Effect Of Heat Conduction Research Articles

Temperature Variation of Rock during Deformation and Fracturing: Particle Flow Modeling Method and Mechanism Analyses

The rock deformation and failure characteristics and mechanisms are very important for stability evaluation and hazard control in rock engineering. The process of rock deformation and failure is often accompanied by temperature changes. It is of great significance to study the characteristics and mechanism of temperature variation in rock under deformation and fracturing for a better understanding of rock failure and to obtain some probable precursor information for guiding the prediction of the mechanical behavior of rock. However, most of the studies are based on observations in the field and laboratory tests, while it is still required to develop an effective method for modeling and calculating the temperature variation of rock during the deformation and failure processes. In this paper, a particle flow modeling method based on energy analyses is proposed for simulating the temperature variation of rocks, considering four temperature effects, including the thermoelastic effect, friction effect, damping effect, and heat conduction effect. The four effects are analyzed, and the theoretical equations have been provided. On this basis, the numerical model is built and calibrated according to the laboratory uniaxial compressive experiment on a marble specimen, and a comparison study has been conducted between the laboratory and numerical experiment results. It is found that the numerical model can well simulate the average value and distribution of the temperature variation of rock specimens, so this method can be applied for studying the mechanism of temperature variation more comprehensively during the whole process of rock deformation and fracturing compared with the continuous modeling methods. With this method, it is shown that the temperature change has three different stages with different characteristics during the uniaxial compression experiments. In the different stages, the different effects play different roles in temperature variation, and stress distribution and crack propagation have obvious influences on the local distribution of temperature. Further investigations have also been conducted in a series of sensitive analyses on the influences of four factors, including the thermal conductivity, friction coefficient, thermal expansion coefficient, and particle size ratio. The results show that they have different influences on the thermal and mechanical behaviors of the rock specimens during the deformation and failure process, while the thermal expansion coefficient and the particle size ratio have more significant impacts than the other two factors. These findings increase our knowledge on the characteristics and mechanism of temperature variation in rock during the deformation and fracturing process, and the proposed modeling method can be used in more studies for deformation and fracturing analyses in rock experiments and engineering.

Modeling the Thermal Performance of Anisotropic Heat Conduction Fabric with Different Structural Parameters

ABSTRACT Differences in yarn and fabric structures lead to different thermal properties of the fabric, and even the thermal comfort of the textile. The heat transfer model of the cotton woven fabric with different structural parameters was established by considering the effect of the anisotropic heat conduction of the fiber. The finite element method and experiment were combined to explore the influence of woven structure, yarn fineness, and yarn count of fabric on the heat properties of fabrics. A stronger correlation was found between experimental results and the anisotropic model than the isotropic model. Also, plain fabrics have the strongest heat transfer properties followed by twill then satin fabric. As the yarn fineness increases from 18.5 to 35.5 tex, the heat transfer property of the samples decreases. When warp/weft density goes from 260 to 330 ends/10 cm, the heat transfer capacity of the samples shows an increasing trend. The fiber volume fraction of the fabric may be an important factor that can explain the above-mentioned relationship.

Experimental study and numerical analysis of vacuum thermal characteristics of brush DC motor

Brush direct current (DC) motors have several qualities that make them very attractive for space flight applications. Considering the high reliability requirements of aerospace missions, the thermal characteristics and thermal failure of the brush DC motor in the space environment were studied. Using a motor thermal resistance network model, a special thermal test method was determined and combined with a thermal conductivity analysis model, the thermal parameters were obtained via item-by-item stripping, and the motor temperature field was constructed. By introducing the arc discharge factor to evaluate the electric-corrosion heat consumption, the numerical analysis results were in good agreement with the test results under the conditions of stalled rotor, normal rotation, single brush, and multiple brushes. The analysis and test results show that continuous operation for 110 s will lead to melting of the brush solder joints, and electrical corrosion heat consumption is one of the main factors that cannot be ignored. The reliability model of vacuum applications should be established in the normal working mode of at least two brushes in both the positive and negative electrodes. To improve the reliability, a sealed air-filled structure of the motor was proposed, a heat-flow co-simulation model of a continuous medium flow with a large curvature and constant without a gravity field was established, and the temperature and velocity fields under different sealed pressures were obtained. The results show that the temperature of the single brush reduced to below 140 °C from 204.5 °C in vacuum, which can meet the long-term continuous working requirement of high reliability of brush motors in space missions. In addition, it was found that with the decrease in pressure, the effect of convective heat transfer gradually weakens, the temperature gradually increases and converges to the unique heat conduction process of the gas, while the effect of convection is negligible. As the pressure continues to decrease, the sealed gas evolves from continuous medium flow to transitional and free molecular flow, and the heat conduction effect of the gas weakens again until it approaches the singleness solid conduction process.

