Conjugated heat transfer in double-pass laminar counterflow concentric-tube heat exchangers with sinusoidal wall fluxes

An analytical method is proposed to predict the temperature distribution and local Nusselt number for laminar flow in a double-pass countercurrent heat exchanger with sinusoidal heat flux distribution. A design of inserting in parallel an impermeable barrier to divide an open conduit into two subchannels for conducting double-pass operations, resulting in substantially improved the heat transfer rate, has been evaluated theoretically in the fully developed region. Comparison with the theoretical results shows that the heat-transfer efficiency improvement for double-pass concentric circular heat exchangers is generally higher than those in the single-pass operations without an impermeable barrier inserted. The influences of the impermeable-barrier location on the heat-transfer efficiency improvement and power consumption increment, as indicated from theoretical predictions, can be used to determine the economical feasibility in operating double-pass devices.     

Vascularization with trees matched canopy to canopy: Diagonal channels with multiple sizes

The vascularization of smart materials with self-healing functionality requires the distribution of fluids continuously and uniformly throughout the material volume. This paper shows how to configure the architecture such that the single stream that flows through the vascularized body has access to every volume element. The configuration is two trees matched canopy to canopy, and has freedom to morph in several directions: channel orientations (diagonal vs. orthogonal), channel sizes, and system sizes. Tree–tree configurations provide greater access when diagonal channels are combined with orthogonal channels, and when multiple and optimized channel sizes are used.     

Linear analysis of rapidly switched heat regenerators in counterflow

This paper is intended to provide an accurate analytical solution to the 1D differential equations modelling cyclic steady heat transfer processes in rapidly switched heat regenerators for any value of the flush ratio. The temperature solution for the fluid is initially given in an integral form along the path of a gas particle as a function of the matrix temperature for different space and time intervals. In particular, as a Lagrange system of reference is assumed, the above solution deals separately with gas particles of three possible types (‘cold’, ‘hot’ and ‘internal’) according to Organ’s concept of independent flow regimes. Also, it accounts for the possible superposition of the so-called hot and cold zones of the regenerative matrix depending on the value of the flush ratio. Then, assuming a linear distribution for the matrix temperature, the fluid temperature may analytically be calculated. A closed-form expression for the regenerator effectiveness as a function of NTU and flush ratio is given. It provides a simple but accurate tool to estimate the regenerator effectiveness in rapid cyclic flow situations and the deriving results indicate that it is underestimated by the conventional regenerator theory.     

Improvement in performance on laminar counterflow concentric circular heat exchangers with external refluxes

Considerable improvement of heat transfer in laminar counterflow concentric heat exchangers is obtainable by inserting in parallel an impermeable, resistless sheet to divide an open duct into two subchannels for double-pass operations with external refluxes. Efficiency improvement in heat transfer has been investigated analytically by using an orthogonal expansion technique. The results of improvement in heat transfer efficiency are represented graphically and compared with those in a single-pass operation. The influences of improvement-sheet location and reflux ratio on the enhancement of transfer efficiency as well as on the increment of power consumption have been discussed.     

Extinction of counterflow diffusion flames with radiative heat loss and nonunity Lewis numbers

The structure and extinction characteristics of counterflow diffusion flames with flame radiation and nonunity Lewis numbers of the fuel and oxidant are examined using multiscale asymptotic theory, and a model expressed in terms of the jump relations and reactant leakages with the proper consideration of the excess enthalpy overlooked in previous analyses is developed. The existence of the dual extinction limits in the presence of radiative heat loss, namely the kinetic limit at small Damköhler number (high stretch rate) and the radiative limit at large Damköhler number (low stretch rate), are identified. It is found that the former is minimally affected by radiative loss, while a substantial amount of heat loss is associated with the radiative limit. Reactant leakage, however, is the root cause for both limits. The influence of radiative loss on the extinction Damköhler numbers is found to be through its effects on the flame temperature, the excess enthalpy, and the reduced extinction Damköhler number. At both extinction limits, the contribution from the flame temperature is always important and dominant. The contributions from the other two, however, could be important in some special cases. At small Le_F, the contribution from the reduced extinction Damköhler number is large and even dominant under small radiative loss. The contribution from the excess enthalpy is important for small Le_O and it may be comparable to the contribution from the flame temperature when radiative loss is small. Thus, overlooking the excess enthalpy in previous analyses may have resulted in rather large error in the predicted extinction Damköhler numbers, especially the kinetic one.     

