Flow boiling in horizontal flattened tubes: Part II – Flow boiling heat transfer results and model

Experiments of flow boiling heat transfer were conducted in four horizontal flattened smooth copper tubes of two different heights of 2 and 3 mm. The equivalent diameters of the flattened tubes are 8.6, 7.17, 6.25, and 5.3 mm. The working fluids were R22 and R410A. The test conditions were: mass velocities from 150 to 500 kg/m² s, heat fluxes from 6 to 40 kW/m² and saturation temperature of 5 °C. The experimental heat transfer results are presented and the effects of mass flux, heat flux, and tube diameter on heat transfer are analyzed. Furthermore, the flow pattern based flow boiling heat transfer model of Wojtan et al. [L. Wojtan, T. Ursenbacher, J.R. Thome, Investigation of flow boiling in horizontal tubes: Part I – A new diabatic two-phase flow pattern map, Int. J. Heat Mass Transfer 48 (2005) 2955–2969; L. Wojtan, T. Ursenbacker, J.R. Thome, Investigation of flow boiling in horizontal tubes: Part II – Development of a new heat transfer model for stratified-wavy, dryout and mist flow regimes, Int. J. Heat Mass Transfer 48 (2005) 2970–2985], using the equivalent diameters, were compared to the experimental data. The model predicts 71% of the entire database of R22 and R410A ±30% overall. The model predicts well the flattened tube heat transfer coefficients for R22 while it does not predicts well those for R410A. Based on several physical considerations, a modified flow boiling heat transfer model was proposed for the flattened tubes on the basis of the Wojtan et al. model and it predicts the flattened tube heat transfer database of R22 and R410A by 85.8% within ±30%. The modified model is applied to the reduced pressures up to 0.19.     

Fluid flow and heat transfer characteristics of low temperature two-phase micro-channel heat sinks – Part 2. Subcooled boiling pressure drop and heat transfer

This second part of a two-part study explores the performance of a new cooling scheme in which the primary working fluid flowing through a micro-channel heat sink is indirectly cooled by a refrigeration cooling system. The objective of this part of study is to explore the pressure drop and heat transfer characteristics of the heat sink. During single-phase cooling, pressure drop decreased with increasing heat flux because of decreased liquid viscosity. However, pressure drop began increasing with increasing heat flux following bubble departure. These opposite trends produced a minimum in the variation of pressure drop with heat flux. Increasing liquid subcooling decreased two-phase pressure drop because of decreased void fraction caused by strong condensation at bubble interfaces as well as decreased likelihood of bubble coalescence. It is shown macro-channel subcooled boiling pressure drop and heat transfer correlations are unsuitable for micro-channel flows. However, two new modified correlations produced good predictions of the present heat transfer data.     

Flow and heat transfer in a micro-cylindrical gas–liquid Couette flow

Analytic solutions for the gas and liquid velocity and temperature distribution are determined for steady state one-dimensional microchannel cylindrical Couette flow between a shaft and a concentric cylinder. The solution is based on the continuum model and takes into consideration the velocity slip and temperature jump in the gaseous phase defined by the Knudsen number range of 0.001 < Kn < 0.1. The two fluids are assumed immiscible. The gas layer is adjacent to the shaft which rotates with angular velocity ω_s and is thermally insulated. The outer cylinder rotates with angular velocity ω_o and is maintained at uniform temperature. The governing parameters are identified and the effects of the Knudsen number and accommodation coefficients on the velocity and temperature profiles, reduction in the overall temperature rise due to the gas layer, the Nusselt number and shear reduction are examined. It was found that the required torque to rotate the liquid in the annular space is significantly reduced by introducing a thin gas layer adjacent to the shaft. Also, reduction in shaft temperature is enhanced through a combination of high energy accommodation coefficient and low momentum accommodation coefficients. Results also indicate that the gas layer becomes more effective in reducing the shaft temperature when the housing angular velocity is much larger than the shaft angular velocity.     

