Determination of heat transfer correlations for plate-fin-and-tube heat exchangers

This paper presents a numerical method for determining heat transfer coefficients in cross-flow heat exchangers with extended heat exchange surfaces. Coefficients in the correlations defining heat transfer on the liquid- and air-side were determined using a non-linear regression method. Correlation coefficients were determined from the condition that the sum of squared fluid temperature differences at the heat exchanger outlet, obtained by measurements and those calculated, achieved minimum. Minimum of the sum of the squares was found using the Levenberg-Marquardt method. The outlet temperature of the fluid leaving the heat exchanger was calculated using the mathematical model describing the heat transfer in the heat exchanger. Since the conditions at the liquid-side and those at the air-side are identified simultaneously, the derived correlations are valid in a wide range of flow rate changes of the air and liquid. This is especially important for partial loads of the exchanger, when the heat transfer rate is lower than the nominal load. The correlation for the average heat transfer coefficient on the air-side based on the experimental data was compared with the correlation obtained from numerical simulation of 3D fluid and heat flow, performed by means of the commercially available CFD code. The numerical predictions are in good agreement with the experimental data.     

Concepts and realization of microstructure heat exchangers for enhanced heat transfer

Microstructure heat exchangers have unique properties that make them useful for numerous scientific and industrial applications. The power transferred per unit volume is mainly a function of the distance between heat source and heat sink—the smaller this distance, the better the heat transfer. Another parameter governing for the heat transfer is the lateral characteristic dimension of the heat transfer structure; in the case of microchannels, this is the hydraulic diameter. Decreasing this characteristic dimension into the range of several 10s of micrometers leads to very high values for the heat transfer rate.

Another possible way of increasing the heat transfer rate of a heat exchanger is changing the flow regime. Microchannel devices usually operate within the laminar flow regime. By changing from microchannels to three dimensional structures, or to planar geometries with microcolumn arrays, a significant increase of the heat transfer rate can be achieved.

Microheat exchangers in the form of both microchannel devices (with different hydraulic diameters) and microcolumn array devices (with different microcolumn layouts) are presented and compared. Electrically heated microchannel devices are presented, and industrial applications are briefly described.     

Radiant heat gain from indoor heat sources

A new parameter, equivalent emissivity, ε_e, is introduced to reflect radiant feature of the surface of a heat source with different shapes and different temperatures in an air conditioned room. Radiant heat gain from medium- or low-surface-temperature equipment and from commonly used light fixtures and the occupant are examined and analyzed in detail. The main affecting factors are also examined. In addition, the percentages of radiant heat gain are presented under different temperatures.     

Non-fourier heat conduction in a plane slab with prescribed boundary heat flux

The non-stationary heat conduction in an infinitely wide plane slab with a prescribed boundary heat flux is studied. An arbitrary time dependent boundary heat flux is considered and a non-vanishing thermal relaxation time is assumed. The temperature and the heat flux density distributions are determined analytically by employing Cattaneo-Vernotte's constitutive equation for the heat flux density. It is proved that the temperature and the heat flux density distributions can be incompatible with the hypothesis of local thermodynamic equilibrium. A comparison with the solution which would be obtained by means of Fourier's law is performed by considering the limit of a vanishing thermal relaxation time.     

Evaporator critical heat flux in the double-wall artery heat pipe

The fact that heat is transferred into a heat pipe through the liquid-saturated evaporator wick gives rise to the so-called boiling limit on the heat pipe capacity. The composite nature of the double-wall artery heat pipe (DWAHP) wick structure makes the prediction of the evaporator superheat (Δ T_crit) and the critical radial heat flux (q_r) very difficult. The effective thermal conductivity of the wick, the effective radius of critical nucleation cavity, and the nucleation superheat, which are important parameters for double-wall wick evaporator heat transfer, have been evaluated based on the available theoretical models. Empirical correlations are used to corroborate the experimental results of the 2 m DWAHP. A heat choke mounted on the evaporator made it possible to measure the evaporator external temperatures, which were not measured in the previous tests. The high values of the measured evaporator wall temperatures are explainable with the assumption of a thin layer of vapor blanket at the inner heating surface. It has been observed that partial saturation of the wick (lean evaporator) causes the capillary limit to drop even though it may be good for efficient convective heat transfer through the wick. The 2 m long copper-water heat pipe had a peak performance of 1850 W at 23 W/cm² with a horizontal orientation.     

