Number Of Heat Transfer Units Research Articles

Determination of the Optimum Geometry of the Heat Exchanger Body Via A Genetic Algorithm

ABSTRACT In the heat industry, design of the best-fitting heat exchanger in energy-converting systems has gained vital importance. In addition to fitness, the time needed to design an exchanger is also of great importance. In order to obtain the optimum heat exchanger, the geometry, the number of heat transfer units (NTU), and the pressure drop (ΔP) must be in harmony such that the requirements will be satisfied. The most important feature of this study, which makes it distinguishable from others, is the determination of optimum geometry, given performance limits, using a genetic algorithm. Therefore, this study offers an alternative way to calculate the needed geometry with a set of given initial values.

Studies on simultaneous energy and water minimisation—Part I: Systems with no water re-use

This paper addresses the simultaneous management of energy and water. A new systematic methodology has been developed for targeting and design that simultaneously minimises the requirements of energy and water. Using this new approach, the design of a water system for maximum energy recovery can be achieved, taking into account the mixing opportunities offered by water networks, while maintaining the water quality to processes in terms of contamination. Direct and indirect energy recovery are analysed and a strategy developed to decrease the number of heat transfer units based on the generation of separate systems and non-isothermal stream mixing. Initially, the analysis is restricted to no water re-use.

Constructal multi-scale tree-shaped heat exchangers

This paper describes the conceptual design and performance of balanced two-stream counterflow heat exchangers, in which each stream flows as a tree network through its allotted space. The two trees in counterflow are like two palms pressed against each other. The paper develops the relationships between effectiveness and number of heat transfer units for several tree-counterflow configurations: (i) constructal dichotomous trees covering uniformly a rectangular area, (ii) trees on a disk-shaped area, and (iii) trees on a square-shaped area. In configurations (ii) and (iii) each stream flows between the center and the periphery of the area. Configurations (i) and (ii) are trees with minimal resistance to fluid flow. Configuration (iii) is designed by minimizing the length of each duct in the network. The paper reports the formula for the number of heat transfer units in each configuration. Unlike in counterflows formed by two parallel streams, in which the longitudinal temperature gradient is constant, in the counterflow formed by two trees the longitudinal temperature gradient is steeper as one approaches the periphery of the tree canopy. The application of dendritic heat exchangers to devices with maximal transport density is discussed, e.g., electronics cooling, fuel cell architectures, etc.

On Minimization of the Number of Heat Exchangers in Water Networks

This article addresses the problem of minimizing the number of heat exchangers for heat recovery as well as the number of mixing and splitting junctions within water networks while maintaining the energy targets determined by the classical pinch analysis. A new systematic approach is proposed to eliminate the kink points and linearize the composite curves. This is based on a systematic strategy that indicates how to mix and split the water streams in order to modify the shape of the initial composite curves. A new graphical thermodynamic rule that avoids the deterioration of energy targets while minimizing the number of heat transfer units as well as the mixing and splitting network complexity has been formalized. This rule permits the control of the procedure of mixing and splitting on the T-H diagram in order to guarantee the pre-established targets. The proposed approach can be used for either the manual design of heat recovery within water networks or the building of a superstructure with a limited number of feasible design options.

Performance of a Regenerative MHD Power Plant

A theoretical model for investigating the performance of a regenerative magnetohydrodynamic (MHD) power plant is presented. Using continuity, momentum, and energy equations of the flowing gas in the MHD generator, we investigate the effect of constant velocity and constant Mach number cases as operating conditions of the generator on the power plant performance. Internal as well as external irreversibilities are taken into consideration. The effects of temperature ratio across the compressor and number of heat transfer units of regenerator are analyzed numerically. The results show that at low temperature ratios, the regenerative power plant produces higher power and has greater efficiency. However, the use of regenerators decreases the maximum power and the corresponding thermal efficiency. Both constant velocity and constant Mach number cases are identical in performance when the plant is endoreversible without regenerator. General expressions for power and efficiency are also given.