Heat transfer in a reaction–diffusion system with a moving heat source

A general formulation is presented for a moving boundary problem in which heat is generated at the boundary due to an exothermic reaction involving a species which diffuses into a dispersed phase from an external medium of finite volume. The speed of the moving boundary is prescribed based on the solution of the mass diffusion problem and an analysis is presented of the thermal dynamics of the system. The set of equations describing heat transport leads to a Green’s function type problem with time dependent boundary conditions and the Galerkin finite element method is employed to develop a numerical solution. Transformations are introduced to freeze the moving boundary and partition the domain for ease of computation, and an iterative scheme is defined to satisfy the heat flux jump boundary condition and match the temperature field across the moving boundary. The numerical results are used to set the limits of applicability of an analytical perturbation solution. Essential aspects of thermal dynamics in the system are described and parametric regions resulting in a local temperature hot spot are delineated. Computed contour plots describing thermal evolution are presented for different combinations of parameter values. These may be of utility in the prediction of thermal development, for control and avoidance of hot spot formation, and in physical parameter estimation.     

Regional energy system optimization – Potential for a regional heat market

Energy supply companies and industrial plants are likely to face new situations due to, for example, the introduction of new energy legislation, increased fuel prices and increased environmental awareness. These new prerequisites provide companies with new challenges but also new possibilities from which to benefit. Increased energy efficiency within companies and increased cooperation between different operators are two alternatives to meet the new conditions. A region characterized by a high density of energy-intensive processes is used in this study to find the economic potential of connecting three industrial plants and four energy companies, within three local district heating systems, to a regional heat market, in which different operators provide heat to a joint district heating grid. Also, different investment alternatives are studied. The results show that the economical potential for a heat market amounts to between 5 and 26 million EUR/year with payback times ranging from two to eleven years. However, the investment costs and the net benefit for the total system need to be allotted to the different operators, as they benefit economically to different extents from the introduction of a heat market. It is also shown that the emissions of CO₂ from the joint system would decrease compared to separate operation of the systems. However, the valuation of CO₂ emissions from electricity production is important as the difference of emitted CO₂ between the accounting methods exceeds 650 kton/year for some scenarios.     

Experimental study on desulfurization efficiency and gas–liquid mass transfer in a new liquid-screen desulfurization system

This paper presents a new liquid-screen gas–liquid two-phase flow pattern with discarded carbide slag as the liquid sorbent of sulfur dioxide (SO₂) in a wet flue gas desulfurization (WFGD) system. On the basis of experimental data, the correlations of the desulfurization efficiency with flue gas flow rate, slurry flow rate, pH value of slurry and liquid–gas ratio were investigated. A non-dimensional empirical model was developed which correlates the mass transfer coefficient with the liquid Reynolds number, gas Reynolds number and liquid–gas ratio (L/G) based on the available experimental data. The kinetic reaction between the SO₂ and the carbide slag depends on the pressure distribution in this desulfurizing tower, gas liquid flow field, flue gas component, pH value of slurry and liquid–gas ratio mainly. The transient gas–liquid mass transfer involving with chemical reaction was quantified by measuring the inlet and outlet SO₂ concentrations of flue gas as well as the characteristics of the liquid-screen two-phase flow. The mass transfer model provides a necessary quantitative understanding of the hydration kinetics of sulfur dioxide in the liquid-screen flue gas desulfurization system using discarded carbide slag which is essential for the practical application.     

High heat flux flow boiling in silicon multi-microchannels – Part II: Heat transfer characteristics of refrigerant R245fa

This article is the second in a three-part study. This second part focuses on flow boiling heat transfer of refrigerant R245fa in a silicon multi-microchannel heat sink and their comparison with the results presented in part I for refrigerant R236fa. This heat sink was the same as utilized in part I. The test conditions covered base heat fluxes from 3.6 to 190 W/cm², mass velocities from 281 to 1501 kg/m² s and the exit vapour qualities from 0% to 78%. The effect of saturation pressure on heat transfer was tested from 141 to 273 kPa for R245fa and the effect of sub-cooling from 0 to 19 K. The R245fa database includes 693 local heat transfer coefficient measurements, for which four different heat transfer trends were identified, although in most cases the heat transfer coefficient increased with heat flux, was almost independent of vapour quality and increased with mass velocity. The entire database, including both R245fa and R236fa measurements, was compared with four prediction methods for flow boiling heat transfer in microchannels. The three-zone model of Thome et al. (J.R. Thome, V. Dupont, A.M. Jacobi, Heat transfer model for evaporation in microchannels. Part I: presentation of the model, International J. Heat Mass Transfer 47 (2004) 3375–3385) was found to give the best predictions, capturing 90% of the data within ±30% in the slug and annular flow regimes (x > 5%).     