Entropy generation minimization in parallel‐plates counterflow heat exchangers

This paper shows that the main architectural features of a counterflow heat exchanger can be determined based on thermodynamic optimization subject to volume constraint. It is assumed that the channels are formed by parallel plates, the two fluids are ideal gases, and the flow is fully developed, laminar or turbulent. In the first part of the paper, it is shown that the irreversibility of the heat exchanger core is minimized with respect to (1) the ratio of the two‐channel spacings, and (2) the total heat transfer area between the two streams. In the second part, the entropy generation rate also accounts for the irreversibility due to discharging the spent hot stream into the ambient. It is shown that the design can be optimized with respect to (1), (2) and (3) the ratio of the capacity rates of the two streams. The optimized features of the geometry are robust with respect to whether the external discharge irreversibility is included in the entropy generation rate calculation. Copyright © 2000 John Wiley & Sons, Ltd.     

Improvement in device performance on laminar counterflow concentric circular heat exchangers with uniform wall fluxes

The effects of recycle at the ends on the heat transfer through a concentric circular tube with uniform wall fluxes are studied analytically by an orthogonal expansion technique with eigenfunction power series expansion. The heat transfer problem is solved for fully developed laminar velocity profiles in a double-pass circular heat exchanger with ignoring axial conduction and fluid properties of temperature independence. Analytical results show the external recycle can enhance the heat transfer efficiency compared with that in an open tube (without an impermeable circular tube inserted and without recycle). The compensation between the forced-convection increment and heat-transfer driving force decrement are used to study the heat transfer behavior. The effects of the impermeable-tube location on heat transfer efficiency enhancement as well as the power consumption increment have been also discussed.     

Solution of heat and mass transfer in counterflow wet-cooling tower fills

Model of heat and mass transfer in wet cooling tower fills is presented. The model consist of a set of four 1D ODEs describing the mass and energy conservation and kinetics with boundary conditions prescribed on opposite sides of the computational domain. Shooting technique with self adaptive Runge–Kutta step control is applied to solve the resulting model equations. The developed model is designed to be included in a large scale CFD calculations of a natural draft cooling tower where the fill is treated as a porous medium with prescribed distributions of mass and heat sources. Thus, the technique yields the spatial distributions of all flow parameters, specifically the heat and mass sources. Such distributions are not directly available in standard techniques such as Merkel, Poppe and e-NTU models of the fill where the temperature of the water is used as an independent variable. The method is validated against benchmark data available in the literature.     

Heat transfer of conjugated Graetz problems with laminar counterflow in double-pass concentric circular heat exchangers

A device of external recycle at the ends of double-pass concentric circular heat exchangers with uniform wall temperature, resulting in substantially improving the heat transfer, has been designed and studied theoretically. The theoretical analysis on heat transfer efficiency improvement has been developed using orthogonal expansion technique in power series. The analytical results are also represented graphically and compared with that in an open conduit (without an impermeable plate inserted and without recycle). Considerable improvement in heat transfer is obtainable by employing the external recycle at both ends with a suitable adjustment of the impermeable-sheet position and recycle ratio, instead of using an open conduit.     

Laminar counterflow parallel-plate heat exchangers: Exact and approximate solutions

Multilayered, counterflow, parallel-plate heat exchangers are analyzed numerically and theoretically. The analysis, carried out for constant property fluids, considers a hydrodynamically developed laminar flow and neglects longitudinal conduction both in the fluid and in the plates. The solution for the temperature field involves eigenfunction expansions that can be solved in terms of Whittaker functions using standard symbolic algebra packages, leading to analytical expressions that provide the eigenvalues numerically. It is seen that the approximate solution obtained by retaining the first two modes in the eigenfunction expansion provides an accurate representation for the temperature away from the entrance regions, specially for long heat exchangers, thereby enabling simplified expressions for the wall and bulk temperatures, local heat-transfer rate, overall heat-transfer coefficient, and outlet bulk temperatures. The agreement between the numerical and theoretical results suggests the possibility of using the analytical solutions presented herein as benchmark problems for computational heat-transfer codes.     

Cooling characteristics of ground source heat pump with heat exchange methods

The objective of this study is to investigate the influence of the cooling performance for a water-to-water ground source heat pump (GSHP) by using the counter flow and parallel flow methods. The GSHP uses R-410A as a refrigerant, and its main components are a scroll compressor, plate heat exchangers as a condenser, an evaporator, a thermostatic expansion valve, a receiver, and an inverter. Based on our modeling results, the heat transfer rate of the counter flow evaporator is higher than that of the parallel flow evaporator for a heat exchanger length greater than 0.42 m. The evaporator length of the GSHP used in this study was set to over 0.5 m. The performance of the water-to-water GSHP was measured by varying the compressor speed and source-side entering water temperature (EWT). The cooling capacity of the GSHP increased with increased compressor RPMs and source side EWT. Also, using the counter flow method, compared to the parallel flow method, improves the COP by approximately 5.9% for an ISO 13256-2 rated condition.     

