A general calculation method for plate heat exchangers

The possibilities of process stream guidance within plate heat exchangers are very complex. There exist constructional solutions, in which the process-streams are led through stream-passages connected in series or parallel. Other constructions realize the heat transfer between more than two process streams. Known are also constructions, where the stream passages are spirals. All these constructions deviate more or less from the ideal principle of uniflow or counterflow guidance. While the approximate interpretation of plate heat exchangers is solved methodically, the only methods used for the calculation of existing apparatus are either mathematically extremely exacting or not generally valid. To analyse the behaviour of plate heat exchangers, exact and easy to apply calculation methods are required. This article presents a general calculation method for the stationary simulation of plate heat exchangers of any type required. The method allows a mathematically exact determination of the temperature profiles of types of apparatus mentioned above. In a further step the proposed method can also be used for the simulation of the heat flux along the walls of the plates as well as the dispersion in the passages. The basic idea of the presented method is the simulation of a heat exchanger network with generalized operating characteristics. The “classic formulas” of this operating characteristic are given in this method as special cases. The general calculation method for plate heat exchangers can be used without any iteration. Only the consideration of temperature dependent properties as well as phase transitions require iterations. This method is characterized by a great numerical stability.     

Optimal configuration design for plate heat exchangers

A screening method is presented for selecting optimal configurations for plate heat exchangers. The optimization problem is formulated as the minimization of the heat transfer area, subject to constraints on the number of channels, pressure drops, flow velocities and thermal effectiveness, as well as the exchanger thermal and hydraulic models. The configuration is defined by six parameters, which are as follows: number of channels, numbers of passes on each side, fluid locations, feed relative location and type of channel flow. The proposed method relies on a structured search procedure where the constraints are successively applied to eliminate infeasible and sub-optimal solutions. The method can be also used for enumerating the feasible region of the problem; thus any objective function can be used. Examples show that the screening method is able to successfully determine the set of optimal configurations with a very reduced number of exchanger evaluations. Approximately 5% of the pressure drop and velocity calculations and 1% of the thermal simulations are required when compared to an exhaustive enumeration procedure. An optimization example is presented with a detailed sensitivity analysis that illustrates the application and performance of the screening method.     

Turbulent convective transfer in plate heat exchangers

Readily available data on turbulent transfer in plate heat exchangers can be correlated by a heat transfer-energy dissipation analogy:

$\text{Nu}\text{g}{}_1\text{(pr, Vi)}\text{=C}{}_3\text{(fRe}{}_3\text{)}{}_{\mathrm{\delta }}$

in which the Nusselt number modified for changes in the Prandtl number and bulk to wall viscosity ratio Vi is related to the friction factor f and the Reynolds number. The exponent e is a weak function of the coefficient C₃ which depends on the corrugation geometry.When using chevron or herringbone type patterns the heat transfer depends significantly on the angle between the plate corrugation and the main flow direction. If this angle is π/4 the heat transfer per unit of mechanical energy dissipated is a maximum. Although maximum transfer (with maximum pressure drop) is obtained at π/2, a more practical angle giving high transfer at moderate pressure drops in 2π/5.     

A new method for heat transfer and fluid flow performance simulation of plate heat exchangers

Successful numerical simulation on heat transfer and fluid flow performances of plate heat exchangers is vital. Their complex structures often make the numerical calculation quite difficult and time-consuming. Conclusions drawn by the present work are promising for greatly simplifying the simulation. Different types of plates consisting of different numbers of periods are analyzed and it is concluded that the Nusselt number remains constant for different periods of different plates under different inlet velocities. The central friction coefficients behave the same as Nusselt number. For the first and last periods, the respective friction coefficient also remains for different plates. A small plate fraction with four periods is enough for performance prediction of any-sized plates.     

Local effects of longitudinal heat conduction in plate heat exchangers

In a plate heat exchanger, heat transfer from the hot to the cold fluid is a multi-dimensional conjugate problem, in which longitudinal heat conduction (LHC) along the dividing walls often plays some role and can not be neglected. Large-scale, or end-to-end, LHC is always detrimental to the exchanger’s effectiveness. On the contrary, if significant non-uniformities exist in the distribution of either convective heat transfer coefficient, small-scale, or local, LHC may actually enhance the exchanger’s performance by improving the thermal coupling between high heat transfer spots located on the opposite sides of the dividing wall.     