Convective heat transfer from molten salt droplets in a direct contact heat exchanger

This paper presents a new predictive model of droplet flow and heat transfer from molten salt droplets in a direct contact heat exchanger. The process is designed to recover heat from molten CuCl in a thermochemical copper–chlorine (Cu–Cl) cycle of hydrogen production. This heat recovery occurs through the physical interaction between high temperature CuCl droplets and air. Convective heat transfer between droplets and air is analyzed in a counter-current spray flow heat exchanger. Numerical results for the variations of temperature, velocity and heat transfer rate are presented for two cases of CuCl flow. The optimal dimensions of the heat exchanger are found to be a diameter of 0.13 m, with a height of 0.6 and 0.8 m, for 1 and 0.5 mm droplet diameters, respectively. Additional results are presented and discussed for the heat transfer effectiveness and droplet solidification during heat recovery from the molten CuCl droplets.     

Predict the temperature distribution in gas-to-gas heat pipe heat exchanger

A theoretical model has been developed to investigate the thermal performance of a continuous finned circular tubing of an air-to-air thermosyphon-based heat pipe heat exchanger. The model has been used to determine the heat transfer capacity, which expresses the thermal performance of heat pipe heat exchanger. The model predicts the temperature distribution in the flow direction for both evaporator and condenser sections and also the saturation temperature of the heat pipes. The approach used for the present study considers row-by-row heat-transfer in evaporator and condenser sections of the heat pipe heat exchanger.     

Perturbation solution to heat conduction in melting or solidification with heat generation

The Stefan problem involving a source term is considered in this technical note. As an example, planar solidification with time-dependent heat generation in a semi-infinite plane is solved by use of a perturbation technique. The perturbation solution is validated by reducing the problem to the case without heat generation whose exact solution is available. An application to the case with constant heat generation is presented, for which a closed-form solution is obtained. The effects of heat generation and Stefan number on the evolution of solidification are examined using the perturbation solution.     

Effect of inertial particles with different specific heat capacities on heat transfer in particle-laden turbulent flow

The effect of inertial particles with different specific heat on heat transfer in particle-laden turbulent channel flows is studied using the direct numerical simulation(DNS) and the Lagrangian particle tracking method. The simulation uses a two-way coupling model to consider the momentum and thermal interactions between the particles and turbulence. The study shows that the temperature fields display differences between the particle-laden flow with different specific heat particles and the particle-free flow,indicating that the particle specific heat is an important factor that affects the heat transfer process in a particle-laden flow. It is found that the heat transfer capacity of the particle-laden flow gradually increases with the increase of the particle specific heat. This is due to the positive contribution of the particle increase to the heat transfer. In addition,the Nusselt number of a particle-laden flow is compared with that of a particle-free flow.It is found that particles with a large specific heat strengthen heat transfer of turbulent flow, while those with small specific heat weaken heat transfer of turbulent flow.     

Transient heat transfert in coflow heat exchanger

More than ever before, dynamic investigation techniques are becoming widely used in the control systems, parameter implementation and state estimators. Indeed, dynamical models describing the response of process systems that are subject to disturbances play a vital role in controlling and optimising these systems. Recently developed in literature, the method of step response analysis provides a promising means towards solving some of the problems associated with the characterisation of transient response of heat exchangers. In Abdelghani-Idrissi et al. (Int J Heat Mass Transfer 44:3721–3730, 2001), authors present analytical expressions of fluids temperatures response time of counter-current heat exchanger when hot fluid step change is applied in the internal tube. This paper describes the extension of this technique to a coflow heat exchanger for which the exact solution of its mathematical model is unavailable.     