The influences of recycle on a double-pass laminar counterflow concentric-tube heat exchangers with sinusoidal wall fluxes

The effects of external recycle at the ends on double-pass laminar countercurrent heat exchangers with sinusoidal heat flux distribution are investigated analytically by setting a general solution to separate the original boundary value problem into a partial differential equation, which is solved by Frobenius method, and an ordinary differential equation. Analytical results show that recycle effects enhance the heat-transfer efficiency due to that the desirable effect of forced-convection increment has more influence than the undesirable effect of the heat-transfer driving-force decrement, and hence the forced-convection increment by increasing the recycle ratio leads to improved device performance in heat-transfer rate as compared with that in the single-pass operation (without an impermeable sheet inserted).     

The influences of recycle on a double-pass laminar counterflow concentric circular heat exchangers

A new device of inserting an impermeable sheet with negligible thermal resistance to divide a circular tube into two subchannels with uniform wall temperature and external refluxes at the ends, resulting in substantially improving the heat transfer, has been designed. The mathematical formulation and theoretical analysis to such a conjugated Graetz problem of double-pass concentric circular heat exchangers have been developed by the use of an orthogonal expansion technique. The analytical results are represented graphically and compared with that in an open conduit of the same size without recycle. Considerable improvement in heat transfer is obtainable by employing double-pass operations with inserting an impermeable sheet instead of using single-pass operations without external refluxes. Two numerical examples in heat transfer efficiency by arranging the recycle effect as well as the power consumption were illustrated. The effects of the channel thickness ratio on the enhancement of heat transfer efficiency as well as on the power consumption increment have been also discussed.     

Thermodynamic optimization of geometric structure in the counterflow heat exchanger for an environmental control system

This paper shows that the internal geometric configuration of a component can be deduced by optimizing the global performance of the installation that uses the component. The example chosen is the counterflow heat exchanger that serves as condenser in a vapor-compression-cycle refrigeration system for environmental control of aircraft. The optimization of global performance is achieved by minimizing the total power requirement or the total entropy generation rate. There are three degrees of freedom in the heat exchanger configuration, which is subjected to two global constraints: total volume, and total volume (or weight) of wall-material. Numerical results show how the optimal configuration responds to changes in specified external parameters such as refrigeration load, fan efficiency, and volume and weight. In accordance with constructal theory and design [1], it is shown that the optimal configuration is robust: major features such as the ratio of diameters and the flow length are relatively insensitive to changes in the external parameters.     

Hydrodynamics and heat exchange in water suntraps

Heat exchange in water suntraps (WS) is discussed. It is shown that the heat exchange and the hydrodynamic characteristics of the flow in the initial sections of the heat removal channels of the WS can be calculated with the help of the laminar boundary layer model, using the assumptions adopted in boundary layer theory.     

Minimizing the entropy production in heat exchange

We present a theoretical proof that the entropy production due to heat exchange in a heat exchanger is minimum when the local entropy production is constant in all parts of the system. The solution for the minimum is independent of the value of the heat transfer coefficient. The general case is compared to the minimization problem that has equipartition of forces as solution. It is found that equipartition of forces predicts the minimum from the general solution well for typical heat exchange conditions. The discrepancy between the two solutions depends largely on the temperature dependency of the heat transfer coefficient. The optimal heat exchange conditions are very well approximated in practice with a counter-current heat exchanger; since the minimum in the entropy production space probably is flat.     

A critical investigation into the heat and mass transfer analysis of counterflow wet-cooling towers

This study gives a detailed derivation of the heat and mass transfer equations of evaporative cooling in wet-cooling towers. The governing equations of the rigorous Poppe method of analysis are derived from first principles. The method of Poppe is well suited for the analysis of hybrid cooling towers as the state of the outlet air is accurately predicted. The governing equations of the Merkel method of analysis are subsequently derived after some simplifying assumptions are made. The equations of the effectiveness-NTU method applied to wet-cooling towers are also presented. The governing equations of the Poppe method are extended to give a more detailed representation of the Merkel number. The differences in the heat and mass transfer analyses and solution techniques of the Merkel and Poppe methods are described with the aid of enthalpy diagrams and psychrometric charts. The psychrometric chart is extended to accommodate air in the supersaturated state.     

Evaluation of heat exchange rate of GHE in geothermal heat pump systems

Total thermal resistance of ground heat exchanger (GHE) is comprised of that of the soil and inside the borehole. The thermal resistance of soil can be calculated using the linear source theory and cylindrical source theory, while that inside the borehole is more complicated due to the integrated resistance of fluid convection, and the conduction through pipe and grout. Present study evaluates heat exchange rate per depth of GHE by calculating the total thermal resistance, and compares different methods to analyze their similarities and differences for engineering applications. The effects of seven separate factors, running time, shank spacing, depth of borehole, velocity in the pipe, thermal conductivity of grout, inlet temperature and soil type, on the thermal resistance and heat exchange rate are analyzed. Experimental data from several real geothermal heat pump (GHP) applications in Shanghai are used to validate the present calculations. The observations from this study are to provide some guidelines for the design of GHE in GHP systems.