The impact of random porosity distribution on the composite metal foam-phase change heat transfer for thermal energy storage

The goal of this work is to investigate the phase change material (PCM) embedded with a high thermal conductive solid structure (metal foam). In order to boost the effective heat conductivity and therefore quicken the storage process, metal foam is incorporated. The resultant storage medium is handled as a porous material. Most of earlier investigations of a similar type assumed that the medium's porosity in the porous zone is uniform. However, a random porosity is more accurate and realistic. Various sets of random structures were created using a pseudo-random generator. The mathematical formulation utilizes the Darcy-Brinkman model and volume-averaging method. The governing equations are numerically solved using the control-volume-based finite element approach. Various samples with high random porosity distributions were simulated and compared to the case of uniform porosity. The results were reported in the form of isotherms, liquid fractions, and streamlines. The outcomes revealed that a random porous medium could provide a lower rate of PCM melting (up to 10 %) for a similar average porosity compared to a uniform porous medium.

Tunable liquid–solid hybrid thermal metamaterials with a topology transition

Thermal metamaterials provide rich control of heat transport which is becoming the foundation of cutting-edge applications ranging from chip cooling to biomedical. However, due to the fundamental laws of physics, the manipulation of heat is much more constrained in conventional thermal metamaterials where effective heat conduction with Onsager reciprocity dominates. Here, through the inclusion of thermal convection and breaking the Onsager reciprocity, we unveil a regime in thermal metamaterials and transformation thermotics that goes beyond effective heat conduction. By designing a liquid-solid hybrid thermal metamaterial, we demonstrate a continuous switch from thermal cloaking to thermal concentration in one device with external tuning. Underlying such a switch is a topology transition in the virtual space of the thermotic transformation which is achieved by tuning the liquid flow via external control. These findings illustrate the extraordinary heat transport in complex multicomponent thermal metamaterials and pave the way toward an unprecedented regime of heat manipulation.

RADIATIVE AND MHD DISSIPATIVE HEAT EFFECTS ON UPPER-CONVECTED MAXWELL FLUID FLOW AND MATERIAL TIME RELAXATION OVER A PERMEABLE STRETCHED SHEET

Combined investigation of the generalized paradox of fluid flow and heat flux with upper-convected Maxwell (UCM) fluid and the Cattaneo-Christov model over a porous stretchable sheet is considered. In proffering an effective fluid flow and heat conduction, Fourier's law proved faulty. Consequently, a true estimation of non-Newtonian fluid characterizations is required due to their wide application in the biomedical science and engineering industries, among others. To these, nonlinear coupled partial differential equations (PDEs) governing the aforementioned conditions are modeled and transformed to ordinary differential equations (ODEs) using adequate similarity transformation. The solutions of these ODEs were obtained using Legendre collocation method (LCM). The results identified that a rise in geometrical inclination retards the velocity field, and an increase of the Deborah number brings about retardation in the flow fields, thus indicating a highly viscous fluid. Since fluids with high Deborah number are highly elastic, there exists flow friction, hence resulting in large heat accumulation. Therein, the material relaxation phenomenon explains that more time will be needed for successful circulation/transfer of heat from one medium to another.

Optimal design of E-type coaxial thermocouples for transient heat measurements in shock tunnels