Determining parameters of heat exchangers for heat recovery in a Cu–Cl thermochemical hydrogen production cycle

A heat exchanger is a device built for efficient heat transfer from one medium to another. Shell and tube heat exchangers are separated wall heat exchangers and are commonly used in the nuclear and process industry. The CuCl cycle is used to thermally crack water in to H₂ and O₂. The present study presents the heat exchanger thermal design using analysis of variance for heat recovery from oxygen at 500 °C, coming from the molten salt reactor. Polynomial regressions in terms of the amount of chlorine in the oxygen, the mass flow rate on the tube side, and the shell's outlet temperature are estimated for various exchanger parameters and the results are compared with the bell Delaware method. Based on energy and exergy analysis, this study also discusses the best possible path for the recovered heat from oxygen. Optimal heat exchanger parameters are estimated by Design-Expert^® Stat-Ease for most effective heat recovery.     

Condensation in a vertical tube bundle passive condenser – Part 2: Complete condensation

An experimental study of the tube bundle effect on heat removal capabilities in complete condensation mode of a passive condenser was performed. A full scale test section, with four condenser tubes, was designed and constructed to simulate operating conditions of a passive containment cooling system. For complete condensation analysis, pure steam was supplied to the test section and heat transfer properties were measured for pressure from 100 to 280 kPa. The condensation heat transfer results were similar to the findings from single tubes, except for a slightly higher condensate mass flux. This was determined to be a result of turbulent mixing in the secondary boiling water caused by the tube bundle.     

New prediction methods for CO2 evaporation inside tubes: Part II—An updated general flow boiling heat transfer model based on flow patterns

Corresponding to the updated flow pattern map presented in Part I of this study, an updated general flow pattern based flow boiling heat transfer model was developed for CO₂ using the Cheng–Ribatski–Wojtan–Thome [L. Cheng, G. Ribatski, L. Wojtan, J.R. Thome, New flow boiling heat transfer model and flow pattern map for carbon dioxide evaporating inside horizontal tubes, Int. J. Heat Mass Transfer 49 (2006) 4082–4094; L. Cheng, G. Ribatski, L. Wojtan, J.R. Thome, Erratum to: “New flow boiling heat transfer model and flow pattern map for carbon dioxide evaporating inside tubes” [Heat Mass Transfer 49 (21–22) (2006) 4082–4094], Int. J. Heat Mass Transfer 50 (2007) 391] flow boiling heat transfer model as the starting basis. The flow boiling heat transfer correlation in the dryout region was updated. In addition, a new mist flow heat transfer correlation for CO₂ was developed based on the CO₂ data and a heat transfer method for bubbly flow was proposed for completeness sake. The updated general flow boiling heat transfer model for CO₂ covers all flow regimes and is applicable to a wider range of conditions for horizontal tubes: tube diameters from 0.6 to 10 mm, mass velocities from 50 to 1500 kg/m² s, heat fluxes from 1.8 to 46 kW/m² and saturation temperatures from ?28 to 25 °C (reduced pressures from 0.21 to 0.87). The updated general flow boiling heat transfer model was compared to a new experimental database which contains 1124 data points (790 more than that in the previous model [Cheng et al., 2006, 2007]) in this study. Good agreement between the predicted and experimental data was found in general with 71.4% of the entire database and 83.2% of the database without the dryout and mist flow data predicted within ±30%. However, the predictions for the dryout and mist flow regions were less satisfactory due to the limited number of data points, the higher inaccuracy in such data, scatter in some data sets ranging up to 40%, significant discrepancies from one experimental study to another and the difficulties associated with predicting the inception and completion of dryout around the perimeter of the horizontal tubes.     

