Axial Heat Conduction Research Articles

Frequency-domain axisymmetric and thermomechanical viscoelastic analysis of thermoplastic composite pipe

ABSTRACT Thermoplastic composite pipe (TCP), composed of polymers and composite laminates, shows significant potential for deep-water offshore oil field development due to its lightweight and high strength. However, current mechanical studies primarily focus on the elastic domain, ignoring the critical viscoelasticity of non-metallic materials. To solve this, we introduce a comprehensive theoretical model that incorporates viscoelastic properties under both axisymmetric and thermal loads, considering radial convective thermal gradients and axial heat conduction. This model accurately predicts TCP's mechanical behavior by using stiffness coefficients, differential geometry, and radial-axial temperature transfer curves. By applying the principle of elastic-viscoelastic correspondence, we obtain viscoelastic solutions in the frequency domain, showing strong agreement with Finite Element (FE) models particularly under cyclic loading. Viscoelasticity introduces larger equivalent axial stiffness and viscoelastic damping within complex structures, which become more obvious with temperature fluctuations.

Orbit-attitude-structure-thermal coupled modelling method for large space structures in unified meshes

Large space structures would exhibit orbit-attitude-structure-thermal coupled effects in complicated space environment. Thus, a new thermal-structure coupled modelling method is proposed using gradient-deficient absolute nodal coordinate formulation beam elements. Compared to the previous methods, both axial and circumferential heat conduction are considered. The cubic interpolation in temperature field instead of the linear interpolation is adopted to obtain a unified-mesh temperature-displacement description. The gravitational force and gravity gradient are modelled, and the effects of attitude motion and structural deformation on solar radiation intensity are considered. In addition, three kinds of quasi-static thermal-structure coupled models are proposed based on Euler-Bernoulli beam theory. Based on the quasi-static models, the theoretical formulas are derived to effectively predict the thermally induced vibrations of the beam in space. Four numerical examples are studied to validate the proposed models, including the heat conduction examples with three boundary conditions and a thermal-structure coupled cantilever beam example. Based on the proposed formulation, the orbit-attitude-structure-thermal coupled dynamics of a multibody system consisted of a rigid body and a large flexible appendage is investigated considering the gravity gradient, solar radiation, Earth's shadow, and self-shadow.

Flame-retardant wire burning behavior by jet flame heating: Ignition, charring, and secondary flame spread

This research presents an in-depth examination of the combustion characteristics of flame-retardant electrical wires, contrasting behavior with non-flame-retardant counterparts under jet flame heating. The study systematically investigates the pyrolysis process, ignition patterns, charring behavior, and the development of secondary flames in wires with different core diameters and insulation materials. Findings indicate the heightened susceptibility of thinner wires to rapid heating, pyrolysis and charring, leading to faster ignition and more intense secondary flame development. This insight is crucial for tailoring flame-retardant formulations to specific wire dimensions. The research also delves into the thermal dynamics within the wires, highlighting how the core diameter influences axial heat conduction and, consequently, the overall flame spread behavior and pyrolysis rate. A critical discovery is the relationship between heating duration and flame sustainability, establishing a specific range of heating times for sustaining secondary flames in flame-retardant wires. Theoretical models used in the study explained the critical heat flux heating time for wire ignition, offering insights into improved fire prevention strategies, particularly in prolonged heat exposure scenarios. These findings not only advance our understanding of flame-retardant wire behavior under fire conditions but also provide guidance for selecting and using electrical wires, thereby optimizing fire safety in diverse applications.

Establishment and analysis of a piezoelectric actuator dynamic model with temperature-dependent damping, stiffness, and piezoelectric constant

The characteristics of the piezo-stack and the flexible mechanism are both influenced by temperature, which induces the performance change of piezoelectric actuators in low-temperature. This study investigates how temperature affects the dynamics model's stiffness, damping, driving force, and friction. An axial heat conduction model based on Fourier's heat conduction law was established, and finite element analysis was carried out to study the temperature distribution of the piezo-stack. Moreover, finite element analysis was carried out at various temperatures to investigate the impact of temperature on the flexible mechanism's deformation. Based on the aforementioned study, a dynamics model with variable stiffness and damping is proposed in this paper, and the simulation results are verified. In the experiment, the effects of temperature, voltage, and frequency on the output performance of the piezoelectric actuator were investigated separately using impedance and amplitude-frequency characteristic curves to determine the resonant frequency and damping ratio of the flexible mechanism at low temperatures. Theory and experiment show that high stiffness and low piezoelectric constants at low temperatures reduce the piezoelectric actuator's output displacement, friction reduction will enhance the driving displacement of the piezoelectric actuator, and the effect of damping on output displacement is insignificant. This study offers significant theoretical value and guidance for the use of piezoelectric actuators in low-temperature situations.

