Effect Of Axial Heat Conduction Research Articles

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.

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

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.

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.

Effect analysis on thermohydraulic characteristics of microchannel direct liquid cooling under swing condition

In this paper, the thermohydraulic characteristics of direct liquid cooling in rectangular microchannels were studied under swing condition. Deionized water was used as the coolant. The effects of coolant flow rate, coolant inlet temperature, microchannel equivalent diameter and heating power on the thermohydraulic performances were studied. In addition, the wall temperature uniformity and axial heat conduction effect were discussed. Furthermore, the influence of swing speed on the performances of microchannel direct liquid cooling was studied. The performance factor was defined to evaluate the microchannel comprehensive thermohydraulic performance. The results show that the transition Reynolds number of microchannels with equivalent diameters of 0.9–1.6 mm is between 500 and 2000. The wall temperature uniformity is improved with the increase of coolant flow and the decrease of coolant inlet temperature. The axial heat conduction demonstrates a great influence on the microchannels, which accounts for about 40%-50% to the total heat. With the increase of swing speed, the drag coefficient decreases slowly within 4%. Meanwhile, the flow rate should be in 0.14–0.2 L/min to obtain an optimal effect of the performance factor.

Influence of axial heat conduction in solid walls and fins on the overall thermal performance of an additively manufactured high-temperature heat exchanger

Due to the increasing use of high-temperature processes in mobile applications, the demand for compact and efficient high-temperature heat exchangers continues to rise. However, with increasingly reduced installation space, the parasitic effect of axial heat conduction in the wall material of the heat exchanger is also gaining considerable influence. In this manuscript, the influence of axial heat conduction in the wall and fin material on the thermal performance of an additively manufactured high temperature heat exchanger is to be examined. For this purpose, an analytical calculation model as well as the analytical solution method is presented and successfully validated by means of experimentally recorded measurement data of an additively manufactured heat exchanger, which was tested at temperatures up to 750 °C. Subsequently, the calculation programme is used to determine the influence of the axial heat conduction on the effectiveness as well as on the NTU value of an additively manufactured Plate-Fin heat exchanger. The results show a drop in the NTU value of up to 50% at balanced flow compared to the case without heat conduction, which reduces the effectiveness and thus the performance of the heat exchanger by up to 5.5%.

Probing the Accuracy of Experimental Data on Nusselt Numbers Within Miniature Heat Sinks

Abstract Achieving accurate experimental data in conjugate heat transfer studies to calculate Nusselt number can be challenging due to its complex three-dimensional thermal hydraulics nature. This study is devoted to evaluating the accuracy and reliability of experimental approaches used to calculate the Nusselt number in miniature heat sinks. It is observed that three major parameters including (1) axial heat conduction within the solid substrate of heat sinks, (2) thermal contact resistance, and (3) assumed uniform wall temperature, as well as wall heat flux distributions, influence the reported experimental data in the literature. The results obtained from the developed analytical and computational models in this study revealed that the assumptions of local uniform wall temperature and heat flux distributions for small-scale heat sinks result in underestimated Nusselt numbers calculated from experiments. At lower Reynolds number (<200) flows in miniature heat sinks with a high solid to fluid thermal conductivity ratio (>> 1), it is shown that the fluid bulk temperature should be measured away from the heat sink inlet and outlet to minimize the effect of axial heat conduction within the solid substrate of the microscale heat sinks on calculated Nusselt numbers. As the third important parameter, the influence of thermal contact resistance on the Nusselt number calculation in a miniature heat sink is studied where thermal slip length is considered. Finally, the concurrent effects of thermal contact resistance and thermal developing region are considered to explicate the obtained trends in the experimental Nusselt numbers dataset.

Influence of gas axial conduction enhancement factor on the oscillating flow behavior of an inertance pulse tube cryocooler

Most one-dimensional simulation models developed so far to estimate the theoretical performance of pulse tube cryocoolers ignore the effect of heat loss arising out of thermal dispersion in porous media and turbulent conduction in pipes. In this paper one-dimensional numerical simulation of an inertance type pulse tube cryocooler has been carried out to illustrate the effect of thermal dispersion and turbulent conduction on the oscillating gas flow and heat transfer behavior. The study has been conducted under three conditions: simulation of cryocooler without considering gas axial heat conduction effects, simulation of cryocooler with gas axial heat conduction but neglecting the influence of thermal dispersion and turbulent conduction, and simulation of the cryocooler with gas axial heat conduction including the influence of thermal dispersion and turbulent conduction. The effect of thermal dispersion and turbulent conduction in the gas phase has been expressed in terms of an axial-conduction-enhancement-factor in the gas energy equation. It is revealed that the inclusion of axial-conduction enhancement factor in the porous media and tubes of the pulse tube cryocooler creates a positive phase shift in all oscillating physical quantities. This phase change causes an adverse effect on the cooling mechanism of the pulse tube cryocooler. It is found that, the coefficient of performance decreases by 8.6% and the minimum cooling temperature increases by 6.67% when the axial-conduction enhancement factor is included in the one-dimensional simulation model.