Viscous Joule heating MHD–conjugate heat transfer for a vertical flat plate in the presence of heat generation

The problem of steady conjugate heat transfer through an electrically-conducting fluid for a vertical flat plate in the presence of transverse uniform magnetic field taking into account the effects of viscous dissipation, Joule heating, and heat generation is formulated. The general governing equations which include such effects are made dimensionless by means of an apposite transformation. The ultimate resulting equations obtained by introducing the stream function with the similarity variable are solved numerically using the implicit finite difference method for the boundary conditions based on conjugate heat transfer process. A representative set of numerical results for the velocity and temperature profiles, the skin friction coefficients as well as the rate of heat transfer coefficient and the surface temperature distribution are presented graphically and discussed. A comprehensive parametric study is carried out to show the effects of the magnetic parameter, viscous dissipation parameter, Joule heating parameter, conjugate conduction parameter, heat generation parameter and the Prandtl number on the obtained solutions.     

Convective-diffusive heat transfer in a packed-bed with constant heat flux at the wall: An asymptotic solution for ξ → large

Packed-bed systems with axial convective, radial diffusive heat transfer and with a constant heat flux at the wall are studied. Asymptotic solutions valid for axial distances sufficiently away from the inlet position of the packed-bed are presented and their behavior investigated. Two geometrical configurations (i.e., the parallel plate and the cylindrical tube) are analyzed. Also, lower bounds for the axial coordinate are derived and their effect on the validity of the asymptotic solution are investigated. The asymptotic temperature profile is shown to yield the correct bulk temperature profile and to predict the correct Nusselt number for both types of geometries.     

Estimation of parameters in multi-mode heat transfer problems using Bayesian inference – Effect of noise and a priori

Parameter estimation problems and heat source/flux reconstruction problems are some of the most frequently encountered inverse heat transfer problems. These problems find their application in many areas of science and engineering. The primary focus of this paper is on the heat transfer parameter estimation for a two-dimensional unsteady heat conduction problem with (a) convection boundary condition and (b) convection and radiation boundary condition. The paper demonstrates the effect of a priori model on the performance of the algorithm at different noise levels in the measured data. The inverse problem is solved using three different a priori models namely normal, log normal and uniform. The posterior PDF is sampled using the Metropolis–Hastings sampling algorithm. Both single-parameter estimation and multi-parameter estimation problems are addressed and the effects of corresponding a priori models are studied. It was found that the mean and maximum a posteriori estimates for thermal conductivity and the convection heat transfer coefficient were insensitive to the a priori model at all the considered noise levels for the single-parameter estimation problem. At high noise levels in the two-parameter estimation problem, the estimates for thermal conductivity and convection coefficient were sensitive to the a priori model. It was also found that the standard deviation of the samples was correlated to the error in estimation in the single-parameter estimation case. In three parameter estimation case, alternate solutions to the same problem were retrieved due to a strong correlation between the convection coefficient and the emissivity. However, a more informative a priori model could address this issue.     

Effectiveness–NTU relation for packed bed liquid desiccant–air contact systems with a double film model for heat and mass transfer

One-dimensional models were usually utilized to describe the coupled heat and mass transfer processes in packed bed liquid desiccant–air contact systems. In this paper, a double film model was utilized for both parallel and countercurrent flow configurations. The model considered the effects of non-unity values of Lewis factor, unequal effective heat and mass transfer areas, liquid phase heat and mass transfer resistances, changes in solution mass flow rate and concentration. Within the relatively narrow range of operating conditions usually encountered in a specified application, a linear approximation was made to find out the dependence of equilibrium humidity ratio on solution temperature and concentration. Constant approximations of some properties and coefficients were further made to render the coupled equations linear. The original differential equations were rearranged and an analytical solution was developed for a set of newly defined parameters. Analytical expressions for the tower efficiency and other effectiveness values were further developed based on the analytical solution. Comparisons were made between analytical results and numerical integration of the original differential equations and the agreement was found to be quite satisfactory.     