Comprehensive analysis method of acquiring wall heat fluxes in rotating detonation combustors

Accurate perception of the combustor thermal environment is crucial for thermal protection design of a rotating detonation combustor (RDC). In this study, a comprehensive analysis method is established to calculate the non-uniform heat flux distribution of the RDC by utilizing the measured temperature distribution of the combustor outer wall obtained by the high-speed infrared thermal imager. Firstly, a physical model based on the geometric characteristics of the RDC is constructed and its thermal conductive process is simulated, given by different heat flux boundary conditions. The analysis results indicate that the method used in current research for computing the heat flux of RDC leads to significant discrepancies, particularly in regions of obvious axial heat flux gradients near the top of the combustor. Then the Levenberg-Marquardt (L-M) method for inversely solving non-uniform heat flux is developed based on the two-dimensional heat conduction equation, and the wall heat fluxes are inversely calculated by the L-M method based on the above numerical data. Results show that the L-M method can obtain more accurate heat flux distribution even in the zones with large heat flux gradients, considering the axial heat conduction within the combustor outer wall caused by the non-uniform heat flux. Finally, the wall heat flux distribution is analyzed coupling the L-M method together with the experimental measurements in kerosene two-phase RDC. The analyses show that the wall heat flux exhibits non-uniform distributions both circumferentially and axially, with axial non-uniformity being particularly pronounced. The highest temperature of combustor outer surface and the highest wall heat flux occurs within the region of 20 mm from the combustor head, which corresponds to nearly 14 % of the combustor length. The heat flux peak and thermal heat rate are positively correlated with the combustor equivalence ratio in the range between 0.44 and 0.64. In this study, the distribution of wall temperature field in the two-phase RDC is obtained for the first time and the wall heat flux is calculated inversely by L-M method. This work provides a more accurate method for calculating heat flux in RDC and offers references for thermal protection designs in RDCs.

Modeling of quenching temperature with the effects of axial conduction resulting from quench front propagation

Efficient quenching of fuel rods in a post-critical heat flux (post-CHF) film boiling environment is of utmost importance to maintain the nuclear fuel integrity. In the event of a loss of coolant accident (LOCA) in light water reactors, the ability to quench the fuel element surface is crucial to not compromise the core coolability. Many studies over the past several decades have indicated a dependence of the minimum film boiling temperature (Tmin) on system factors such as pressure and subcooling as well as local factors like surface properties. However, recent quenching analysis using high-resolution optical fiber sensors have indicated a substantial axial heat conduction present at the quenching front, which has the potential to change the local quenching temperature by a significant margin. In this paper, this axial conduction effect is investigated and applied to a previous Tmin model. A new semi-empirical model which considers distance from initial rewetting point as well as rod diameter is proposed using the optical fiber quenching data. This correlation assumes an initial rewetting temperature which initiates the quenching front propagation, and predicts the temperature drop locally due to ongoing film boiling beyond the quench front as well as heat conduction across the cladding from the significant axial temperature gradient. By doing so, this new correlation provides a significant improvement on earlier Tmin models by accounting for this temperature variation which has previously not been considered.