Coaxial thermocouples have been widely used for transient heat transfer measurements in high-enthalpy shock tunnels. The one-dimensional semi-infinite heat conduction theory is typically used for temperature data processing. However, lateral heat transfer occurs due to material differences between the two electrodes and the junction, causing a deviation in the heat flux measurement from the prediction results of the one-dimensional semi-infinite heat conduction theory. Thus, the lateral heat conduction effect should be investigated to improve the accuracy and reliability of heat flux measurements. In this paper, the heat transfer in E-type (Chromel-Constantan) coaxial thermocouples was analyzed by numerically solving the two-dimensional axisymmetric heat conduction equation with the Du Fort-Frankel scheme. The maximum temperature point on the surface of the coaxial thermocouples shifted to the positive electrode during the heating process. The numerical simulation indicated that the surface temperature of the coaxial thermocouples and the derived heat flux were larger than the theoretical value. The heat flux measurement error of the coaxial thermocouples can be reduced by increasing the width of the positive electrode. Hence, 13 combinations of the diameters of positive electrode and negative electrode were designed for analysis. With the increase of positive electrode diameter or decrease of negative electrode, the heat flux measurement error kept on decreasing, which can be lower than 0.5% in some cases. The results of this study can provide a reference for the design and optimization of coaxial thermocouples.

Experimental investigation of sub-millimeter thermomagnetic pumps with temperature-sensitive magnetic fluid

• The sub-millimeter thermomagnetic pump was successfully fabricated and operated. • Temperature-sensitive magnetic fluid was used as the working fluid. • The input heat flux and channel height affect the thermomagnetic pump flow rate. • The high Prandtl number limits the pump’s flow rate while increasing channel height. • The axial heat conduction effect was observed in the sub-millimeter thermomagnetic pump. A thermomagnetic pump represents a novel pumping system that can be operated by simply heating and applying an external magnetic field. The working fluid in the thermomagnetic pump is temperature-sensitive magnetic fluid (TSMF). The magnetization of the TSMF decreases as its temperature increases. In the present study, a set of sub-millimeter thermomagnetic pumps was fabricated in microchannel systems with channel heights of 180, 290, 350, and 420 μm. A microheater was placed underneath the microchannel to control the input heat flux. A flow meter and five thermocouples were installed to examine the performance of these thermomagnetic pumps under different heating conditions. Although the flow rate increases as the height of the microchannel rise, the highest flow rate of 81.74 μl/min was achieved under the highest heating condition of 459.8 kW/m 2 and channel height of 350 μm, instead of 420 μm, due to the high Prandtl number of the TSMF.

NATURAL CONVECTION FLOW AND HEAT TRANSFER IN AN L-SHAPED CAVITY PARTIALLY FILLED WITH POROUS MEDIUM: NUMERICAL ANALYSIS

In an L-shaped cavity partially filled with a porous material, natural convection flow and heat transfer are quantitatively investigated. The effect of numerous significant parameters on isotherms, streamlines, and heat transport characteristics is investigated within the enclosure. The Rayleigh number, Darcy number, effective heat conductivity of the porous medium, aspect ratio, and thickness of the porous layer are all investigated. The governing equations are solved using the Galerkin technique with weighted residuals. The findings of this study demonstrate that an L-shaped cavity exhibits fascinating properties. As a result, as the aspect ratio of the L-shaped cavity increases, the average Nusselt number decreases. Furthermore, raising the Rayleigh number, as well as the effective thermal conductivity of porous media, improved the average Nusselt number. In the case of natural convection, the thickness of the porous layer is shown to be inconsequential.

Evaluating the Impact of Soil Enthalpy upon the Thawing Process of the Active Layer in Permafrost Regions of the Qinghai–Tibet Plateau Using CLM5.0

The hydrothermal dynamics of the active layer is a key issue in the study of surface processes in permafrost regions. Even though the soil energy budget is controlled by thermal conduction and latent heat transfer, few studies have focused on their effects upon the active layer thickness (ALT). In the present study, the community land model (CLM) version 5.0 is used to simulate the soil temperature and moisture of the active layers at the Tanggula (TGL) and Beiluhe (BLH) stations in permafrost regions of the Qinghai–Tibet Plateau based on the theory of soil enthalpy in order to estimate the soil energy state and analyze the energy changes in the active layer during freezing and thawing. The results indicate that the soil enthalpy has significant seasonal variation characteristics, which accurately reflected the freezing and thawing processes of the active layer. The change in soil enthalpy is significantly related to the thawing depth of the active layer in TGL and BLH, and its changing process can be expressed as an exponential relationship. Near the surface, the variation of the energy due to temperature gradient and actual evaporation can also be expressed as an exponential relationship. The promoting effect of heat conduction on the ALT is greater than the inhibiting effect of latent heat transfer, with the energy contribution from the phase change accounting for about 20–40% of the energy due to the temperature gradient. The thawing depth increases by 14.16–18.62 cm as the energy due to the temperature gradient increases by 1 MJ/m2 and decreases by 2.75–7.16 cm as the energy due to the phase change increases by 1 MJ/m2. Thus, the present study quantifies the effects of soil energy upon the ALT and facilitates an understanding of the hydrothermal processes in soils in permafrost regions.