Combined heat and mass transfer analyses in solar distillation systems – The restrictive conditions and a validity range investigation

The present work aims at the investigation of the validity range and accuracy of earlier developed theories which have been proposed for the modeling of heat and mass transfer within confined spaces in solar distillation systems. The investigation which is based on the evaluation of agreement between theoretical results and an extensive body of earlier field and laboratory measurements covers a very wide range of operating conditions and allows a comparable validation of the earlier proposed theories. It also clearly defines the restrictions, limitations and the validity range in relationship to yield as well as to the operating temperature level, beyond which significant deviations between predictions from both the earlier Dunkle’s as well as more recent analogy models and measurements occur for practical solar stills.     

CO2 payback–time assessment of a regional-scale heating and cooling system using a ground source heat–pump in a high energy–consumption area in Tokyo

We present an assessment of installing a regional heating and cooling system in the Nishi(West)-Shinjuku area of Tokyo, Japan. In this assessment, we estimate the CO₂ payback–time, when air source heat–pumps (ASHP) are replaced with a ground–source heat–pump (GSHP) system. We calculate CO₂ emissions from transportation of the cooling tower, materials for the underground heat exchanger, and the digging loads and transportation loads incurred when the GSHP system is installed to replace the air source cooling system. The total CO₂ emission from the installation of the GSHP system was estimated to be 67,701t-CO₂, with 87% of the CO₂ emissions resulting from the digging process. CO₂ emissions from the operation of the GSHP system were estimated from the total energy-efficiency of the system and the heating and cooling demand in Nishi-Shinjuku area. Using the GSHP system, 33,935t-CO₂ would be emitted per year. We estimate that using the GSHP system would result in a reduction of 54% of the CO₂ emissions, or 39,519t-CO₂ per year. From these results, the CO₂ payback–time for replacing the conventional ASHP in the 1 km² studied region with the GSHP system is assessed to be 1.7 years.     

Measurements of critical heat flux and liquid–vapor structure near the heating surface in pool boiling of 2-propanol/water mixtures

Saturated pool boiling of 2-propanol/water mixtures on a 12 mm diameter horizontal disk under atmospheric pressure was investigated. The CHF of the mixtures increased up to 1.7 times the CHF of water at 3.0–4.7 mol% concentrations of 2-propanol. To examine the mechanism of the CHF enhancement in the mixtures, liquid–vapor structures close to the heating surface were measured using a conductance probe. It was found that in the boiling of the mixtures, liquid–vapor structures show strong non-uniformity in the radial direction of the heating surface. The void fractions at 0.1–1 mm above the heating surface are small at the central region and large near the periphery of the heating surface. The liquid layer between the vapor mass and the heating surface is considerably thicker than that of water at the central region and becomes thinner near the periphery of the heating surface. This thicker liquid layer is likely to be the cause of the CHF enhancement in the 2-propanol/water mixtures.     

Analysis of pinch point in liquid–vapour heat exchanger of R134a–DMAC vapour absorption refrigeration system

R134a (1,1,1,2 tetrafluro ethane)–DMAC (N,N Dimethyl Acetamide) vapour absorption refrigeration system can be used for sub-zero temperature applications and in industries where ammonia is forbidden. But it needs rectification of vapour from generator and draining of residual R134a–DMAC liquid from evaporator. As such, owing to the comparatively low ratio of latent heat of vapourisation to vapour specific heat of R134a, liquid vapour heat exchanger (LVHX) is required and the residual liquid further enhances its prominence in sub-cooling the incoming condensate to improve COP. In this paper LVHX is analyzed in detail by varying operating parameters like rectifier efficiency and evaporation and generator temperatures. Heat capacity rate of the cold stream (vapour and residual liquid) changes continuously due to the progressive phase change of the residual liquid. Depending on the rectifier efficiency, the maximum temperature difference shifts from one end of LVHX to the other, while at certain efficiencies it occurs within the heat exchanger indicating that normal design procedure would lead to its design oversize. The importance of LVHX increases with a decrease in both rectifier efficiency and evaporator temperature.