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• A simplified two-fluid model is proposed for critical two-phase flow in microchannels. • The model preserves precision while incorporating fewer constitutive relations. • Proposed an enhanced metastable liquid nucleation model, achieving precise predictions of nucleation pressure. • Advance the understanding of critical flow in microchannels. Critical flow phenomena are present in many chemical engineering processes, such as microchannel heat exchangers, modeling of jet pumps, nuclear safety analysis, and various industrial facilities that involve subcooled or two-phase pressurized fluids. This paper presents a simplified, reliable two-fluid model for accurately simulating critical flow in microchannels. This study develops a five-equation two-fluid model by constructing a mixed energy equation based on the assumption of metastable liquid phase and saturated gas phase. The model utilizes an improved metastable liquid nucleation model as the gas–liquid phase transition boundary to obtain a more accurate flashing inception. It also uses fewer interfacial constitutive relation equations to reduce the occurrence of unstable solutions. The improved nucleation model is validated using experimental data from previous researchers, with prediction errors controlled within 10%. Furthermore, the five-equation model demonstrates substantial improvements in numerical convergence compared to its six-equation counterpart. By comparing critical mass flux predictions, along-channel pressure variations, and interfacial transfer terms, the five-equation model effectively mitigates instability issues observed in the six-equation model while maintaining prediction accuracy. As a result, this model boasts a broader range of applicability and excels in accurately predicting critical flow, even under more complex conditions. [ABSTRACT FROM AUTHOR]

Highlights • Large-scale HEN synthesis is a first step towards Total Site synthesis. • Two-step MILP/MINLP approach was developed for larges-scale HEN synthesis. • Number of potential matches is significantly reduced, solutions are directed to global optima using MILP TransHEN model. • MINLP model HENSyn use reduced superstructure for HEN synthesis. • Problem with 173 process streams and multiple hot utilities solved. Abstract Although different methodologies for the synthesis of heat exchanger network (HEN) problems have been introduced in the last forty years, there are still significant challenges to be addressed, such as solving large-scale problems. This study focuses on synthesizing large-scale HENs using mathematical programming to achieve near globally optimal solutions based on a two-step MILP/MINLP approach. In the first step a mixed-integer linear programming (MILP) model, TransHEN, is used that obtains a globally optimal solution at selected Δ T min. By utilisation of this model, the most promising matches are selected based on feasibility and viability. The second step entails using the matches selected in the TransHEN of Step 1 in a mixed-integer nonlinear programming (MINLP) model, HENsyn, using a reduced superstructure, to generate a feasible HEN. This study presents also a simultaneous Total Site synthesis with direct heat transfer between processes, and is the first step in the wider project of synthesising an entire Total Site with direct and indirect heat transfer; and is the first step in the wider scope of synthesising an entire Total Site with direct and indirect heat transfer; however, in order to attain this goal, a tool capable of an appropriately handling large number of streams is required. The newly developed procedure has been tested on several case studies, two of which are presented in this paper. For Case study 1 the results obtained lie within the range of best solutions obtained by other authors. Case study 2, consisting of 173 process stream and involving multiple hot utilities, shows the applicability of the developed method to handle large-scale HEN problems. [ABSTRACT FROM AUTHOR]

The boiling flow or condensation is widely encountered in many industrial applications for both cooling as well as heating processes. Compact heat transfer devices, such as micro-heat exchangers and evaporators, are extensively used for both cooling as well as heating processes over conventional heat exchangers, such as microelectronic circuits, automobile and aerospace industries, due to high surface area to volume ratio and heat transfer rates, compactness and easy thermal control. For better design of micro- or mini-heat exchangers, a detailed specific knowledge of the multiphase flow and its properties such as the flow pattern during flow boiling, critical heat flux (CHF) and stable operation are very important. This paper provides a state of art review on boiling flow in microchannels since year 2000 till date. Flow patterns formed and the parameters influencing flow pattern transitions, during multiphase heat transfer in micro- or mini-channels, have been reviewed in detail. The flow regimes and flow pattern maps, and modeling approaches considered for boiling flow in micro-channels/devices with various challenges have been discussed. A lot of contradiction between the experimental data has been observed for the analysis of flow regimes and flow pattern maps. Further, the effect of hydrodynamics during flow boiling and CHF on heat transfer coefficient has been discussed in detail. Recently, with the advancement in measurement techniques, the heat transfer measurement technologies have been synchronized with the visualization techniques, which helped in understanding the boiling flow physics in micro- and mini-channels. Therefore, an in-depth understanding of flow patterns and regimes under boiling flow conditions in mini- and micro-channels can be used to predict the boiling heat transfer mechanism, which can be further used for developing better heat transfer models for boiling flow. Further, enhancement in heat transfer coefficient for boiling flow in microchannels, either by using complex microchannel configurations or nanocoating on the microchannel surface, have received attention recently, which have been discussed and analyzed in the present review. Both micro- and mini-channels have number of applications in aerospace, refrigeration and computational systems; therefore further attention is needed for more robust and precise design. [ABSTRACT FROM AUTHOR]

