both radiators calculated using the developed mathematical model were compared with the results of experimental studies. The plate-fin and tube heat exchanger (PFTHE) modeling procedure developed in the article does not require the use of empirical correlations to calculate HTCs on both sides of the pipes. The suggested method of calculating plate-fin and tube heat exchangers, taking into account the different air-side HTCs estimated using CFD modelling, may significantly reduce the cost of experimental research for a new design of heat exchangers implemented in manufacturing.

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.

A 3D MRI-based Numerical Model Dedicated to Industrial Thawing of Large Tuna Fishes

ABSTRACTIndustrial thawing of raw tuna fishes for the canning industry is of great importance in the global economy. Due to the heat transfer limitations within large sample pieces, these processes need to be improved to reduce fluid and energy consumption. In this work, the water immersion thawing process of yellowfin tuna was studied from both experimental and numerical approaches. First, the heat transfer model is validated with precooked tuna samples undergoing forced-air convection thawing. Then, the water immersion thawing process of yellowfin was studied with temperature measurements performed under an industrial environment. The numerical model considers the real geometry of the yellowfin using magnetic resonance imaging (MRI) integrated into a 3D finite element model. Overall, good agreement was found between experimental and predicted temperatures by considering a uniform convective heat transfer coefficient. A simplified 2D model can accurately predict the thawing time, but a 3D model is needed to predict the spatiotemporal temperature distribution in the product. The results have also shown the strong influence of the ambient temperature on the thawing time. This original approach considering the real fish geometry could now be used with different sized-tuna and various thawing kinetics to reach optimal processing conditions while improving product quality.

Influence of different parameters of preparing self-assembled monolayers on copper surfaces in the dropwise condensation heat transfer: an experimental study

Dropwise condensation (DWC) is one of the phase change heat transfer regimes, which due to its high capacity has received much attention from investigators. To produce DWC, it is necessary to have hydrophobic surfaces. Low surface energy coatings have been usually used to produce hydrophobic surfaces. These coatings due to their low thermal conductivities must have the minimum thickness. Therefore, self-assembled monolayers coatings like stearic acid or 1-octadecanethiol coatings (with thicknesses as high as a few nanometers) have been used in the literature. To create hydrophobic coatings by these materials, the surfaces are immersed in hydrophobic solutions with particular concentrations and in a specific time. There is not any general investigation on the effects of the time and concentration of these coatings on DWC in the literature. In this study, first, a proper apparatus for DWC experiments is designed and fabricated. Then, the effects of concentration and immersing time of the two mentioned materials on DWC phenomena have been studied. Between four coating times and solution concentrations of 1-octadecanethiol, concentration of 0.025 M at coating time of 30 min increases DWC heat transfer coefficient by about 4–7 times with respect to filmwise condensation in different subcooling temperatures. Concentration of 0.0025 M at coating time of 1 hour of stearic acid also increases the heat transfer coefficient by about 3–4 times. As well as the 1-octadecanethiol coating has a more uniform structure and higher heat transfer coefficient with respect to stearic acid coating.

Numerical investigation on phase change materials (PCM): The melting process of erythritol in spheres under different thermal conditions

In this paper, a numerical study on the melting process of the PCM erythritol in 12 and 7 mm diameter spheres subjected to external flow has been carried out. This configuration is analyzed varying the temperature difference between the PCM melting point and the external flow, the Reynolds number as well as the sphere position in the array. The problem is considered two-dimensional in geometry and transient in time. The numerical model here developed consists of the continuity, momentum and energy equations. The results have been initially validated using numerical and experimental data from literature. Afterwards, results of liquid fraction, heat flux and total melting time have been proposed and illustrated. Based on pure observation, a slight difference in the phase change phenomena when comparing different sphere positions in the array has emerged. These phenomena proved to be much more influenced by the external flow temperature and by the Reynolds number. In all cases, at 30% of the total melting time, 50% of the total energy had been absorbed by the PCM. The liquid PCM layer above the solid has a great influence on the heat flux, precisely the more extensive the PCM layer, the lower the heat exchange. The local heat flux value decreases significantly in regions in contact with air and liquid PCM. Contrarily, at the sphere base, where there is solid PCM during the whole process, the local heat flux value is almost constant during the whole melting. Finally, significant differences have emerged when comparing the results referred to the hypothesis here contemplated of uniform heat transfer coefficient and local heat transfer coefficient function of the sphere angle.

A CFD modeling investigation for structure optimization of a rotary steam tube dryer

This paper presents an optimized structure to improve the performance of rotary steam tube dryer by assembling the so called ‘Y’ shape flights. A verified CFD model, which was developed and validated in the previous work, was employed to verify the optimized structure by the comparisons of concentration distribution, velocity distribution and heat transfer coefficient. The simulation results showed that assembling ‘Y’ shape flights in a rotary steam tube dryer is an effective approach to increase material filling ratio and heat exchanging area. The optimized construction is able to reduce the wear of the material to the tube surface, due to the low maximum particle velocity. The optimized structure yields a uniform particle velocity distribution and high average surface heat transfer coefficient of tubes which is about ten times of that without flights.