A three-dimensional inverse problem in imaging the local heat transfer coefficients for plate finned-tube heat exchangers

A three-dimensional inverse heat conduction problem in imaging the local heat transfer coefficients for plate finned-tube heat exchangers utilizing the steepest descent method and a general purpose commercial code CFX4.4 is applied successfully in the present study based on the simulated measured temperature distributions on fin surface by infrared thermography.It is assumed that no prior information is available on the functional form of the unknown local heat transfer coefficients in the present study. Thus, it can be classified as function estimation for the inverse calculations.Two different heat transfer coefficients for in-line tube arrangements with different measurement errors are to be estimated. Results show that the present algorithm can obtain the reliable estimated heat transfer coefficients.     

Modeling of plate heat exchangers with generalized configurations

A mathematical model is developed in algorithmic form for the steady-state simulation of gasketed plate heat exchangers with generalized configurations. The configuration is defined by the number of channels, number of passes at each side, fluid locations, feed connection locations and type of channel-flow. The main purposes of this model are to study the configuration influence on the exchanger performance and to further develop a method for configuration optimization. The main simulation results are: temperature profiles in all channels, thermal effectiveness, distribution of the overall heat transfer coefficient and pressure drops. Moreover, the assumption of constant overall heat transfer coefficient is analyzed.     

New design equations for liquid/solid fluidized bed heat exchangers

Liquid/solid fluidized bed heat exchangers have originally been developed for desalination plants. However, due to their substantial benefits with respect to significantly improved heat transfer and fouling reduction, successful applications also exist in areas such as petrochemical, minerals and food processing as well as in the paper and power industries. The excellent performance of fluidized bed heat exchangers is related to the interaction between particles and heat transfer surface and to mixing effects in the viscous sublayer. In this paper, the results of experimental investigations on heat transfer for a wide range of Newtonian and non-Newtonian fluids are presented. New design equations have been developed for the prediction of bed voidage and heat transfer coefficients. The predictions of these correlations and of numerous correlations recommended by other authors are compared with a large database compiled from the literature.     

Dynamics of plate heat exchangers subject to flow variations

A predictive model has been presented to suggest the transient response of plate heat exchangers, subjected to a step flow variation. The work also brings out the effect of the port to channel maldistribution on the performance of plate heat exchangers under the condition of flow variation. The results indicate that flow maldistribution affects the performance of the plate heat exchangers in the transient regime. A wide range of the parametric study has been presented which brings out the effects of NTU and heat capacity rate ratio on the response of the plate heat exchanger, subjected flow perturbation.To verify the presented theoretical model, appropriate experiments have been carried out. Experiments include the responses of the outlet temperatures subjected to inlet temperature transient in the circuit followed by a sudden change in flow rate in one of the fluids. Simulated performance has been compared to the performance measured in the experiments. Comparisons indicate that theoretical model developed for flow transient is capable of predicting the transient performance of the plate heat exchangers satisfactorily, under the given conditions of changed flow rates.     

Absorption of organic fluid mixtures in plate heat exchangers

It is well known that the absorber is the key component in energy conversion systems that are based on absorption cycles. This paper describes an experimental investigation into the absorption process of organic fluid mixtures in an absorption system which has a spray and a plate heat exchanger. The absorber consists of an adiabatic mixing chamber with a spray, where the solution that is weak in refrigerant is sprayed into the refrigerant vapour. A two-phase mixture is formed and enters a plate heat exchanger, where the solution is cooled to complete the absorption process.We carried out experiments with different types of spray nozzles using the organic fluid mixtures methanol–tetraethyleneglycol dimethylether (TEGDME) and trifluoroethanol (TFE)–TEGDME. We analyse how the solution mass flow rate, absorber pressure and cooling water temperature affected the absorber performance and we discuss the results in terms of the absorber load, absorbed mass flux, degree of subcooling of the solution at the absorber outlet, solution film heat and mass transfer coefficients.The results indicate that the absorption system proposed is suitable for relatively low pressures. For water temperatures of 30 °C and absorber pressures between 2 and 6 kPa, the absorption rates for TFE–TEGDME were 1 to 2.5 g·s⁻¹·m⁻². The corresponding values for methanol–TEGDME with absorber pressures between 10 and 15 kPa were 0.4 to 1.2 g·s⁻¹·m⁻².     

