Single-phase and two-phase cooling using hybrid micro-channel/slot-jet module

This paper explores the single-phase and two-phase cooling performance of a hybrid micro-channel/slot-jet module using HFE-7100 as working fluid. Three-dimensional numerical simulation using the k–ε turbulent model is used to both assess the single-phase performance and seek a geometry that enhances heat removal capability and surface temperature uniformity while decreasing mean surface temperature. This geometry is then tested experimentally to validate the numerical findings and aid in the development of correlations for both the single-phase and two-phase heat transfer coefficients. The hybrid module is shown to maintain surface temperature gradients below 2 °C for heat fluxes up to 50 W/cm². Even without phase change, the hybrid module is capable of dissipating heat fluxes as high as 305.9 W/cm². Highly accurate single-phase correlations are developed using a superpositioning technique that consists of assigning a different heat transfer coefficient for each portion of the heat transfer area based on the dominant heat transfer mechanism for that portion. Increasing subcooling and/or flow rate is shown to delay the onset of nucleate boiling to a higher heat flux and higher surface temperature, as well as enhance critical heat flux (CHF). A correlation previously developed for hybrid micro-channel/micro-circular-jet module is deemed equally effective at predicting two-phase heat transfer data for the present hybrid module.     

The effects of thermal non-equilibrium and inlet temperature on two-phase flow pressure drop type instabilities in an upflow boiling system

In this paper a theoretical model for the two-phase flow pressure drop type instabilities in an upflow boiling system is presented. The thermal non-equilibrium effect between the two phases is included assuming the enthalpy profile in the subcooled boiling region. The system of differential equations describing the single-phase and boiling regions of the system (drift-flux model) is solved using finite difference method for the steady state characteristics of the system over a wide range of operating conditions. Upon obtaining the steady state characteristics, the dynamic formulation of the pressure drop type oscillation is solved numerically. The modeling results are verified by the experimental findings. The effect of the thermal non-equilibrium on the steady state characteristics, stability boundaries and oscillation periods at different heat inputs and inlet temperatures are presented as being compared with the experimental measurements as well as the results obtained from the thermal equilibrium model.     

Effect of dry hydrocarbons and critical point temperature on the efficiencies of organic Rankine cycle

Higher efficiencies and optimal utilization of geothermal energy require a careful selection of the working fluid in organic Rankine cycles (ORC). The objectives of this study are to analyze and explain the effect of using alternative dry fluids on the efficiencies of the ORC and compare them with other refrigerants. In addition, the effect of the critical temperature on the thermal and exergetic efficiencies will also be determined. Results showed that iso-pentane is a good replacement for R-113, while neo-pentane outperformed C₅F₁₂. In addition, n-butane showed better efficiency than RC-318, R-236fa, and R-245fa. The best working fluid in the studied system was n-hexane, while R-227ea was the worst. It was also found that efficiencies correlate with the critical temperature of the working fluid where a strong functionality was noticed in the studied range. The contribution of the evaporator to the total exergy destruction was the most relevant, while the pump contribution was marginal. It is concluded that thermodynamically, hydrocarbons are superior to some refrigerants and could be the next generation working fluids for geothermal or waste heat recovery systems.     

Generalized model of thermal boundary conductance between SWNT and surrounding supercritical Lennard-Jones fluid – derivation from molecular dynamics simulations

Using classical molecular dynamics simulations, we have studied thermal boundary conductance (TBC) between a single-walled carbon nanotube (SWNT) and surrounding Lennard-Jones (LJ) fluids. With an aim to identify a general model that expresses the TBC for various surrounding materials, TBC was calculated for three different surrounding LJ fluids, hydrogen, nitrogen, and argon in supercritical phase. The results show that the TBC between an SWNT and surrounding LJ fluid is approximately proportional to local density (ρ_L) formed on the outer surface of SWNT and energy parameter (ε) of LJ potential, and inverse proportional to mass (m) of surrounding LJ fluid. In addition, the influence of the molecular mass of fluid on TBC is far more than other inter-molecular potential parameters in realistic range of molecular parameters. Through these parametric studies, we obtained a phenomenological model of the TBC between an SWNT and surrounding LJ fluid.     