Convective Heat Transfer and Entropy Generation Analysis in Elliptic Microchannels

Abstract In this paper, we investigate analytically the first and the second law characteristics of fully developed gaseous slip flow with the H1 boundary condition through elliptical microchannels. The closed-form solution of temperature distribution was obtained with the separation of variables method. Expressions for the Nusselt number, the nondimensional entropy generation rate, and the Bejan number were further deduced. The influences of crucial factors, including viscous dissipation, rarefaction, aspect ratio, and fluid axial heat conduction, have been carefully evaluated. The results indicated that viscous dissipation has a dramatic impact on heat transfer characteristics. But the rarefaction effect was found to significantly reduce the effect of the viscous dissipation on the Nusselt number, and the former may not deteriorate the heat transfer performance when considering the viscous dissipation. The main source of the entropy generation rate is controlled by fluid axial heat conduction when the Peclet number is less than one. The impacts of the viscous dissipation, the rarefaction, and the aspect ratio on entropy generation are magnified when fluid axial conduction dominates the irreversibility. The analytical solutions of the current study will make it possible to compare, evaluate, and optimize alternative elliptical microchannel heat exchanger design options.

Influence of the Main Working Parameters and Geometrical Parameters on the Supercritical CO2 Flow Instability in a Heated Tube

Supercritical CO2 (sCO2) flow instability is an issue that must be considered in the reasonable design of sCO2 boiler. Because it can cause equipment vibration and heat transfer deterioration. In this article, a numerical model for the sCO2 flow instability in the single tube was developed. Different from the traditional model, the effects of metal heat storage and axial heat conduction in the tube wall were considered. The influence of main parameters on trans-pseudo-critical number (N TPC) and oscillation period (t 0) was studied, with the tube length (L) from 3 to 11 m and the inner diameter (D in) from 10 to 22 mm. N TPC increases with increasing the inlet pressure (P in), mass flux (G), inclination angle (α), and the inlet local resistance coefficient (K in). N TPC decreases with D in and outlet local resistance coefficient (K out). The effects of the sub-pseudo-critical number (N SUBPC), wall thickness (WT) and L on N TPC are nonlinear. With increasing N SUBPC, WT, L, D in, and K out, t 0 increase. As G, α, and K in increase, t 0 becomes smaller. When N SUBPC is lower than 0.9146, t 0 rises with P in increasing. It is opposite with N SUBPC higher than 0.9146.

Numerical modeling and experimental verification for anisotropic heat conduction process in velocity probe of the thermal mass flowmeter

Traditional models ignore the temperature gradients caused by anisotropic heat conduction process in the axial and radial directions of the velocity probe of a thermal mass flowmeter (TMF), essentially assuming constant wall temperature. Recently, a novel TMF with a large length–diameter ratio of the velocity probe and more evident temperature gradient was proposed; although this novel TMF is insensitive to the radial velocity profile, it leads to significant calculation errors. To reduce the error of this TMF, this study proposes a numerical model of pipeline flow heat transfer that considers the axial and radial heat conduction of the velocity probe. The velocity probe axial heat conduction numerical model is proposed, and the results of apparent thermal conductivity are verified using empirical formulas. A feedback adjustment convergence program is performed to maintain the average temperature of the velocity probe at 10 K above the temperature of the observed fluid. The simulation results showed that a temperature gradient forms in both the axial and radial directions of the velocity probe of the improved model. Moreover, the higher the flow velocity and the farther it is from its central axis, the lower the temperature. Experimental results revealed that, at a velocity rang of 1.0–7.0 m/s, the average relative error between the improved simulated results and current experimental data is 2.92 % and the maximum relative error is 10.91 %, whereas the average relative error between the traditional simulated results and original experimental data is 7.44 % and the maximum relative error is 19.45 %. Thus, the improved model better simulates the real process.

Avoiding false runaway prediction by properly describing axial conductive heat transfer in a low dt/dp industrial-scale packed bed reactor