Three-dimensional numerical analysis of heat and mass transfer in heat pipes

A three-dimensional finite-element numerical model is presented for simulation of the steady-state performance characteristics of heat pipes. The mass, momentum and energy conservation equations are solved for the liquid and vapor flow in the entire heat pipe domain. The calculated outer wall temperature profiles are in good agreement with the experimental data. The estimations of the liquid and vapor pressure distributions and velocity profiles are also presented and discussed. It is shown that the vapor flow field remains nearly symmetrical about the heat pipe centerline, even under a non-uniform heat load. The analytical method used to predict the heat pipe capillary limit is found to be conservative.     

Shell-and-double concentric-tube heat exchangers

This study concerns a new type of heat exchangers, which is that of shell-and-double concentric-tube heat exchangers. These heat exchangers can be used in many specific applications such as air conditioning, waste heat recovery, chemical processing, pharmaceutical industries, power production, transport, distillation, food processing, cryogenics, etc. The case studies include both design calculations and performance calculations. It is demonstrated that the relative diameter sizes of the two tubes with respect to each other are the most important parameters that influence the heat exchanger size.     

Rewetting analysis of hot surfaces with internal heat source by the heat balance integral method

A two region conduction-controlled rewetting model of hot vertical surfaces with internal heat generation and boundary heat flux subjected to constant but different heat transfer coefficient in both wet and dry region is solved by the Heat Balance Integral Method (HBIM). The HBIM yields the temperature field and quench front temperature as a function of various model parameters such as Peclet number, Biot number and internal heat source parameter of the hot surface. Further, the critical (dry out) internal heat source parameter is obtained by setting Peclet number equal to zero, which yields the minimum internal heat source parameter to prevent the hot surface from being rewetted. Using this method, it has been possible to derive a unified relationship for a two-dimensional slab and tube with both internal heat generation and boundary heat flux. The solutions are found to be in good agreement with other analytical results reported in literature.     

Two phase flow and heat transfer characteristics of a separate-type heat pipe

Two phase flow and heat transfer characteristics of a separate-type heat pipe have been studied experimentally and theoretically. The experimental apparatus have the same geometry for the evaporator and the condenser which consist of 5-tube-banks, with working temperature ranges of 80–125°C. The experimental working fluid is dual-distilled water with corrosion-resistant agents. Heat transfer coefficients for boiling and condensation along with heat flux and working temperature are measured at different filling ratio. According to the results of the experiments, the optimized filling ratio ranges from 16 to 36%. Fitted correlations of average heat transfer coefficients of the evaporator and Nusselt numbers of the condenser at the proposed filling ratio are obtained. Two phase flow characteristics of the evaporator and the condenser as well as their influence on heat transfer are described on the basis of simplified analysis. Reasons for the pulse-boiling process remain to be studied.     

Topology optimization and heat dissipation performance analysis of a micro-channel heat sink

Junction temperature in the electronic packaging process is one of the critical factors affecting the service life of electronic devices. A micro-channel heat sink is a common heat dissipating device used to reduce the thermal resistance between components and substrate. In order to maximize the heat dissipation while minimizing the pressure drop, this paper adopts a topology optimization method. A material interpolation method based on variable density principle is used together with a moving asymptote algorithm for the optimization. The physics is governed by the heat and mass transfer, coupled with the momentum conservation in the fluid. Four parameters are varied in order to investigate their influence on the optimization process. A three-dimensional geometry has been constructed to study the flow field and the results are compared to a reference case to verify the temperature uniformity and thermal performance of the model. It is demonstrated that the optimized design of the micro-channel heat sink is reliable and effective.     