Prediction of heat transfer coefficient on the fin inside one-tube plate finned-tube heat exchangers

The finite difference method in conjunction with the least-squares scheme and the experimental temperature data is proposed to predict the average heat transfer coefficient and the fin efficiency on the fin inside one-tube plate finned-tube heat exchangers for various air speeds and the temperature difference between the ambient temperature and the tube temperature. Previous works showed that the heat transfer coefficient on this rectangular fin is very non-uniform. Thus the whole plate fin is divided into several sub-fin regions in order to predict the average heat transfer coefficient and the fin efficiency on the fin from the knowledge of the fin temperature recordings at several selected measurement locations. The results show that the surface heat flux and the heat transfer coefficient on the upstream region of the fin can be markedly higher than those on the downstream region. The fin temperature distributions depart from the ideal isothermal situation and the fin temperature decreases more rapidly away from the circular center, when the frontal air speed increases. The average heat transfer coefficient on the fin increases with the air speed and the temperature difference between the ambient temperature and the tube temperature. This implies that the effect of the temperature difference between the tube temperature and the ambient temperature is not negligent.     

Local heat transfer measurements of plate finned-tube heat exchangers by infrared thermography

An experimental study is performed using an infrared thermovision to monitor temperature distribution over a plate-fin surface inside the plate finned-tube heat exchangers. The differentiation of the temperature function is derived to determine the local convective heat transfer coefficients on the tested fin, using a local element lumped conduction equation included the convective effect on the boundaries with experimental data. It is disclosed that the infrared thermography is capable of rapidly detecting location and extent of transition and separation regions of the boundary layer over the whole surface of the tested models. Through the comparison of the test results on the strategy region of the in-line and staggered arrangements, it is more easy to understand or interpret the detailed dynamic phenomena of flow existed in the heat exchangers. In addition, the experimental results demonstrate that the averaged heat transfer coefficient of staggered configuration is 14-32% higher than that of in-lined configuration     

Dimensional analysis for the heat transfer characteristics in the corrugated channels of plate heat exchangers

Using the Buckingham Pi theorem, this study derives dimensionless correlations to characterize the heat transfer performance of the corrugated channel in a plate heat exchanger. The experimental data are substituted into these correlations to identify the flow characteristics and channel geometry parameters with the most significant influence on the heat transfer performance. Simplified correlations by omitting the factors with less influence are then obtained. The results show that Nu_x is affected primarily by Re, R/D_h, x/D_h, and β. Neglecting the minor effect of factors on Nu_x, it is shown that Nu_m is determined primarily by Re, R/D_h and β.     

Modeling of turbulent heat transfer and thermal dispersion for flows in flat plate heat exchangers

In this paper, heat transfer and dispersion for both laminar and turbulent regimes in heat exchangers and nuclear cores are considered. Such hydraulic systems might be seen as spatially periodic porous media. The existence of a turbulent flow within a porous medium structure suggests the use of a spatial average operator, combined to a statistical average operator. Previous works [M.H.J. Pedras, M.J.S. De Lemos, Macroscopic turbulence modeling for incompressible flow through undeformable porous media, Int. J. Heat Mass Transfer 44 (2001) 1081–1093; F. Kuwahara, A. Nakayama, H. Koyama, A numerical study of thermal dispersion in porous medium, J. Heat Transfer 118 (1996) 756–761] have applied a double average procedure to the thermal balance equation, which led to a macroscopic turbulent transport and a subsequent macro-scale equation featuring dynamic dispersion. Considering the heat flux at the solid surfaces as a boundary condition for the fluid energy balance, the model proposed in this paper allows one to take into account this dispersion as the sum of two contributions. The first one is the classical dispersion due to velocity heterogeneities [G. Taylor, Dispersion of solute matter in solvent flowing slowly through a tube, Proc. Roy. Soc. Lond. A 219 (1953) 186–203] and the second one is due to wall heat transfer. Applying Whitaker up-scaling method [S. Whitaker, Theory and applications of transport in porous media: the method of volume averaging, Kluwer Academic Publishers, 1999], a “closure problem” is then derived for a representative elementary volume, using the so-called Boussinesq approximation to account for small scale turbulence. The model is used to compute macro-scale heat transfer properties for turbulent flows inside a flat plate heat exchanger. It is shown that, for such flows, both dispersive fluxes strongly predominate over the macroscopic turbulent heat flux.     