The impact of axial conductive heat transfer on the simulation and prediction of hot spots and, more particularly, runaway, within an industrial-scale wall-cooled packed-bed reactor with low tube-to-particle diameter ratio (dt/dp ∼ 3) has been assessed in this work. To this purpose, the effective axial conductivity (keff,z) was first determined from adiabatic experiments in a bench-scale packed bed in the absence of reaction. Next, non-adiabatic and non-isothermal bench-scale and industrial-scale packed bed experimental data were used in the assessment of the impact of axial heat conduction on the prediction of the temperature profile. The so-called Pseudo-local Internal Heat Transfer Approach (PL-IHTA) was used for the adequate description of the radial temperature gradients. Finally, an industrial-scale wall-cooled packed bed reactor for the highly exothermic catalytic oxidative dehydrogenation of ethane was modeled to assess the impact of the axial thermal conductivity on temperature profile simulations. When disregarding axial heat conduction or adopting literature-based values for keff,z, determined from either experiments at low dt/dp ratios (<8) and Rep ≤ 1000 or high dt/dp ratios (>8) and Rep ≤ 700 at a wide panel of operating configurations, runaway is simulated at conditions where it has not been observed experimentally or a negligible hot-spot prediction is obtained. When considering the keff,z determined for the specific reactor configuration in this work, hot spots are predicted at Rep of 700 and 1400, but no runaway. The discrepancies between experimental findings and temperature profiles simulated using literature-based values for keff,z indicate the need for a specific determination of keff,z in packed bed reactors with low dt/dp ratio to more accurately predict hot spots, resulting in more reliable reactor design and operation.

Dynamic performance analysis of the discharging process of a solar aided liquid air energy storage system

As a clean and high energy density large-scale energy storage technology, liquid air energy storage (LAES) has great development prospects. Among various LAES technologies, solar aided liquid air energy storage (SALAES) is becoming a hotspot for its cleanness and high efficiency, but its dynamic performance characteristics have not yet been revealed. In this paper, the dynamic model and control systems of the discharging process of an SALAES system considering the metal thermal inertia and axial heat conduction are established and two different start-up methods, rated parameter start-up and variable parameter start-up, are proposed and compared. Meanwhile, a parabolic trough collector control strategy with fixed outlet fluid temperature is designed to avoid DNI fluctuations that greatly affect the system's operation. Furthermore, off-design start-ups and predictable molten salt-air heat exchangers trip due to the lack of solar energy caused by continuous bad weather are noted and analyzed. Research results show that the variable parameter start-up is faster and more stable, in which the heat exchange time of two evaporators is about 895 s, the rotor speed stability time is about 12–15 s, and the load stability time is about 75–80 s. The required air quantity for the design condition start-up is 6.84 tons and will rise to 9.02 tons for the off-design start-up. The response times for the unit load to decrease from the rated value to different levels (taking 75 %, 50 %, and 25 % of the rated load as examples) are around 15–20 s, and for the trip of salt-air heat exchangers, the response time is about 20–25 s, resulting in a load fluctuation from 85.5 % to 103.6 %. The research results of this study can guide the dynamic operation of the SALAES system.

Viscous Dissipation and Fluid Axial Heat Conduction Effect on the Heat Transfer to a Laminar Non-Newtonian Fluid Flow in Cylindrical Annular Duct with an Axially Moving Core

Viscous Dissipation and Fluid Axial Heat Conduction Effect on the Heat Transfer to a Laminar Non-Newtonian Fluid Flow in Cylindrical Annular Duct with an Axially Moving Core

A Review of the Complex Flow and Heat Transfer Characteristics in Microchannels.

Continuously improving heat transfer efficiency is one of the important goals in the field of energy. Compact heat exchangers characterized by microscale flow and heat transfer have successfully provided solutions for this purpose. However, as the characteristic scale of the channels decreases, the flow and heat transfer characteristics may differ from those at the conventional scale. When considering the influence of scale effects and changes in special fluid properties, the flow and heat transfer process becomes more complex. The conclusions of the relevant studies have not been unified, and there are even disagreements on some aspects. Therefore, further research is needed to obtain a sufficient understanding of flow structure and heat transfer mechanisms in microchannels. This article systematically reviews the research about microscale flow and heat transfer, focusing on the flow and heat transfer mechanisms in microchannels, which is elaborated in the following two perspectives: one is the microscale single-phase flow and heat transfer that only considers the influence of scale effects, the other is the special heat transfer phenomena brought about by the coupling of microscale flow with special fluids (fluid with phase change (pseudophase change)). The microscale flow and heat transfer mechanisms under the influence of multiple factors, including scale effects (such as rarefaction, surface roughness, axial heat conduction, and compressibility) and special fluids, are investigated, which can meet the specific needs for the design of various microscale heat exchangers.