Single-phase and two-phase magnetohydrodynamic pipe flow

Experimental results are presented for a range of measured temperatures and other parameters of vertically downward flows, both single-phase (sodium) and two-phase (sodium-nitrogen), in a conducting-wall pipe in the presence of a transverse magnetic field. Existing MHD theory predicted, to within experimental error, all single-phase pressure differences for magnetic interaction parameter values of up to approximately 100, beyond which the single-phase normalized resistance coefficients were noticeably lower than the laminar-flow predictions. The magnetic interaction parameter at which such deviation occurred was governed by the conductivity ratio. Two-phase pressure differences were obtained across a range of void fractions, approximately 0.3-0.8, where two distinct flow regimes were encountered. For those two regimes, the normalized resistance coefficients of pressure difference were predicted to within experimental error by the corresponding two-phase MHD pressure-difference models. In half of the two-phase cases examined, decreases were observed in normalized resistance coefficients at high values of the magnetic interaction parameter, a trend similar to that found in single-phase flow. The wall-voltage profiles of single-phase flows were symmetric with respect to the center of the applied magnetic field region; two-phase wall-voltage profiles were asymmetric because of the expansion of the gaseous nitrogen along the length of the test section. The influence of temperature and other system parameters upon pressure differences and wall voltages, and the possible effect of ‘M-shaped’ velocity profiles in the two types of flow are discussed.     

Effects of mass transfer on the transient free convection flow of a dissipative fluid along a semi-infinite vertical plate with constant heat flux

Effect of mass transfer on the transient free convection flow of a dissipative fluid along a semi-infinite vertical plate in presence of constant heat flux, is studied by solving coupled non-linear system of partial differential equations, using Crank-Nicolson technique which is stable and convergent. Transient temperature, concentration and velocity profiles, local and average skin-friction, Nusselt number and Sherwood number are shown graphically for air. The effects of ε, viscous dissipative parameter, Schmidt number, buoyancy ratio parameter on the transient state are discussed.     

Development of generalized (rate dependent) availability

We treat the irreversible extension of the classical problem of maximum mechanical work that may be obtained from a system composed of: a resource fluid at flow, a set of sequentially arranged engines, and an infinite bath. In the engine mode the fluid’s temperature T decreases along the path, thus tending to the bath temperature T^e, and the system delivers work. In a related classical problem the process rates vanish due to the reversibility; here, however, finite rates and consistent losses of the work potential are admitted. The variational calculus leads to a finite-rate generalization of the maximum-work potential called the finite-rate exergy. This finite-rate exergy is a function of the usual thermal coordinates and the overall number of transfer units τ or a rate index h, which is, in fact the Hamiltonian of optimal, active (energy-generating) relaxation process to equilibrium. The resulting bounds on the work delivered or supplied are stronger than the classical reversible bounds.     

Finite time thermodynamics study and exergetic analysis of ammonia–water absorption systems

This paper presents an optimization study of a single stage absorption machine operating with an ammonia–water mixture under steady state conditions. The power in the evaporator, the temperatures of the external fluids entering the four external heat exchangers as well as the effectiveness of these heat exchangers and the efficiency of the pump are assumed fixed. The results include the minimum value of the total thermal conductance UA_tot as well as the corresponding mean internal temperatures, overall irreversibility and exergetic efficiency for a range of values of the coefficient of performance (COP). They show the existence of three optimum values of the COP: the first minimises UA_tot, the second minimises the overall irreversibility and the third maximises the exergetic efficiency. They also show that these three COP values are lower than the maximum COP which corresponds to the convergence of the internal and external temperatures towards a common value. The influence of various parameters on the minimum thermal conductance of the heat exchangers and on the corresponding exergy efficiency has also been evaluated. From an exergetic viewpoint it is interesting to reduce the temperature at the desorber and at the evaporator and to raise the values of that parameter at the condenser and the absorber. However these changes must be accompanied by an important increase in the total UA if it is desired to conserve a constant COP. The internal heat exchangers between the working fluid and the solution improve both the overall exergy efficiency and the coefficient of performance of the absorption apparatus.     