An alternate algorithm for the analysis of multistream plate fin heat exchangers

A new algorithm has been developed for the analysis of multistream heat exchangers. The numerical technique involves partitioning of the exchanger in both axial and normal directions. Conservation equations written for each segment are solved using an iterative procedure. In the axial direction, the exchanger is successively partitioned to 2^k segments, the final value of k being determined by the point where further partitioning has only marginal effect. In the normal direction, the exchanger is divided into a stack of overlapping two-stream exchangers interacting through their common streams. The algorithm has been tested against published results and good agreement has been observed.     

CFD analysis of two types of welded plate heat exchangers

A numerical and experimental study has been carried out on the heat transfer and fluid flow in two types of welded plate heat exchangers (PHEs). A new approach providing a proper clearance between two adjacent corrugated plates is proposed to improve the mesh quality around the contact points. The clearance value and the influence on the mesh quality and computational results are carefully studied. The results show that a relative clearance of 0.02 is proper. The computational fluid dynamics (CFD) results agree with the experimental results with a deviation of 15%. The proposed approach is proved effective and practical because it can increase the grid quality without losing the accuracy of the results. This paper shows that CFD is a reliable tool for studying the effects of various geometrical configurations on the optimum design of a PHE.     

Performance evaluation criteria for heat exchangers based on second law analysis

This paper presents second-law based performance evaluation criteria to evaluate the performance of heat exchangers. First, the need for the systematic design of heat exchangers using a second law-based procedure is recalled and discussed. Then, a classification of second-law based performance criteria is presented:

• 1.criteria that use entropy as evaluation parameter, and
• 2.criteria that use exergy as evaluation parameter.

Both classes are collectively presented and reviewed, and their respective characteristics and constraints are given. It is shown how some of these criteria are related to each other. Emphasis is also placed on the importance of second law-based thermoeconomic analysis of heat exchangers, and these methods are discussed briefly.     

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.     

Numerical computation for parallel plate thermoacoustic heat exchangers in standing wave oscillatory flow

A simplified computational method for studying the heat transfer characteristics of parallel plate thermoacoustic heat exchangers is presented. The model integrates the thermoacoustic equations of the standard linear theory into an energy balance-based numerical calculus scheme. Details of the time-averaged temperature and heat flux density distributions within a representative domain of the heat exchangers and adjoining stack are given. The effect of operation conditions and geometrical parameters on the heat exchanger performance is investigated and main conclusions relevant for HX design are drawn as far as fin length, fin spacing, blockage ratio, gas and secondary fluid-side heat transfer coefficients are concerned. Most relevant is that the fin length and spacing affect in conjunction the heat exchanger behavior and have to be simultaneously optimized to minimize thermal losses localized at the HX-stack junctions. Model predictions fit experimental data found in literature within 36% and 49% respectively at moderate and high acoustic Reynolds numbers.     

A robust learning based evolutionary approach for thermal-economic optimization of compact heat exchangers

This paper presents a robust, efficient and parameter-setting-free evolutionary approach for the optimal design of compact heat exchangers. A learning automata based particle swarm optimization (LAPSO) is developed for optimization task. Seven design parameters, including discreet and continuous ones, are considered as optimization variables. To make the constraint handling straightforward, a self-adaptive penalty function method is employed. The efficiency and the accuracy of the proposed method are demonstrated through two illustrative examples that include three objectives, namely minimum total annual cost, minimum weight and minimum number of entropy generation units. Numerical results indicate that the presented approach generates the optimum configuration with higher accuracy and a higher success rate when compared with genetic algorithms (GAs) and particle swarm optimization (PSO).