Spreading Resistance in Multilayered Orthotropic Flux Channels With Different Conductivities in the Three Spatial Directions

In the microelectronics industry, the multilayered structures are found extensively where the microelectronic device/system is manufactured as a compound system of different materials. Recently, a variety of new materials have emerged in the microelectronics industry with properties superior to Silicon, enabling new devices with extreme performance. Such materials include β-Gallium-oxide (β-Ga2O3), and black phosphorus (BP), which are acknowledged to have anisotropic thermal conductivity tensors. In many of these devices, thermal issues due to self-heating are a problem that affects the performance, efficiency, and reliability of the devices. Analytical solutions to the heat conduction equation in such devices with anisotropic thermal conductivity tensor offer significant computational savings over numerical methods. In this paper, general analytical solutions for the temperature distribution and the thermal resistance of a multilayered orthotropic system are obtained. The system is considered as a multilayered three-dimensional (3D) flux channel consisting of N-layers with different thermal conductivities in the three spatial directions in each layer. A single eccentric heat source is considered in the source plane while a uniform heat transfer coefficient is considered along the sink plane. The solutions account for the effect of interfacial conductance between the layers and for considering multiple eccentric heat sources in the source plane. For validation purposes, the analytical results are compared with numerical solution results obtained by solving the problem with the finite element method (FEM) using the ANSYS commercial software package.

Practical analytical modeling of 3D multi-layer Printed Wired Board with buried volumetric heating sources

Ceaseless efforts have been made by the electronic companies to increase the density of electronic boards. A new design concept consists of burying active and passive electronic components inside inner layers of a Printed Wiring Board (PWB). However this alternative leads to higher thermal stress due to heat concentration at the core of a temperature-sensitive substrate.In order to help the electronic designers to find the optimum placement of these heating devices, a guideline based on analytical approach model is proposed. This presented work focuses on the steady-state solution of the heat equation, resolved by separation of variables and the use of Fourier's series. The domain is an anisotropic, multi-layer parallelepiped, submitted to uniform heat transfer coefficients on its upper and lower surfaces and assumed adiabatic edges. These assumptions can be employed, with confidence, to valid the predictions of chip temperatures at laboratory conditions.To determine its ability to predict the maximum operating temperature of a set of buried chips, that practical solution is compared to its corresponding numerical model representing all the layers of realistic electronic board. Moreover the need to consider each PWB's layer is debated with the aim to faster the chip temperature evaluation. Thus a layer-selection method is investigated to find the best balance between accuracy and computation time. By using such optimised approach the computation time can be shortened by a factor of 600, compared to a detailed numerical analysis, while keeping a similar accuracy. Further, it could be a practical way to proceed to a smart simplification of the numerical model of PWB substrate for actual equipment.

Spreading Resistance in Multilayered Orthotropic Flux Channel with Temperature-Dependent Thermal Conductivities

Anisotropic materials have received remarkable attention in the development of microelectronic devices. In many materials, the thermal conductivities are temperature-dependent and usually are approximated by constant thermal conductivities when considering thermal analysis. In this paper, analytical solutions of the temperature rise and the thermal resistance of a multilayered three-dimensional flux channel with orthotropic temperature-dependent thermal conductivities are addressed by means of the Kirchhoff transform, which is considered as a powerful method for dealing with nonlinear conduction problems with temperature-dependent thermal conductivities. A single eccentric heat source is considered in the source plane of the flux channel, where heat enters the system and flows by conduction through the layers to reach a convective heat sink with uniform heat transfer coefficient. The solutions are extended to account for multiple eccentric heat sources in the source plane. Further, the analytical solutions have been validated by solving the problem numerically with the finite element method using the ANSYS commercial software package.

Critical Biot Numbers of Periodic Arrays of Fins

In this paper, we consider the heat transfer problems associated with a periodic array of triangular, longitudinal, axisymmetric, and pin fins. The problems are modeled as a wall where the flat side is isothermal and the other side, which has extended surfaces/fins, is subjected to convection with a uniform heat transfer coefficient. Hence, our analysis differs from the classical approach because (i) we consider multidimensional heat conduction and (ii) the wall on which the fins are attached is included in the analysis. The latter results in a nonisothermal temperature distribution along the base of the fin. The Biot number (Bi=ht/k) characterizing the heat transfer process is defined with respect to the thickness/diameter of the fins (t). Numerical results demonstrate that the fins would enhance the heat transfer rate only if the Biot number is less than a critical value, which, in general, depends on the geometrical parameters, i.e., the thickness of the wall, the length of the fins, and the period. For pin fins, similar to rectangular fins, the critical Biot number is independent of the geometry and is approximately equal to 3.1. The physical argument is that, under strong convection, a thick fin introduces an additional resistance to heat conduction.

