A general solution for one-dimensional multistream heat exchangers and their networks

A mathematical model for predicting the steady-state thermal performance of one-dimensional (cocurrent and countercurrent) multistream heat exchangers and their networks is developed and is solved analytically for constant physical properties of streams. By introducing three matching matrices, the general solution can be applied to various types of one-dimensional multistream heat exchangers such as shell-and-tube heat exchangers, plate heat exchangers and plate-fin heat exchangers as well as their networks. The general solution is applied to the calculation and design of multistream heat exchangers. Examples are given to illustrate the procedures in detail. Based on this solution the superstructure model is developed for synthesis of heat exchanger networks.     

Heat transfer characteristics of in-ground heat exchangers

Most in-ground heat storage installations use a system of horizontal or vertical plastic pipes to carry heat exchanger fluid. In designing these systems it is generally assumed that the thermal effects of the plastic pipe can be neglected. This paper reports a laboratory study of the pattern of heat flow around fluid-carrying plastic pipe buried in clay soil. Heat flow measurements as well as estimated contact resistances are presented for a number of configurations. In addition, numerical model computations are given for steady-state, transient and cyclic behaviour of several configurations, and it is shown that substantially reduced heat flows are obtained when plastic pipe is used.     

Dynamic behaviour of one-dimensional flow multistream heat exchangers and their networks

The dynamic behaviour of one-dimensional flow (cocurrent and countercurrent) multistream heat exchangers and their networks is modelled and simulated. The problems can be classified into two types: (1) dynamic responses to arbitrary temperature transients and to sudden flow rate transients from a uniform temperature initial condition or a steady-state condition, which yield a linear mathematical model; (2) dynamic responses to disturbances in thermal flow rates, heat transfer coefficients or flow distributions, which are non-linear problems and should be solved numerically. A linearized model is developed to solve the non-linear problems with small disturbances. The linear model and the linearized model for small disturbances are solved by means of Laplace transform and numerical inverse algorithm. Introducing four matching matrices, the general solution can be applied to various types of one-dimensional flow multistream heat exchangers such as shell-and-tube heat exchangers and plate heat exchangers as well as their networks. The time delays in connecting and bypass pipes are included in the models. The software TAIHE (transient analysis in heat exchangers) is further developed to include the present general solution and is applied to the simulation of fluid temperature responses of multistream heat exchangers. Examples are given to illustrate the procedures in detail.     

Hierarchic modeling of heat transfer processes in heat exchangers

An alternate approach based on hierarchic modeling is proposed to simulate fluid and heat flow in heat exchangers. On the first level, the direct simulations have been performed for the geometry that is similar to a segment of the examined heat sink. Based on the obtained results, the Reynolds number dependencies of the scaling factors f and StPr^2/3 have been established. On the second level, the integral model of the whole heat sink has been built using the volume averaging technique (VAT). The averaging of the transport equations leads to a closure problem. The direct model Reynolds number dependencies f and StPr^2/3 have been used to calculate the local values of the drag coefficient and the heat transfer coefficient , which are needed in the integral model. The example calculations have been performed for 14 different pressure drops across the aluminum heat sink. The whole-section drag coefficient and Nusselt number have been calculated and compared with the experimental data [M. Rizzi, M. Canino, K. Hu, S. Jones, V. Travkin, I. Catton, Experimental investigation of pin fin heat sink effectiveness, in: Proc. of the 35th National Heat Transfer Conference Anaheim, California, 2001]. A good agreement between the modeling results and the experiment data has been reached with same discrepancies in the transitional regime. The constructed computational algorithm offers possibilities for geometry improvements and optimization, to achieve higher thermal effectiveness.     