In this paper, the study of the heat exchange effect on the dynamic behaviour of single-phase natural circulation with internal heat generation is presented. In order to predict natural circulation instabilities, two different methods of analysis are developed and compared. The first approach is a linear analysis in which the governing equations are firstly linearized around a steady-state solution of the system and then treated by means of the Fourier transform. This strategy is adopted to compute, in a semi-analytical way, dimensionless stability maps for different system configurations, highlighting the heat exchange effect on the system dynamics. The second approach consists in numerically solving the nonlinear governing equations and allows investigating some transients of interest. For this purpose, an object-oriented one-dimensional model of natural circulation loops has been developed, and the corresponding results have been compared with RELAP5 and Computational Fluid-Dynamics (CFD) time-dependent simulations. The developed models have been applied to investigate the dynamic behaviour of two loop configurations characterized by large instability regions, namely the Horizontal Heater–Horizontal Cooler (HHHC) and the Vertical Heater–Horizontal Cooler (VHHC). [ABSTRACT FROM AUTHOR]

Abstract: The optimal integration of work and its interaction with heat can represent large energy savings in industrial plants. This paper introduces a new optimization model for the simultaneous synthesis of work exchange networks (WENs), with heat integration for the optimal pressure recovery of process gaseous streams. The proposed approach for the WEN synthesis is analogous to the well-known problem of synthesis of heat exchanger networks (HENs). Thus, there is work exchange between high-pressure (HP) and low-pressure (LP) streams, achieved by pressure manipulation equipment running on common axes. The model allows the use of several units of single-shaft-turbine-compressor (SSTC), as well as stand-alone compressors, turbines and valves. Helper motors and generators are used to respond to any demand and excess of energy. Moreover, between the WEN stages the streams are sent to the HEN to promote thermal recovery, aiming to enhance the work integration. A multi-stage superstructure is proposed to represent the process. The WEN superstructure is optimized in a mixed-integer nonlinear programming (MINLP) formulation and solved with the GAMS software, with the goal of minimizing the total annualized cost. Three examples are conducted to verify the accuracy of the proposed method. In all case studies, the heat integration between WEN stages is essential to improve the pressure recovery, and to reduce the total costs involved in the process. [Copyright &y& Elsevier]

Abstract: Conventional network structure modifications for retrofitting heat exchanger networks (HENs) usually require a large network superstructure, which might lead to very large scale retrofit models, and thus increases the computational difficulties of optimization, especially for industrial applications. This paper presents a novel optimization approach of retrofitting HENs for both small scale and industrial scale problems. To overcome the drawback of the existing retrofit research, a simple but efficient method is proposed to determine the network retrofit superstructure based on the concept of pinching match. Then two optimization stages (network structure optimization and investment optimization) are solved with the MILP-based iteration method that has been developed. The proposed approach has many benefits for solving HEN retrofit problems. First, smaller size of retrofit superstructure is provided based on the pinching match analysis. Second, the MILP-based iteration method developed converts conventional a mixed integer non-linear programming (MINLP) to a mixed integer linear programming (MILP), and significantly reduce the computational difficulties of nonlinear programming associated with configurational changes or structural modifications for existing heat exchanging arrangements, which is upgraded based on the MILP-based iterative method proposed by Pan et al. (2012a) for retrofitting HENs with heat transfer intensifications, as the earlier work was only applicable to the cases without network topology modification. In case studies, the new proposed approach is compared with the existing methods in two literature examples and one industrial problem, demonstrating that the new proposed approach is able to obtain better and more realistic solutions for HEN retrofitting considering the economic trade-offs between energy savings and investments. [Copyright &y& Elsevier]

Abstract: This paper presents the mathematical modeling of the ice crystallization process occurring during the freezing of sorbet in a continuous scraped surface heat exchanger (SSHE). Two different modeling approaches have been used, both of which include the nucleation, growth and breakage phenomena of the ice crystals. For both models, the rate of ice crystal nucleation and growth were determined by the subcooling degree. The first model combines heat transfer and population balance equations (PBE), assuming plug flow. The evolution of the values of product temperature, mean chord length, ice volume fraction and apparent viscosity were determined as a function of the residence time. The second model is a coupled model of heat transfer and PBE combined with an empirical model of residence time distribution (RTD), which makes it possible to take into account the fact that the fluid fractions flowing throughout the SSHE do not have the same time–temperature history. The values of the variables (product temperature and mean chord length) were determined for each fraction of fluid exiting the SSHE, and the bulk values were then calculated using the RTD. Simulation results were compared to a set of experimental data obtained during the ice crystallization process of sorbet in a continuous SSHE at the laboratory pilot scale. With a first estimated set of model parameters, it has been shown that the experimental tendencies are represented very satisfactorily by the two models within a 10% error limit. These modeling approaches can then be considered as a promising tool for the understanding and the prediction of the ice crystallization process in SSHEs so as to identify new ways to improve the performance of the process. [Copyright &y& Elsevier]