Phase change characteristics and their effect on the performance of hydrogen recirculation ejectors for PEMFC systems

The working fluid of the hydrogen recirculation ejector in proton exchange membrane fuel cell (PEMFC) systems is humid hydrogen containing water vapour. However, previous studies on the hydrogen recirculation ejector using computational fluid dynamics (CFD) were based on the single-phase flow model without considering the phase change of water vapour. In this study, the characteristics of the phase change and its effect on the ejector performance are analysed according to a two-phase CFD model. The model is established based on a non-equilibrium condensation phase change. The results show that the average deviation of the entrainment ratio predicted by a single-phase flow model is 25.8% compared with experiments involving a hydrogen recirculation ejector, which is higher than the 15.1% predicted by the two-phase flow model. It can be determined that droplet nucleation occurs at the junction of the primary and secondary flow, with the maximum nucleation rate reaching 4.0 × 10²⁰ m^?3s^?1 at a primary flow pressure of 5.0 bar. The higher temperature, lower velocity, and higher pressure of the gas phase can be found in the mixing region due to condensation, resulting in a lower entrainment performance. The nucleation rate, droplet number, and liquid mass fraction increase remarkably with an increasing primary flow pressure. This study provides a meaningful reference for understanding phase change characteristics and two-phase flow behaviour in hydrogen recirculation ejectors for PEMFC systems.     

Advanced exergetic evaluation of refrigeration machines using different working fluids

Splitting the exergy destruction into endogenous/exogenous and unavoidable/avoidable parts has many advantages for the detailed analysis of energy conversion systems. Endogenous is the exergy destruction obtained when all other system components are ideal and the component being considered operates with its real efficiency. The difference between total and endogenous exergy destruction is the exogenous exergy destruction caused within the component being considered by the irreversibilities in the remaining components and the structure of the overall system. Unavoidable is the part of exergy destruction within one system component that cannot be eliminated even if the best available technology in the near future would be applied. The avoidable exergy destruction is the difference between total and unavoidable exergy destruction. These concepts enhance an exergy analysis and assist in improving the quality of the conclusions obtained from this analysis. The paper presents the combined application of both concepts to vapor-compression refrigeration machines using different one-component working fluids (R125, R134a, R22 and R717) as well as azeotropic (R500) and zeotropic (R407C) mixtures. The purpose of the paper is not to evaluate these working fluids, some of which cannot be used in future, but to demonstrate the effect of different material properties on the results of advanced exergy analysis.     

The onset of Lapwood-Brinkman convection using a thermal non-equilibrium model

The stability of a horizontal fluid saturated sparsely packed porous layer heated from below and cooled form above when the solid and fluid phases are not in local thermal equilibrium is examined analytically. The Lapwood-Brinkman model is used for the momentum equation and a two-field model is used for energy equation each representing the solid and fluid phases separately. Although the inertia term is included in the general formulation, it does not affect the stability condition since the basic state is motionless. The linear stability theory is employed to obtain the condition for the onset of convection. The effect of thermal non-equilibrium on the onset of convection is discussed. It is shown that the results of Darcy model for the non-equilibrium case can be recovered in the limit as Darcy number Da → 0. Asymptotic analysis for both small and large values of the inter phase heat transfer coefficient H is also presented. An excellent agreement is found between the exact solutions and asymptotic solutions when H is very small.     

Steady state simulation for the de-bottlenecking of heat recovery networks

This work presents the use of a steady state simulator for the de-bottlenecking of heat recovery networks. It is shown how a heat exchanger network designed for fixed conditions can be de-bottlenecked when process streams undergo changes in operating conditions such as flow rate and supply temperature. A network is said to be flexible if it is capable of maintaining acceptable operation either during normal or under modified conditions. The de-bottlenecking of heat recovery networks can be considered as a special case of the design for improved flexibility. A simulation model for a single phase network of heat exchangers is presented. The model is based on the use of the thermal effectiveness (ε) parameter for heat exchangers. Any type of exchanger configuration and flow arrangement can be modeled by using the appropriate ε–number of transfer units relationships. A general methodology for improving network flexibility is proposed.     