Finite line-source model for borehole heat exchangers: effect of vertical temperature variations

A solution to the three-dimensional finite line-source (FLS) model for borehole heat exchangers (BHEs) that takes into account the prevailing geothermal gradient and allows arbitrary ground surface temperature changes is presented. Analytical expressions for the average ground temperature are derived by integrating the exact solution over the line-source depth. A self-consistent procedure to evaluate the in situ thermal response test (TRT) data is outlined. The effective thermal conductivity and the effective borehole thermal resistance can be determined by fitting the TRT data to the time-series expansion obtained for the average temperature.     

Experimental evaluation of commercial heat exchangers for use as PCM thermal storage systems

Phase change materials (PCM) possess a great capacity of accumulation of energy in their temperature of fusion thanks to the latent heat. These materials are used in applications where it is necessary to store energy due to the temporary phase shift between the offer and demand of thermal energy. Thus, possible applications are the solar systems as well as the recovery of residual heat for its posterior use in other processes. In spite of this great potential, the practical feasibility of latent heat storage with PCM is still limited, mainly due to a rather low thermal conductivity. This low conductivity implies small heat transfer coefficients and, consequently, thermal cycles are slow and not suitable for most of the potential applications.     

Analytic model for transient heat exchanger response

The temperature transient response of a single-phase fluid and a wall in a heat exchanger is investigated for when the other constant temperature fluid is subjected to a step change in temperature or when the single-phase fluid is subjected to a step change in mass flow rate. The dynamic behavior of the heat exchanger is approximated by an integral method assuming that the single-phase fluid temperature distribution can be expressed by a combination of the initial and final temperature distributions and a determined time function. The results are validated by comparison against numerical simulations. Excellent agreement is obtained.     

An experimental study in determining the local heat transfer coefficients for the plate finned-tube heat exchangers

A three-dimensional inverse problem in determining the local heat transfer coefficients for the plate finned-tube heat exchangers utilizing the steepest descent method (SDM) and a general purpose commercial code CFX4.4 is applied successfully in the present study based on the measured temperature distributions on fin surface by infrared thermography.Two different tube arrangements (i.e. in-line and staggered) with different fin pitch and air velocity are considered and the corresponding local heat transfer coefficients are to be determined. Results show that some interesting phenomena of the local heat transfer coefficients for the finned surface are found in the work and the averaged heat transfer coefficient of the staggered configuration is about 8–13% higher than that of the in-line configuration.     

Evaluation of storage configurations with internal heat exchangers

An international standard, ISO/DP 9459-4A, 1996 has been proposed to establish a uniform standard of quality for small solar heating systems. In this proposal, system components are tested separately and total system performance is calculated using system simulations based on validated component model parameter values. Another approach is to test the whole system in operation under representative conditions, where the results can be used as a measure of the general system performance. Component testing and system simulation is flexible, but requires an accurate and reliable simulation model. The advantage of system testing is that it is not dependent on simulations and that it shows the actual system performance. Its disadvantage is that it is restricted to the boundary conditions for the test.

The heat store is a key component concerning system performance. Thus, this work focuses on the storage system consisting of store, electrical auxiliary heater, internal heat exchangers (solar and load loops) and tempering valve. Four different storage system configurations with a volume of 750 l were tested in an indoor system test using a statistically generated six-day test sequence and a solar collector simulator. A store component test and system simulation was carried out on one of the four configurations, applying the proposed standard for stores, ISO/DP 9459-4A, 1996 and the MULTIPORT store model. Three test sequences for internal load side heat exchangers, not in the proposed ISO standard, were also carried out. This paper discusses the results of the indoor system test, the store component test, the validation of the store model parameter values and the system simulations.     

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.     