Abstract: Accurate predictions of the sulfuric acid condensation behavior on the surfaces of heat exchangers are crucial for understanding the local low-temperature corrosion characteristics of heat exchangers and designing them. In this paper, a new numerical model has been developed to predict the condensation rate of sulfuric acid and condensate acidic solution concentration on heat exchanger surfaces. By correlating the vapor–liquid equilibrium (VLE) data of H2SO4–H2O solutions from experiments and in conjunction with multi-component diffusion theory, the proposed model obtains numerical solutions of condensation heat transfer under the conditions of a coupled wall and fluid boundary condition and a multi-component mixture of flue gas and the sulfuric acid solution (saturated partial pressure of sulfuric acid and water vapor). The numerical model has been validated by a comparison of the simulation results with available experimental data, and applied to an analysis of the H-type finned tube heat exchanger, which has been widely used in the field of waste heat recovery. The distributions of the condensation rate and condensate concentration on the fin surface are also calculated. The results show that the three dimensional distribution of acid solution concentration is consistent with the fin temperature. An increase in water vapor could result in a sharp reduction of the acid solution concentration and an increase in deposition, which may indicate a serious risk for low-temperature corrosion. In contrast, increasing the flue gas temperature will reduce the corrosion risk by reducing the condensation rate and increasing the acid concentration. [Copyright &y& Elsevier]

Abstract: In this paper, the regulation problem of convection governed dynamical processes described by linear distributed parameter models with position-independent inputs is addressed by combining the method of characteristics (MC) and the Malek-Zavarei and Jamshidi theorem. In this approach, the MC is used to transform the first order partial differential equations model of such processes into a set of time-delayed ordinary differential equations whose elements are used to generate certain matrices that satisfy linear matrix inequalities that render the proportional integral (PI) control parameters that guarantee the process stability. The performance of the proposed PI controller is tested via numerical simulations in the temperature regulation of a linear heat exchanger and compared to a tightly tuned classical PI controller. The application of the proposed controller is extended to regulate the outlet concentration in a nonlinear non-isothermal plug flow reactor. It is shown that the proposed controller is able to handle the infinite dimensional nature of the process model yielding smooth and unsaturated responses around the predetermined set-point trajectory in the face of load changes, time varying boundary conditions and set-point changes. [Copyright &y& Elsevier]

Abstract: Presented in this paper are experimental test and comparison for several shell-and-tube heat exchangers, one with segmental baffles and four with helical baffles at helix angles of , , and , respectively. The results show that, based on the same shell-side flow rate, the heat transfer coefficient of the heat exchanger with helical baffles is lower than that of the heat exchanger with segmental baffles while the shell-side pressured drop of the former is even much lower than that of the later. Further enhancement techniques should be incorporated in order to enhance shell-side heat transfer based on the same flow rate. The comparison of heat transfer coefficient per unit pressure-drop (and pumping power) versus shell-side volume flow rate shows that (1) the heat exchanger with helical baffles have significant performance advantage over the heat exchanger with segmental baffles; (2) for the same shell inner diameter, the performance of heat exchanger with helical baffles with 30° helix angle is better than that of 20°, and the performance of 40° helix angle is better than that of 50° helix angle. The heat exchanger with helical baffles of 40° angle shows the best performance among the five heat exchangers tested. [Copyright &y& Elsevier]

Abstract: This paper aims to provide experimental heat transfer results for boiling of CaSO4 solutions on the outside of tube bundles, and also to shed some light into the mechanisms which influence heat transfer fouling under pool boiling conditions. Heat transfer coefficients for three heater rods with an identical diameter of 10.67mm on a 35mm vertical pitch have been measured. The independent variables bulk concentration and heat flux have been varied from 0.8 to 1.6g/L and 33 to 300kW/m2, respectively. The experimental results show that the mechanisms of fouling on the middle and top heater substantially differ from those at the bottom heater, due to the dominant effects of bubble impingement on the heat transfer surfaces. In particular, the competing effects on the degree of wall superheat and the supersaturation of the boiling liquid play a significant role. Spalling effects are more pronounced on the upper heaters where thin, friable deposits were found with low density and adherence, particularly at higher heat fluxes and lower concentrations. In terms of tube bundle efficiency, the best results were found for lower concentrations. [Copyright &y& Elsevier]