Simulation of air curtains for vertical display cases with a two-fluid model

In a vertical open display case, air curtains are used to weaken the influence of ambient air on the store. The flow and heat transfer characteristics of air curtains in a vertical display case are simulated with a two-fluid turbulence model in this paper, which takes the fluid in the space to be simulated as a mixture of turbulent fluid and non-turbulent fluid. The air curtains are taken as a turbulent fluid and described by the conventional k–ε turbulence model. The ambient air outside the display case is considered as a non-turbulent fluid and calculated by a laminar model. The exchanges of mass, momentum and energy between the turbulent and the non-turbulent fluids are expressed by empirical relations. The simulation results based on the two-fluid model are compared not only with experimental data, but also with the simulation results when the k–ε model is used for the whole simulated space. The comparisons indicate that the two-fluid model enables to predict thermal stratification phenomenon more accurately and shows better agreement with the measured values than the k–ε model.     

Periodic free convection from a vertical plate in a saturated porous medium, non-equilibrium model

The problem of the free convection from a vertical heated plate in a porous medium is investigated numerically in the present paper. The effect of the sinusoidal plate temperature oscillation on the free convection from the plate is studied using the non-equilibrium model, i.e., porous solid matrix and saturated fluid are not necessary to be at same temperature locally. Non-dimensionalization of the two-dimensional transient laminar boundary layer equations results in three parameters: (1) H, heat transfer coefficient parameter, (2) K_r, thermal conductivity ratio parameter, and (3) λ, thermal diffusivity ratio. Two additional parameters arise from the plate temperature oscillation condition which are the non-dimensional amplitude (ε) and frequency (Ω). The fully implicit finite difference method is used to solve the system of equations. The numerical results are presented for 0 ? H ? 10, 0 ? K_r ? 10, 0.001 ? λ ? 10 with the plate temperature oscillation parameters 0 ? Ω ? 10 and 0 ? ε ? 0.5. The results show that the thermal conductivity ratio parameter is the most important parameter. It is found also that increasing the amplitude and the frequency of the oscillating surface temperature will decrease the free convection heat transfer from the plate for any values of the other parameters.     

Effects of dissipation and temperature-dependent viscosity on the performance of plate heat exchangers

The fluid temperature profiles in a multi-passage plate heat exchanger and its effectiveness were calculated with a model which includes dissipation, temperature-dependent viscosity and appropriate correlations for the Nusselt number and the friction coefficient. When the viscosity of the two fluids is low (e.g. water) the results are identical to the classic ε–NTU relations which are obtained by neglecting dissipation and by assuming that fluid properties and heat transfer coefficients are constant. But, when one of the fluids is very viscous (e.g. glycerol) the temperatures of both fluids are significantly higher while the effectiveness can be higher or lower than the value predicted by the classic relations. In particular, for cases with a very viscous hot fluid, the effectiveness may be even higher than unity.     

Analysis of free convection about a horizontal cylinder in a porous media using a thermal non-equilibrium model

The thermally non-equilibrium model is used to study the free convection from a horizontal cylinder immersed in porous media. The governing equations are transformed to dimensionless form by introducing the boundary layer dimensionless variables. The resultant parabolic system of differential equations is solved by using an implicit finite difference method based on Keller box algorithm. The results of the developed code are validated with different mesh sizes, which can be used as benchmark results for thermally equilibrium condition. Numerical results are obtained for non-equilibrium model to analyze the effect of the governing parameters, which are the heat transfer coefficient between the solid and fluid phases H and the porosity scaled thermal conductivity ratio K_r. The results show that increasing H or K_r leads to increase in the total average Nusselt number. The value of the average Nusselt number for both fluid and solid phases as well as the total average Nusselt number have approached the corresponding values of the thermally equilibrium model at high value of H × K_r.     