Thermoeconomic design and analysis of a sensible-heat thermal energy storage system with Joulean heating of the storage element

A second-law-based thermoeconomic model of a sensible heat-storage system with Joulean heating is derived and discussed in which the storage element is cooled by flowing stream of gases. In this analysis, unit cost values are attached to the irreversible losses caused by the finite-temperature difference heat transfer and pressure drop during the heat removal process. Important dimensionless parameters are identified and the results are presented in terms of the optimum number of heat transfer units (NTUopt) as a function of the dimensionless unit cost per unit heat conductance (γUA) and dimensionless temperature difference (τ) of the storage systems. The storage systems studied are optimized by introducing a new performance criterion described as the cost rate number(Γ∗). Performance results of low- and high-temperature storage systems are also examined and the results are compared with that obtained from Krane's analysis to illustrate the usefulness of the present approach. The influence of important unit cost parameters on NTUopt and Γopt∗ are also studied in somewhat more detail.

Theoretical determination of effectiveness for heat pipe heat exchangers operating in naturally ventilated tropical buildings

The thermal performance of wickless thermosyphon based heat pipe heat exchangers (HPHEs) for naturally ventilated buildings was simulated using a computer simulation program. This computer program utilizing Microsoft Visual Basic 6.0 software was developed on the basis of the effectiveness—number of heat transfer units (NTU) method and uses the concept of iteration to predict the temperature distribution across the HPHE and its thermal performance. The overall effectiveness of HPHEs was also studied in this research.

Thermoeconomic considerations in the design and rating of two-phase heat exchangers

We discuss a closed-form model for thermoeconomic design and analysis of two-phase heat exchangers used as condensers and evaporators. The results are presented in terms of the optimum number of heat-transfer units (NTUs) as a function of the dimensionless unit-cost ratio and the exit-to-inlet absolute temperature ratio of the single-phase fluid. The sensitivities of various unit-cost parameters (UCPs) are presented. It is demonstrated that the selection of UCPs play a significant role in sizing heat exchangers.

Thermoeconomic analysis of sensible heat, thermal energy storage systems

The paper considers the advantages of employing a thermoeconomic analysis for describing the complete charging–discharging cycle of sensible heat, thermal energy storage systems. The main task is to find the performance of the storage systems at the minimum total cost of owning, maintaining, and operating such systems. The effect of different monetary values on optimum number of heat transfer units, charging time, and second-law efficiency are presented in graphical form. Comparison with results that are based on exergy analysis alone shows the advantages of adopting such an approach for designing and operating thermal energy storage units.

98/02247 First year of operation of Provence SOPROLIF 250 MW CFB boiler

In this paper we determine the fundamental relation between global performance and flow configuration (constructal design) in the case of steam power generation with superheater and reheater placed in parallel in the same stream of hot gases of combustion. The superheater heats the steam for the high pressure turbine, and the reheater supplies steam to the low pressure turbine. Both turbines operate irreversibly. We consider superheaters and reheaters with balanced counter flows and unbalanced counter flows. The total heat transfer area (or the overall number of heat transfer units) is finite. We show that the heat transfer area can be allocated to the superheater and reheater such that the overall power output is maximum. The optimal area allocation ratio is reported for two scenarios: designs with and without a maximum allowable steam temperature.

Catalytic combustion in a reactor with periodic flow reversal. Part 1. Experimental results

The use of a reactor with periodic flow reversal for catalytic incineration of the model pollutants carbon monoxide and propane has been experimentally studied. The mean axial temperature profile over one period in cycle steady state is a symmetrical curve which can be linearised and subdivided into three regions. The center of reactor with a constant maximum temperature and two reactor ends with a linear temperature profile. The most important parameters influencing the reactor operation were found to be catalytic activity, adiabatic temperature rise (reactant concentration) and heat transfer properties of the fixed bed. Higher catalytic activity leads to a decrease of the maximum temperature profile. Increasing reactant concentrations cause higher values of maximum temperature, temperature gradient in the reactor ends and mean temperature at reactor inlet/outlet. A higher number of heat transfer units as a measure for the heat transfer characteristics of the catalyst bed give rise to higher maximum temperature and higher temperature gradient in the reactor ends, while the mean temperature at reactor inlet/outlet remains constant. Investigation of the ignition and extinction behavior of the reactor has shown that a fixed bed with a lower number of heat transfer units requires higher reactant concentrations to maintain stable operation in the ignited state.