Heat Flux Identification of Aircraft Structure with Artificial Neural Network Compensation

Aerodynamic heating measurement of reusable hypersonic vehicles has always been an important aspect of hypersonic vehicle design. In this paper, a mechanistic-model-based heat flux identification method with artificial neural network (ANN) compensation is established to determine the spatially distributed heat flux of the aircraft structure. A one-dimensional heat conduction model is used to estimate heat flux by a robust and efficient algorithm integrating Tikhonov regularization with Levenberg–Marquardt method. The one-dimensional estimated heat flux has large errors for not considering multidimensional heat conduction effects. The proposed mechanistic-model-based method is then utilized to compensate the multidimensional heat conduction by ANN. The performance of the proposed method will be assessed by the determination of the heat flux of a two-dimensional plate and aircraft structure. Results show that compared with the one-dimensional inversion results, ANN compensation method can significantly improve the accuracy of estimated heat flux and is also applicable for larger levels of heat flux. The proposed compensation method is an effective technique to identify the nonuniform surface heat flux of multidimensional structures.

Transient heat transfer analysis of a cracked strip irradiated by ultrafast Gaussian laser beam using dual-phase-lag theory

With the rapid development of ultrafast laser technology, the effect of non-Fourier heat conduction on the transient process has received considerable attention. In the present article, the non-Fourier dual-phase-lag heat conduction theory is adopted to analyze the transient thermal process of a cracked strip subjected to ultrafast laser heating. The originality of this work lies in considerations of Gaussian type distribution of the laser beam and the insulated crack's disturbance to the heat flow. Fourier transform and Laplace transform are utilized to reduce the complex boundary-value problems to the Cauchy-type singular integral equation, which is then solved numerically by the Lobatto-Chebyshev technique. With the aid of the numerical inversion of Laplace transform, the transient temperature characteristics of the cracked strip are displayed graphically to illustrate the effects of the two non-Fourier thermal lags, laser incident position, and the Gaussian type heating source.

The constitutive behavior and dissociation effect of hydrate-bearing sediment within a granular thermodynamic framework

Considering the energy dissipation caused by hydrate dissociation and granular rearrangement at the micro level, a multiphase constitutive model of hydrate-bearing sediment is established within a granular thermodynamic framework. This model incorporates the nonlinear expression of bonding stress into the elastic energy density function, considers the relative velocities of the gas and liquid phases in terms of the solid phase in the dissipative force system, and introduces the coupling effect of heat conduction into the migration coefficient matrix to capture the complex behavior of the sediment. Defining the migration coefficient matrix and elastic energy function, the effective stress is obtained and is suitable for constant hydrate saturation and hydrate dissociation conditions. Dilatancy equations are improved by considering the effect of compactness, bonding stress, and hydrate saturation. Meanwhile, the calculation method of bonding stress is suitable for both strong and weak cementation conditions. The deduced model is validated against the test results conducted on natural and synthetic samples under different hydrate saturations, sediment porosities, and hydrate habits and can effectively capture the strain hardening and softening as well as the dilatancy properties of the sediments and the loading path effect.

Comprehensive effects of heat and flow on the methane hydrate dissociation in porous media

The dissociation of methane hydrate in porous media is a heat flow coupling process. In this paper, we established a heat flow coupling algorithm for hydrate dissociation. A core-scale hydrate dissociation model was established and was verified against a laboratory dissociation experiment. The evolutions of the key characteristics, such as the temperature, the energy, and the hydrate/ice saturations, were analyzed. The effects of heat conductivity and permeability on dissociation characteristics and gas production rate were studied. It is found that there are three different modes under the coordinate system of heat conductivity and the permeability of porous media. In the flow-controlling mode, the rate of hydrate dissociation is mainly related to the flow resistance. In the heat-controlling mode, the rate of hydrate dissociation is mainly related to heat supply. In the heat flow-coupling mode, both the increase in the permeability and the heat supply have positive effects on the increase in the hydrate dissociation rate. In addition, there are different hydrate dissociation front expanding characteristics for the different modes. This analysis of the dissociation mode improves the understanding of events associated with the hydrate dissociation process.