A numerical study of EGS heat extraction process based on a thermal non-equilibrium model for heat transfer in subsurface porous heat reservoir

With a previously developed numerical model, we perform a detailed study of the heat extraction process in enhanced or engineered geothermal system (EGS). This model takes the EGS subsurface heat reservoir as an equivalent porous medium while it considers local thermal non-equilibrium between the rock matrix and the fluid flowing in the fractured rock mass. The application of local thermal non-equilibrium model highlights the temperature-difference heat exchange process occurring in EGS reservoirs, enabling a better understanding of the involved heat extraction process. The simulation results unravel the mechanism of preferential flow or short-circuit flow forming in homogeneously fractured reservoirs of different permeability values. EGS performance, e.g. production temperature and lifetime, is found to be tightly related to the flow pattern in the reservoir. Thermal compensation from rocks surrounding the reservoir contributes little heat to the heat transmission fluid if the operation time of an EGS is shorter than 15 years. We find as well the local thermal equilibrium model generally overestimates EGS performance and for an EGS with better heat exchange conditions in the heat reservoir, the heat extraction process acts more like the local thermal equilibrium process.     

Investigation of flow and heat transfer in corrugated-undulated plate heat exchangers

 An experimental and numerical investigation of heat transfer and fluid flow was conducted for corrugated-undulated plate heat exchanger configurations under transitional and weakly turbulent conditions. For a given geometry of the corrugated plates the geometrical characteristics of the undulated plates, the angle formed by the latter with the main flow direction, and the Reynolds number were made to vary. Distributions of the local heat transfer coefficient were obtained by using liquid-crystal thermography, and surface-averaged values were computed; friction coefficients were measured by wall pressure tappings. Overall heat transfer and pressure drop correlations were derived. Three-dimensional numerical simulations were conducted by a finite-volume method using a low-Reynolds number k–ɛ model under the assumption of fully developed flow. Computed flow fields provided otherwise inaccessible information on the flow patterns and the mechanisms of heat transfer enhancement. Received on 5 February 1999     

Numerical simulation of heat transfer in a micro channel heat sinks using nanofluids

In this study, a numerical simulation of copper microchannel heatsink (MCHS) using nanofluids as coolants is presented. The nanofluid is a mixture of pure water and nanoscale metallic or nonmetallic particles with various volume fractions. Also, the effects of various volume fractions, volumetric flow rate and various materials of nanoparticles on the performance of MCHS have been developed. A three-dimensional computational fluid dynamics model was developed using the commercial software package FLUENT, to investigate the conjugate fluid flow and heat transfer phenomena in micro channel heatsinks. The results show that the cooling performance of a microchannel heat sink with water based nanofluid containing Al₂O₃ (vol 8%) is enhanced by about 4.5% compared with micro channel heatsink with pure water. Nanofluids reduce both the thermal resistance and the temperature difference between the top (heated) surface of the MCHS and inlet nanofluid compared with that pure water. The cooling performance of a micro channel heat sink with metal nanofluids improves compared with that of a micro channel heat sink with oxide metal nanofluids because the thermal conductivity of metal nanofluid is higher than oxide metal nanofluids. Micro channel heat sinks with nanofluids are expected to be good candidates as the next generation cooling devices for removing ultra high heat flux.     

Calculation of overall heat transfer coefficients in a triple tube heat exchanger

In previous studies, calculation of overall heat transfer coefficients in a triple tube heat exchanger (TTHE) involved assumptions or approaches those are not valid in all cases. In this study a more generic way of calculating overall heat transfer coefficients in a TTHE has been developed. Consequently, temperature profiles of all streams in a TTHE in the axial direction were determined. An effective overall heat transfer coefficient that is related to the total resistance to heat transfer in the TTHE, was also determined to facilitate comparison of a TTHE to an equivalent double tube heat exchanger.     

Non-Fourier heat conduction in a finite hollow cylinder with periodic surface heat flux

Analytical solution of the non-Fourier axisymmetric temperature field within a finite hollow cylinder exposed to a periodic boundary heat flux is investigated. The problem studied considering the Cattaneo–Vernotte (CV) constitutive heat flux relation. The material is assumed to be homogeneous and isotropic with temperature-independent thermal properties. The standard method of separation of variables is used for solving the problem with time-independent boundary conditions, and the Duhamel integral is used for applying the time dependency. The solution is applied for the special cases of harmonic uniform heat flux and an exponentially pulsed heat flux with Gaussian distribution in outer surface for modeling a laser pulse, and their respective non-Fourier thermal behavior is studied.