Thermal design method of bayonet-tube evaporators and condensers

The paper describes an effectiveness-NTU design method of bayonet-tube evaporators and condensers. Including the effect of the wall superheat on the shell-side film coefficient, and using an energy balance on the tube, differential equations for the steady-state fluid temperatures are formulated. Because of the nonlinear nature of the governing equations, the fourth-order Runge-Kutta method is employed to the solution of the finite difference equations. The results are iterated with the combination of integration techniques. An upper bound to the numerical error being ±5% the fluid temperature distribution as well as the exchanger effectiveness are determined, and presented as a function of the Hurd number, the number of heat transfer units and the flow arrangement. For flow entering through the inner tube, the temperature distribution displays the occurrence of a minimum at a point other than the tube-tip of the exchanger. In an extension of the analysis, an effort is made to illustrate the deviation of the results obtained by uniform film coefficient from the present study, and the differences are outlined.

Second-Law Efficiency of an Energy Storage-Removal Cycle in a Phase-Change Material Shell-and-Tube Heat Exchanger

This communication extends the thermodynamic analysis of latent heat storage in a shell-and-tube heat exchanger, developed recently, to the complete heat storage-removal cycle. Conditions for the cyclic operation of this system are formulated within the quasi-steady approximation for the axisymmetric two-dimensional conduction-controlled phase change. Explicit expressions for the overall number of entropy generation units that account for heat transfer and pressure drop irreversibilities are derived. Optimization of this figure of merit with respect to the freezing point of the phase-change material and with respect to the number of heat transfer units is analyzed. When the frictional irreversibilities of the heat removal stage are negligible, the results of these studies are in agreement with those developed recently by De Lucia and Bejan (1991) for a one-dimensional latent heat storage system.

Optimal synthesis of flexible heat-integrated distillation trains

This paper presents an algorithmic approach to the synthesis of a heat-integrated distillation train that accounts for prespecified uncertainties in the composition of the feed stream. It is intended to search for flexible distillation structures at which operability and least utility cost (LUC) are both guaranteed throughout the uncertainty range. In addition to reach such goals through a minimum number of heat transfer units, the sought design involving columns making only sharp separations should also minimize an estimate of the average LUC. This comes from the fact that the least utility cost can change significantly with the feed composition and, consequently, the mean energy efficiency of the distillation train becomes an important issue. To circumvent the problem's inherent complexities, an equivalent one defined in terms of maximum/minimum column heat loads is really tackled. Described through an MILP formulation, the equivalent synthesis problem only requires accounting for a couple of feed compositions providing the highest and the lowest heat duties at each column. Such feed compositions are established through either a low-size NLP or simple rules-of-thumb. Built-in feasibility constraints assure operability of the train everywhere. In the equivalent problem formulation, the original design objectives are all achieved by sequentially reaching the following targets: (i) a minimum global bound on the least utility cost; (ii) a minimum bound on the utility cost at every pinch temperature; and (iii) a minimum number of units. Two examples involving the separation of four-component mixtures into pure chemical species have been successfully solved in a reasonable CPU time on a VAX 11/780. In each case, several near-optimal designs have also been discovered.

Capital cost targets for networks with non-uniform heat exchanger specifications

Heat exchanger networks (HENS) in the chemical and process industries often require exchangers made of special and expensive materials of construction, different pressure ratings, and different heat transfer devices. The economic implications of such network designs are often very significant; it is important that the performance of such networks be reliably determined before their actual designs. Accurate assessment of such networks requires that the differences in the exchanger requirements of the process streams in the network be adequately represented during the targeting stage. The distribution of the heat transfer surface area and of the total number of heat transfer units between the different exchangers specifications can significantly affect the accuracy of the cost target. In this paper, we examine the relative effects of these factors on the network cost; and develop a general procedure for predicting their distributions and determining the total costs for such networks before the design.