Patternable thermal conductive interface materials enabled by vitrimeric phase change materials

Thermal interface materials (TIMs) with mechanical integrity and interfacial adaptability over rough surfaces without applying high pressure to the sandwiched thermal interfaces are challenging. Herein, patternable thermal conductive interface materials enabled by vitrimeric phase change materials (PCMs) for reconfigurable package procedures and reduction in thermal contact resistance are proposed. The incorporated dynamic crosslinked network in paraffin wax/polyolefin elastomer (PW/POE) PCMs forms a robust 3D supporting skeleton, giving rise to the PCMs with mechanical integrity even when POE is melted. Lowered modulus by solid–liquid phase change of PW and activated exchange of dynamic covalent bonds when POE is melted allow for reconfigurable package procedures by plastic deformation with small stress. Hybrid fillers with different sizes and dimensions form effective heat conduction pathways in the vitrimeric PW/POE PCMs. Notably, the resulting composites can still conformally adapt to the rough surfaces of the heat sink and heat source at 80 °C and 13 KPa, resulting in an interlocked structure, which can essentially reduce the thermal contact resistance and promote thermal transport. The prepared composites as TIM demonstrate better heat dissipation performance than the commercial thermal pad. The strategy of vitrimeric PCMs combines mechanical integrity and thermally triggered interfacial adaptability through reconfigurable package procedures, providing inspiration for the bulk compliance of TIMs that can adapt to rough surfaces.

Modeling of Phase Change in Nanoconfinement Using Moment Methods

Abstract Accurate prediction of liquid–vapor phase change phenomena is critical in the design of thin vapor chambers and microheat pipes for the thermal management of miniaturized electronic systems. In view of this, we have considered the heat and mass transfer between two-liquid meniscuses separated by a thin gap of its own vapor. Assuming the heat and mass flow are to be steady and one-dimensional, analytic solutions are obtained to the linearized equations from the regularized 26-moment framework. Our analytic solutions provide excellent predictions for the effective heat conductivity of a dilute gas with those from the molecular dynamics (MD) and Boltzmann equation where Fourier's law fails. We also verified that the predicted heat and mass flow rates over the whole range of the Knudsen number are consistent with the kinetic theory of gases. Further, the model has been used to predict the effect of evaporation and accommodation coefficients on the heat and mass transfer between the liquid layers.

Global sensitivity analysis and optimal design of heat recovery ventilation for zero emission buildings

Energy-efficient building services are necessary to realise zero-emission buildings while maintaining adequate indoor environmental quality. As the share of ventilation heating needs grow in well-insulated and airtight buildings, heat recovery in mechanical ventilation systems is increasingly common. Ventilation heat recovery is one of the most efficient and viable means to reduce ventilation heat losses and save energy. Highly efficient heat exchangers are being developed or applied to maximise the energy-saving potential of heat recovery ventilation. Nevertheless, the effects of practical operating conditions and the constraints of heat recovery – such as variations in ventilation rates, frost protection, and the prevention of an overheated air supply over a long-term period, which may significantly influence realistic recovery rates – have been less considered in efforts to maximise the energy savings. It is unclear which design parameters for heat recovery devices have the greatest effect on the annual energy savings from ventilation.This study proposes annual efficiency and annual net energy saving models for heat recovery ventilation that consider ventilation rate variations, the longitudinal heat conduction effect and operating controls. We use a global sensitivity analysis to quantify the contributions of various design input parameters to the variation in annual recovery efficiency and annual net energy savings. We identify the most influential parameters and their significant interaction effects for the annual energy performance of heat recovery ventilation. More attention should be paid to these most influential parameters during the design process. Furthermore, the optimal designs for rotary heat exchangers (as identified by a pattern-search optimisation algorithm) can improve annual net energy savings in demand-controlled ventilation by 33–48%, depending on the building areas. In combination with the reference year analysis presented in this study, heat recovery and demand-controlled ventilation can help to meet the need for highly efficient ventilation systems and zero-emission buildings.