A complete two-phase model of a porous cathode of a PEM fuel cell

This paper has developed a complete two-phase model of a proton exchange membrane (PEM) fuel cell by considering fluid flow, heat transfer and current simultaneously. In fluid flow, two momentum equations governing separately the gaseous-mixture velocity (u_g) and the liquid-water velocity (u_w) illustrate the behaviors of the two-phase flow in a porous electrode. Correlations for the capillary pressure and the saturation level connect the above two-fluid transports. In heat transfer, a local thermal non-equilibrium (LTNE) model accounting for intrinsic heat transfer between the reactant fluids and the solid matrices depicts the interactions between the reactant-fluid temperature (T_f) and the solid-matrix temperature (T_s). The irreversibility heating due to electrochemical reactions, Joule heating arising from Ohmic resistance, and latent heat of water condensation/evaporation are considered in the present non-isothermal model. In current, Ohm's law is applied to yield the conservations in ionic current (i_m) and electronic current (i_s) in the catalyst layer. The Butler–Volmer correlation describes the relation of the potential difference (overpotential) and the transfer current between the electrolyte (such as Nafion™) and the catalyst (such as Pt/C).     

Second law-based thermodynamic analysis of water-lithium bromide absorption refrigeration system

In this study, the first and the second law of thermodynamics are used to analyze the performance of a single-stage water-lithium bromide absorption refrigeration system (ARS) when some working parameters are varied. A mathematical model based on the exergy method is introduced to evaluate the system performance, exergy loss of each component and total exergy loss of all the system components. Parameters connected with performance of the cycle–circulation ratio (CR), coefficient of performance (COP), Carnot coefficient of performance (COP_c), exergetic efficiency (ξ) and efficiency ratio (τ)–are calculated from the thermodynamic properties of the working fluids at various operating conditions. Using the developed model, the effect of main system temperatures on the performance parameters of the system, irreversibilities in the thermal process and non-dimensional exergy loss of each component are analyzed in detail. The results show that the performance of the ARS increases with increasing generator and evaporator temperatures, but decreases with increasing condenser and absorber temperatures. Exergy losses in the expansion valves, pump and heat exchangers, especially refrigerant heat exchanger, are small compared to other components. The highest exergy loss occurs in the generator regardless of operating conditions, which therefore makes the generator the most important component of the cycle.     

Effect of system pressure on the steady state performance of a CO2 based natural circulation loop

In the present work the effect of system pressure on the steady state performance of a CO₂ based natural circulation loop with end heat exchangers is studied. For a given geometry, the loop pressure (or CO₂ inventory) is considered as an input and its influence on the system performance is obtained. The system operates as a single-phase loop or a two-phase loop depending upon the loop pressure, when other parameters such as external fluid temperatures and external fluid flow rates are kept fixed. Hence the model developed considers both single and two-phase flow regimes. For the two-phase flow, a homogeneous model is used and the influence of different two-phase viscosity models on system performance is observed. Results show that when other things are kept constant, the heat carrying capacity of the loop increases initially as the loop pressure is decreased, reaches a peak and then starts decreasing with further decrease in loop pressure. From the value of optimum pressure at which heat transfer rate becomes maximum, one can obtain the required optimum amount of CO₂ to be charged into a particular system as the property variation of CO₂ along the loop can be obtained by using the model presented. Thus it is expected that the present study will be useful in the design and optimization of natural circulation loops based on carbon dioxide.     

A modified k–ε turbulence model for the simulation of two-phase flow and heat transfer in condensers

A modified k–ε turbulence model is developed in this study to simulate the gas–liquid two-phase flow and heat transfer in steam surface condensers. A quasi-three-dimensional algorithm is used to simulate the fluid flow and heat transfer in steam surface condensers. The numerical method is based on the conservation equations of mass and momentum for both gas-phase and liquid-phase, and mass fraction conservation equation for non-condensable gases. The numerical simulation of an experimental steam surface condenser has been conducted using the proposed modified k–ε turbulence model. The results obtained from the proposed model agree well with the experimental results and the results also show an obvious improvement in the prediction accuracy comparing with previous results where a constant value for the turbulent viscosity was used.