Computer analysis,design and simulation of horizontal ground heat exchangers

This paper presents a new computerized procedure for dealing with the design of horizontal ground heat exchangers (HGHE). The computer program is based on the transient model of coupled nonlinear partial differential equations governing heat and mass flow in soils. The model is two-dimensional and delineates the operation of ground heat storage with the HGHE and such phenomena as freezing/thawing and drying/rewetting of soil moisture. Comprehensive climatological data, such as ambient temperature, solar radiation, wind velocity, rainfall, snowfall, snow characterstics, and water vapour pressure is used to simulate conditions at the ground surface over any required length of time. The package can be applied to any geographical location by changing climatic and soil data input. The designer has the possibility of selecting any of 12 types of soils from sand to clay, 12 commercial heat pumps, nine different configurations of the HGHE, 16 plastic pipes for ground coils, and 13 ground coil fluids. The program, however, does not calculate the length of the HGHE but it evaluates the thermodynamic performance of a ground heat pump system and provides comprehensive data on thermal and hydraulic conditions in ground heat storage. The length of the ground heat exchanger is obtained from a line source theory model or from site dimensions and pipe spacing. Computed results for ground heat exchanger operation correlate fairly well with experimental data. Simulation of temperature and moisture content in the ground for natural conditions (no heat extraction/deposition) showed a fair agreement with field data. The entire computer program is user-friendly, interactive, menu-driven, and written in FORTRAN 77.     

Pressure variation in a natural circulation loop with end heat exchangers

The pressure variation in a natural circulation loop has been investigated for both steady state and transient operating conditions. The loop exchanges heat with hot and cold external fluid streams through counterflow concentric tube heat exchangers. Considering spatial changes only in the direction of the loop length, closed form expressions have been obtained for pressure difference under steady state condition. An iterative scheme based on finite element method (FEM) has been formulated to solve the conservation equations in the transient state. The variation of dynamic pressure and its relationship with the variation of temperature field and circulation rate has been described.     

Investigation of dimpled fins for heat transfer enhancement in compact heat exchangers

Direct and Large-Eddy simulations are conducted in a fin bank with dimples and protrusions over a Reynolds number range of Re_H = 200 to 15,000, encompassing laminar, transitional and fully turbulent regimes. Two dimple-protrusion geometries are studied in which the same imprint pattern is investigated for two different channel heights or fin pitches, Case 1 with twice the fin pitch of Case 2. The smaller fin pitch configuration (Case 2) develops flow instabilities at Re_H = 450, whereas Case 1 undergoes transition at Re_H = 900. Case 2, exhibits higher Nusselt numbers and friction coefficients in the low Reynolds number regime before Case 1 transitions to turbulence, after which, the differences between the two decreases considerably in the fully turbulent regime. Vorticity generated within the dimple cavity and at the dimple rim contribute substantially to heat transfer augmentation on the dimple side, whereas flow impingement and acceleration between protrusions contribute substantially on the protrusion side. While friction drag dominates losses in Case 1 at low Reynolds numbers, both form and friction drag contributed equally in Case 2. As the Reynolds number increases to fully turbulent flow, form drag dominates in both cases, contributing about 80% to the total losses. While both geometries are viable and competitive with other augmentation surfaces in the turbulent regime, Case 2 with larger feature sizes with respect to the fin pitch is more appropriate in the low Reynolds number regime Re_H < 2000, which makes up most of the operating range of typical compact heat exchangers.     

Application of high porosity metal foams as air-cooled heat exchangers to high heat load removal systems

A numerical study has been conducted to investigate the fluid flow and heat transfer of an air-cooled metal foam heat exchanger under the high speed laminar jet confined by two parallel walls for which the range of the Reynolds number is 600–1000. Two independent numerical solvers were used and cross-validated being a FORTRAN code and the commercially available software CFD-ACE. The effects of local thermal non-equilibrium, thermal dispersion, porosity, and pore density on the heat transfer augmentation are examined for different Reynolds numbers. Application of energy flux vectors, for convection visualization, is also illustrated for a more comprehensive analysis of the problem. Finally, the performance of the metal foam heat exchanger is compared to that of conventional finned design. It is observed that the heat removal rate can be greatly improved at almost no excess cost.     