Thermoelastic damping and frequency shift in micro/nano-ring resonators considering the nonlocal single-phase-lag effect in the thermal field

Estimating thermoelastic damping (TED) and frequency shift with sufficient accuracy is of importance for the quality factor prediction of micro/nano-resonators operating in certain special cases containing the ultra-high frequency excitation and the ultra-instantaneous thermal heating etc. At the design stage before the engineering application of micro/nano-resonators, the mathematical modelling of the frequency-shift ratio and TED gets challenging when considering the non-Fourier effect and size-dependent effect in the thermal field. In this paper, one/two-dimensional (1D/2D) analytical formulations of frequency-shift ratio and TED for micro/nano-ring resonators are firstly developed by adopting the nonlocal single-phase-lag (SPL) model. Basing on the present proposed models, the nonlocal thermal-relaxation time τN is firstly introduced in terms of the nonlocal thermal-length lQ and the thermal diffusion coefficient χ. In simulation cases, the typical semiconductor material silicon is selected, the SPL time τQ is computed basing on the second sound, and lQ refers to the mean-free path of energy carriers. The convergence performance of the proposed models is analyzed. Meanwhile, the results of existed TED models for rings are presented for comparison. The impacts of the nonlocal-SPL effect on the TED spectrum and fluctuation temperature are examined emphatically. And the peak phenomenon of TED spectrum characterized by the peak damping, the equivalent relaxation time associated with the peak frequency, and the frequency-shift ratio are explored. Results demonstrate that the thermo-dynamical behaviors of micro/nano-ring resonators are conjunctively determined by the amount relationship of τQ, τN, and the thermal relaxation time. Especially, when the radial thickness of the ring operating at ultra-high frequencies is comparable to lQ, the nonlocal-SPL effect of heat conduction should be considered to estimate the frequency-shift ratio and TED.

Thermodynamic characteristics of counter flow and cross flow plate fin heat exchanger based on distributed parameter model

The distributed parameter models of counter flow and cross flow plate fin heat exchanger (PFHE) are constructed to investigate their thermodynamic characteristics. In practical application, the cold end of PFHE may be directly connected to the cold equipment. Therefore, the effect of longitudinal heat conduction (LHC) under different thermal boundary conditions set on two ends of the separating plates (SPs) is investigated based on the model of counter flow PFHE. It is found that LHC effect transmits the effect of boundary condition on two ends of the SPs into the inner domain of PFHE. The LHC effect on the heat transfer performance of PFHE is positive when setting appropriate boundary condition on two ends of the SPs. When considering LHC, compared with the adiabatic boundary conditions on two ends of the SPs, the effectiveness of constant wall temperature boundary conditions increases by 31.7 ∼ 35.8 %, and the effectiveness of constant heat flux boundary conditions increases by 22.8 %. The model of cross flow PFHE is used to investigate the effect of configuration and operation parameters on the heat transfer amount and the pump power. The cross flow PFHE is optimized to arrive at the maximization of heat transfer amount per unit pump power (HTPUP). In the three-stream cross flow PFHE studied, the heat transfer amount almost doesn’t change when the xz projected area is maintained and one projected length (z side length) is changing. The pump power is the lowest and the HTPUP is the largest when z side length of PFHE (z side is the flow direction of the fluid with large mass flowrate) is 0.15 ∼ 0.2 m.

Experimental study on regenerative effectiveness and flow characteristics of parallel-plate regenerator in Stirling engine

Regenerator is the critical component of the Stirling engine. Its performance directly affects the efficiency of the whole engine. The heat transfer and flow characteristics of the parallel-plate regenerator (PPR) are experimentally investigated, and the influences of material and geometric parameters on regenerative effectiveness and pressure drop are obtained. The results show that the axial heat conduction will reduce the regenerative effectiveness of the PPR. The higher the thermal conductivity of the plate, the lower the regenerative effectiveness. Larger plate thickness and smaller plate length will also increase the axial heat conduction loss. The PPR shows good flow characteristics. The comparative experiment with the wire mesh regenerator shows that its friction coefficient is much lower than that of the wire mesh regenerator. Through the comprehensive index NPH/NTU defined as the ratio of number of pressure heads (NPH) to number of transfer units (NTU), the overall performances of PPR and wire mesh regenerator are compared. The results show that the PPR has better working performance. To reduce the adverse effect of axial heat conduction on the PPR, the optimization experiment was carried out by segmenting the regenerator into several sections. The results show that the regenerative effectiveness of the segmented PPR is increased by 20%, while the increase of pressure drop is within an acceptable range.