End‐winding wire‐insulation heat conduction model for precise thermal predictions of permanent magnet synchronous machines

AbstractAccurate thermal calculations of end‐winding temperature rises are the key issue in designing and developing cooling systems of permanent magnet synchronous machines (PMSMs). Due to the complex connections of the end‐windings, it is challenging to precisely predict the heat dissipation capacities through a traditional wire‐insulation equivalent model. Numerical simulations and lumped parameter thermal networks (LPTN) are used by the authors to develop thermal models that illustrate the end‐winding properties of a 2.1‐kW PMSM. As multi‐strand end wires are bent and bound together by ribbons, they have thermal interrelations which can hardly be considered in LPTN models. An equivalent coefficient enhancing the axial heat conduction capacities of end‐windings is proposed for LPTN calculations to model the aforementioned thermal interrelations with circumferential symmetric structures. To correctly model the mutual thermal coupling between various strands of end‐windings, the thermal conductivity of the equivalent insulation sheets between the multi‐strand end‐windings is determined for exact numerical calculations. The external insulation sheet thickness is calculated based on the equivalent thermal conductivity. After developing heat conduction models for LPTN and numerical simulations, LPTN and FEA are used to determine the PMSM's temperature rise characteristics. To verify the approaches, the computation findings are contrasted with experimental ones.

Multi-Objective Optimization of a Bi-Metal High-Temperature Recuperator for Application in Concentrating Solar Power

Abstract Supercritical CO2 closed Brayton cycles are a major candidate for future power cycle designs in concentrating solar power applications, with high-temperature recuperators playing an essential role in realizing their high thermal efficiency. Printed circuit heat exchangers (PCHEs) are often chosen for this role due to their thermal-hydraulic and mechanical performance at high temperatures and pressures, all while remaining compact. However, PCHEs can be costly because of the high-performance materials demanded in these applications, and the heat exchanger internal geometry is restricted by their manufacturing process. Additively manufactured heat exchangers can address both of these shortcomings. This work proposes a modular bi-metal high-temperature recuperator with integrated headers to be produced with additive manufacturing. Beginning with existing PCHE channel geometries, a 1D heat exchanger model is developed. Then, multi-objective optimization is used to maximize the heat transfer effectiveness of a lab-scale device while limiting its size. Two distinct channel geometries emerge from the optimization. Optimal designs achieve up to 88% effectiveness with negligible pressure drop. Deterioration of effectiveness due to axial conduction of heat in the heat exchanger walls is found to be a notable problem for lab-scale PCHEs, and the optimal designs obtained here minimize its detrimental effects. A sensitivity analysis reveals that the effectiveness of the recuperator is much less sensitive to variation in mass flowrate in off-design operation when axial conduction is significant, while increasing the length of the device easily increases effectiveness.

Highly reliable measurement of temperature fluctuation in near-wall turbulence by a sophisticated cold-wire technique for considering the frequency response and spatial resolution

In turbulence measurement of the thermal field in a non-isothermal turbulent boundary layer, it is necessary to use a small-scale temperature sensor that can provide high spatial resolution. Thus, a fine-wire temperature sensor commonly called “cold-wire” is indispensable for capturing small-scale temperature fluctuations near the wall. However, the length-to-diameter ratio of the cold-wire need generally exceed 1000 to minimize the deterioration in dynamic response due mainly to the axial heat conduction of the thin-wire sensor. To meet such a conflicting requirement, the wire diameter of the cold-wire must be extremely thin. In the present study, we have tested experimentally the performance of several cold-wires of different geometrical features, and examined the effects of the temporal and spatial resolutions of the cold-wire on the temperature fluctuation measurements—root-mean-square (rms) values and instantaneous signal traces—in a canonical turbulent thermal boundary layer. As a result, it was found that the previously-reported response compensation technique for the cold-wire outputs enables us to realize sufficiently accurate temperature fluctuation measurement in the immediate vicinity of the wall while avoiding the deterioration in the spatial resolution of the cold-wire. Furthermore, to improve the spatial resolution of the cold-wire probe, we propose a novel temperature sensor consisting of a fine tungsten wire bent at its center to make an apex angle less than about 30 degrees and have named this sensor a “V-shaped” cold-wire. We have verified its measurement performance in reference to the results obtained by a standard cold-wire probe. As a result, it is shown that the V-shaped cold-wire naturally provides high spatial resolution especially for temperature fluctuation measurement near the wall and can take full advantage of the response compensation technique for the normal cold-wire probe.