Parametric sensitivity study of operating and design variables in wellbore heat exchangers

A numerical study was conducted to evaluate the potential for using Wellbore Heat Exchangers (WBHX) to extract heat for use in electricity generation. Variables studied included operational parameters such as wellbore geometries, working fluid properties, circulation rates, and regional properties including basal heat flux and formation rock type. Energy extraction is strongly affected by fluid residence time, heat transfer contact area, and formation thermal properties. Water appears to be the most appropriate working fluid. The effects of tubing properties and casing lengths are of second-order.On the basis of a sensitivity study, a Best Case model was simulated, and results compared against the geothermal fluid requirements of existing power generation plants that use low-temperature geothermal fluids. Even assuming ideal work conversion to electricity, a WBHX cannot supply sufficient energy to generate 200 kWe at the onset of pseudo-steady-state (PSS) conditions. Using realistic conversion efficiencies it is unlikely that the system would be able to generate 50 kWe at the onset of PSS.     

A probabilistic fouling and cost model for plate‐and‐frame heat exchangers

Fouling in plate‐and‐frame heat exchangers (PHEs) may be defined as the deposition of unwanted material on the heat transfer surface that reduces heat‐transfer and increases the resistance to fluid flow. Once the thermal–hydraulic performance decreases to a minimum acceptable level, cleaning of the equipment has to be done to restore the performance. The decision regarding periodic off‐line maintenance of the heat exchangers is generally based on a thermal–economic performance of the process. In this paper, we discuss a probabilistic maintenance model for PHE by incorporating the risk level and scatter parameter of the four random fouling growth models, namely linear, power law, falling rate and asymptotic models, which are integrated in the dimensionless cost model for a heat exchanger used in a steel plant. All the results are presented in terms of non‐dimensional plots. The results show that there is a strong relationship between t_down and the uptime, particularly in the region where the costs of operation and maintenance are minimum. Copyright © 2005 John Wiley & Sons, Ltd.     

The Thermal Behavior of Coal—Ash Deposits on Heat Exchangers

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Optimising heat exchangers for air-to-air space-heating heat pumps in the United Kingdom

The paper deals with some of the major aspects of heat-exchanger design for electric heat pumps. After a discussion of heat-transfer theory, it describes a method that can be used in the design and sizing of air-to-refrigerant heat exchangers and in calculating temperature distributions. As an illustration, economically optimum sizes for exchanger coils are given for heat pumps of output 13.9 kW, 5.6 kW and 5 kW at 5°C outside the ambient temperature. At several stages, manufacturer's experimental data have been used, and the final results are compared with the design of heat exchangers used in commercially available models. Some temperature measurements made on a heat-pump installation in an experimental house are also reported. At least doubling the size of presently used indoor coils is shown to be economically justifiable, increasing the seasonal coefficient of performance from about 2.4 to 2.8-3.0. Reassessment of outdoor-fan size is also shown to be necessary. Throughout the work it is assumed that the heat pump is required for heating only, as would be the case in the United Kingdom.     

Regenerative rotary heat exchanger for heat recovery in residential ventilation

Increased energy costs have brought about increased concern by building owners as well as governments about the operating costs and energy budgets for buildings and power plants. This growing energy conservation consciousness has brought a considerable interest in reclaiming waste heat from residential, commercial, industrial, and institutional ventilation systems. Based on theoretical considerations, the design and performance of a small rotary heat exchanger for residential houses is discussed in this paper. Laboratory results reveal a high sensible heat recovery maximum effectiveness of 85 percent with acceptable levels of pressure drop and cross leakage. Cost saving analysis indicates annual energy savings up to 15 percent, with even larger savings in the size of the heating and cooling equipment up to 42 percent. As expected the greatest savings could occur when large amounts of outside air are required for ventilation.     

Exact and approximate formulas for cross flow heat exchangers with unmixed fluids

This article addresses the calculation of the effectiveness of a single-pass cross-flow heat exchanger where the two fluids are not mixed. The author proposes an exact formula which is more convenient than using infinite series expansions as has been proposed until now.