Spatial and temporal analysis of wind effects on PV modules: Consequences for electrical power evaluation

Currently, most of the state-of-the-art energy yield prediction and evaluation models reported in the literature assume a uniform photovoltaic (PV) module temperature and air flow. However, during realistic wind flow conditions, local temperature variations occur over PV modules due to forced convection. This study aims to investigate how spatial temperature differences over the surface of a PV module that are caused by wind affect the convection of heat over the module, and how this influences the energy production by the module. A PV module composed of 2 rows of 9 solar cells each was placed horizontally in a wind tunnel. It has then been tested at free-stream wind velocities of 1, 2, 3 and 5m/s. Surface temperatures and ambient air temperatures have been measured along the module and vertical temperature gradients have been determined. The electrical characteristics of each individual cell in the PV module have also been measured. Substantial differences in performance between the solar cells caused by local variations in module temperature have been observed. These data have been used to calculate the heat transfer coefficient along the module. To illustrate the importance of including, in energy yield evaluation models, the temperature variations that occur between the cells of a same module, we have constructed an energy yield evaluation model for a standard 60-cell PV module illuminated at 1000W/m2 and calculated the power output for (1) a uniform heat transfer coefficient over the module, and (2) a realistic distribution of the heat transfer coefficient based on the wind tunnel experiments. Differences up to 4.3% have been observed, indicating that local variations in temperature within a PV module need to be taken into account for accurate energy yield evaluations. Using this improved modelling, the absolute errors remaining in the E-yield estimations can be reduced.

Uniform segment-wise body parametric convection heat transfer coefficient model for sitting posture in vehicles

In many industrial multi-physics engineering applications, models need to capture the heat transfer effects of spatial and temporal changes in conditions around the human body. For thermal comfort assessment, convection heat transfer coefficients (hc) form part of the heat balance equation of the human body. In many non-uniform flow conditions, due to the turbulently mixed or stratified environment, convection heat transfer varies significantly on the human body. Parametric, segment-wise applicable convection heat transfer correlations are seen as an alternative in order to bridge these scales and levels in space and time. Therefore, robust reduced-order convective heat transfer models are needed for predicting heat transfer between the human body and its surroundings. The main goal of this research is to develop a reduced order model database that provides the segment-wise convective heat transfer coefficients (hc) for typical indoor flow responses in multiple applications. In this article, a new parametric approach was detailed for estimating segment-wise body convection heat transfer coefficients for sitting posture in vehicles. The methodology follows a new strategy, i.e., in this application domain, here a car cabin, primarily relevant parameters are identified which affect the convective heat exchange. Following the sensitivity analysis of numerous computational fluid dynamics simulations with varying conditions, we identify relevant primary variables and heat transfer coefficients correlations and test the model robustness accordingly. A database-driven approach is developed in order to make correlations accessible during simulations, for example addressing energy performance. Finally, the experimentally investigated heat transfer analysis around the human body is presented and later compared with numerically reproduced data.

Critical Depth of Buried Isothermal Circular Pipes

ABSTRACTWe address the two-dimensional heat conduction problem due to a periodic array of isothermal pipes buried in a conductive medium. The upper surface of the medium is subjected to convection with a uniform heat transfer coefficient, and the lower surface is insulated. Similar to the concept of critical thickness associated with a slab embedded with isothermal strips, we show that there exists a critical depth such that the heat transfer rate is maximized. As the Biot number tends to infinity, the critical depth approaches zero for a single pipe buried in a semi-infinite medium. For a periodic array of isothermal pipes, there is also a critical Biot number beyond which the critical depth is zero. Furthermore, insulating the pipes reduces the critical depth, and the heat transfer rate does not vary significantly with respect to the depth.

Longitudinal-Fin Heat Sink Optimization Capturing Conjugate Effects Under Fully Developed Conditions

We develop a method requiring minimal computations to optimize the fin thickness and spacing in a fully shrouded longitudinal-fin heat sink (LFHS) to minimize its thermal resistance under conditions of hydrodynamically and thermally developed laminar flow. Prescribed quantities are the density, viscosity, thermal conductivity and specific heat capacity of the fluid, the thermal conductivity and height of the fins, the width and length of the heat sink, and the pressure drop across it. Alternatively, the length of the heat sink may be optimized as well. The shroud of the heat sink is assumed to be adiabatic and its base isothermal. Our results are relevant to, e.g., microchannel cooling applications where base isothermality can be achieved by using a heat spreader or a vapor chamber. The present study is distinct from the previous work because it does not assume a uniform heat transfer coefficient, but fully captures the velocity and temperature fields by numerically solving the conjugate heat transfer problem in dimensionless form using an existing approach. We develop a dimensionless formulation and compute a dense tabulation of the relevant parameters that allows the thermal resistance to be calculated algebraically over a relevant range of dimensionless parameters. Hence, the optimization method does not require the time-consuming solution of the conjugate problem. Once the optimal dimensionless fin thickness and spacing are obtained, their dimensional counterparts are computed algebraically. The optimization method is illustrated in the context of direct liquid cooling.