The role of pellet thermal stability in reactor design for heterogeneously catalysed chemical reactions

For exothermic fluid-phase reactions, a reactor which is cooled at the wall can exhibit multiplicity or parametric sensitivity. Moreover, for heterogeneously catalysed exothermic fluid-phase reactions, each of the catalytically active pellets in the reactor can exhibit multiplicity. Both forms of multiplicity can lead to thermal instability and as such have to be taken into account in reactor design. Here the effect of both instabilities is quantified. To this end, simple first-order kinetics are assumed, and intraparticle resistances and reactor and particle dynamics are not considered. A one-dimensional model, consisting of microscale mass and heat balances, is chosen to describe the reactor. It is assumed that the fluid inlet temperature equals the coolant temperature. The pellet scale model is a combined mass and heat balance for the pellet and it assumes that the Chilton—Colburn analogy holds. For its incorporation in the reactor model it is assumed that for every individual pellet heat removal to neighbouring pellets via the mutual contact spots is negligible as compared to the heat transferred to the surrounding fluid. Consequently every pellets is isolated from its neighbours. In the thermally most critical region, i.e. the hot-spot region, reactor stability is determined by three parameter groups: a dimensionless adiabatic temperature rise, an Arrhenius number or dimensionless activation temperature and the ratio of the number of heat transfer units to the number of reaction units. For pellet multiplicity, a fourth parameter group becomes significant in addition: the ratio of the reaction rate to the pellet mass transfer rate. This number depends on the pellet size. A general recipe is given which enables us to determine whether or not pellet thermal instability can become important in reactor operation. For the situation where it is significant, generalized diagrams are presented indicating which pellet sizes problems must be expected due to pellet multiplicity.

Thermodynamic optimization of regenerators

This paper presents a second law of thermodynamics analysis technique for regenerators in single blow operation. Unlike earlier analyses, this technique accounts for the gas and matrix temperature variation along the temporal and spatial coordinates. The results of this study indicate that: 1, well defined optima exist with regard to charging time and number of heat transfer units for maximizing the useful work stored; and 2, whereas in earlier analyses a finite optimum charging time results as N tu approaches infinity, in the present analysis a square wave of specific irreversibility propagates in the medium. To obtain an appropriate analytical expression, this analysis is approximated to suit a low N tu regenerator.

Thermodynamics of Energy Storage by Melting Due to Conduction or Natural Convection

This paper describes the most basic thermodynamic aspects of the process of energy storage by melting of a phase change material when the energy source is a stream of hot single-phase fluid. The first part of the paper considers the melting process ruled by pure conduction across the liquid phase, and the second part deals with the quasi-steady melting dominated by natural convection. The paper establishes the relationship between the total irreversibility of the melting process and design parameters such as the number of heat transfer units of the heat exchanger placed between the energy source and the phase change material, the duration of the melting process, and the position of the energy storage process on the absolute temperature scale. It is shown that the exergy transfer to the melting material is maximized when the melting temperature (Tm) equals the geometric average of the environment temperature (Te) and the temperature of the energy source (T∞), in other words when Tm=(TeT∞)1/2. This conclusion holds for both conduction-dominated melting and convection-dominated melting.

The Second Law Quality of Energy Transformation in a Heat Exchanger

This paper presents the entropy generation (irreversibility) concept as a convenient method for estimating the quality of the heat exchange process in heat exchanger analysis. The entropy generation caused by finite temperature differences, scaled by the maximum possible entropy generation that can exist in an open system with two fluids, is used as the quantitative measure of the quality of energy transformation (the heat exchange process). This measure is applied to a two-fluid heat exchanger of arbitrary flow arrangement. The influence of different parameters (inlet temperature ratio, fluid flow heat capacity rate ratio, flow arrangements) and the heat exchanger thermal size (number of heat transfer units) on the quality of energy transformation for different types of heat exchangers is discussed. In this analysis it is assumed that the contribution of fluid friction to entropy generation is negligible.

Relation Between the Thermal Effectiveness of Overall Parallel and Counterflow Heat Exchanger Geometries

A simple relation is established between the thermal effectiveness of two heat exchanger configurations that differ from each other in the inversion of either one of the two fluids. Using this relation, if the expression for the effectiveness of a configuration, as a function of the heat capacity rate ratio, and the number of heat transfer units, is known, the corresponding expression for the “inverse” configuration is immediately obtained. The relation is valid under the assumptions of temperature independence of the heat transfer coefficient and heat capacity rates, when one of the fluids proceeds through the exchanger in a single, mixed stream. The property is illustrated with several examples from the available literature.