Effect of thermal dispersion and turbulent conduction on the heat transfer behavior of coaxial pulse tube cryocooler

In this article, a numerical analysis is conducted for a miniature coaxial pulse tube cryocooler including the effect of an axial conduction enhanced term. This term is a representative of supplementary energy loss, which happens because of turbulent conduction, mixing, and thermal dispersion. The complex physical domain of cryocooler is modeled intelligently in one-dimensional model by splitting the total computational domain into two subsections. The individual subsections of the cryocooler have been discretized into a number of small control volumes. Both subsections are merged together to make a complete computational domain for the cryocooler. The conservative form of the nonlinear, coupled partial differential equations demonstrating its heat and fluid flow aspects have been discretized into algebraic equations by utilizing the finite volume technique. Final discretized algebraic equations have been solved iteratively to predict its heat and fluid flow behaviors. Suitable relaxation factors have been incorporated to accelerate the convergence of the simulation. Moreover, the variation of mean cyclic energy, enthalpy, and exergy flow have been visualized along its physical domain with and without fluid axial conduction enhancement loss processes. Influences of different length of inertance tube, outer to inner radius ratio of annular passage, and length to radius ratio of pulse tube on no-load temperature is studied for with and without fluid axial conduction heat loss.

NUMERICAL STUDY ON FLOW AND HEAT TRANSFER PERFORMANCE OF A NOVEL MULTILAYER MINI-CHANNEL HEAT EXCHANGER WITH LOW AXIAL HEAT CONDUCTION

The printed circuit heat exchanger is a typical representative of mini-channel heat exchangers, which are generally applied in many advanced energy and power systems due to their high compactness and efficiency. However, axial heat conduction may significantly decrease efficiency at low mass flow rates, and few studies have focused on enhancing the performance of heat exchangers by reducing axial heat conduction. This study proposes a novel multilayer mini-channel heat exchanger to solve this problem. The axial heat conduction of the new design is reduced by inserting phlogopite layers into the metal sections. The thermal-hydraulic performance of the novel multilayer mini-channel heat exchanger is investigated at different numbers of segments and different mass flow rates using Fluent. The results show that, at low mass flow rate, the performance of the multilayer heat exchanger is superior to that of a traditional heat exchanger. With the increase of heat exchanger segments, the performance of the multilayer heat exchanger is improved. The maximum relative increment in the new heat exchanger efficiency is 1.6&amp;#37;, and the pressure drop is relatively reduced by 12.3&amp;#37;. The difference in performance between the multilayer heat exchanger and the traditional heat exchanger decreases when increasing the mass flow rate. It is recommended that more segments of multilayer heat exchanger should be used for lower mass flow rates to achieve better performance.

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.

Modeling on cryogenic heat exchangers considering variable properties, axial heat conduction and viscous heating

Cryogenic heat exchangers are key components of low temperature refrigerators and determine the ultimate refrigeration performance. Accurate modeling on the cryogenic heat exchangers in sub-Kelvin regime has important theoretical and applied values, yet is still short of study. This study proposes local thermal nonequilibrium models of the heat exchangers in sub-Kelvin regime, including continuous and discrete ones. The effects of the variable properties, axial heat conduction, and viscous heating were investigated. The finite volume method was employed to solve the models numerically; in addition, the temperature and pressure distributions were obtained and analyzed. The proposed models were validated using a comparison of the obtained simulation results with experimental results in the literature. The analysis of the obtained results revealed that: (1) for continuous heat exchangers, the variable Kapitza thermal conductance leads to a large temperature gradient at the entrance. The outlet temperature was negligibly affected by applying different inlet temperature. (2) The axial heat conduction significantly degrades the performance of discrete heat exchangers. The performance was found to be limited by the axial heat conduction when the axial heat conduction parameter was larger than 0.02. (3) For the sintered heat exchanger, both the dimensionless temperature and pressure drop are obviously affected by the geometric impedance when it is greater than 4 × 1014 m−4. Consequently, the proposed mathematical models are useful for the accurate prediction and optimization of cryogenic heat exchangers.