Implementation of fiber optic temperature sensors in quenching heat transfer analysis

The minimum film boiling temperature (Tmin) is one of the primary factors that influence the efficiency of rewetting of nuclear fuel rods after a loss-of-coolant accident (LOCA) in a light water reactor. In order to properly study the mechanisms behind the transient heat transfer phenomena that occurs during quenching, experimentation must be done using the most high-fidelity, high-resolution instrumentation available. In past experiments, thermocouples have been used to measure the temperature change in fuel rod simulators during quenching. However, these devices do not provide a high enough spatial resolution to obtain a full measurement of the temperature change throughout the rods. In order to study the entire test length during quenching, optical fiber temperature sensors are used and compared to the thermocouples. These fiber sensors have the capability of measuring every 0.65 mm with a similar degree of accuracy to the thermocouple measurements. By utilizing optical fiber sensors, the effects of cladding material, liquid subcooling, and surface roughness on the quenching temperature of fuel rod simulators is studied. In addition, the effect of axial heat conduction of the quenching temperature is also made possible to examine using fiber optic sensors. By better understanding the factors that influence quenching, one can properly study the effect of cladding surface properties on the safety of nuclear reactors.

New correlations for heat transfer in parallel-plate ducts at low Peclet number

Calculations of heat transfer in duct flows generally neglect the effect of axial heat conduction within the fluid. However, in some situations, this effect must be taken into account. The decision on whether or not to consider this phenomenon is driven by the value of the Peclet number. A low value, with 100 commonly considered the threshold, indicates that axial conduction, i.e., conduction parallel to the flow, should be accounted for in the calculations. Microfluidic devices, systems using liquid metal coolant or microchannel heat exchangers are some examples of applications where low Peclet flow conditions may be encountered. While exact analytical solutions exist for such cases, they are often impractical to use for common engineering design purposes due to their mathematical complexity. The present work proposes three new correlations for the estimation of the fully developed Nusselt number, thermal entry length and local Nusselt number in the entrance region of a laminar flow within a parallel-plate duct with constant wall temperature. These correlations allow the simple and accurate evaluation of useful engineering quantities, thus avoiding lengthy and complex calculations. They were developed using rational approximation theory and are effective on a wide range of Peclet numbers and axial coordinates. Accuracy of under 1% relative error is achieved with each of the three correlations when results are compared against exact analytical series solution values.

Thermal Performance Analysis in a Zigzag Channel Printed Circuit Heat Exchanger under Different Conditions

In this study, the effect of axial heat conduction on thermal performance in a zigzag channel printed circuit heat exchanger (PCHE) with supercritical liquefied natural gas as the working fluid is studied by a numerical method under different conditions. The influence factors include Reynolds number, operating pressure, inlet temperatures of the cold side, and wall thermal conductivity. The results indicate that the axial heat conduction can greatly affect the thermal performance of the PCHE at low Reynolds numbers but decrease it at high Reynolds numbers for different working conditions. At the same average Reynolds number, the thermal performance of the PCHE decreases as the pressure increases, and the inlet temperature of 195 K provides the best thermal performance while the inlet temperature of 220 K is the worst among the three different inlet temperatures of the cold side. Furthermore, the reduction of wall thermal conductivity can improve the thermal performance of the PCHE due to the influence of axial heat conduction in the separation wall.

GASEOUS SLIP FLOW FORCED CONVECTION IN A MICROPIPE AND PARALLEL-PLATE MICROCHANNEL WITH A PIECEWISE UNIFORM WALL HEAT FLUX AND AXIAL HEAT CONDUCTION

A forced convective heat transfer problem inside a micropipe as well as inside a microchannel with parallel walls in the laminar gaseous slip flow regime, a with finite heating region and a prescribed wall heat flux, including the axial heat conduction effect, is analytically investigated. The temperature field and Nusselt number are derived under the assumption that the flow is hydrodynamically fully developed in the finite-length heating region. The solution is found by applying the functional analysis method, by decomposing the energy equation into a pair of first-order partial differential equations. The first-order slip boundary conditions are imposed at the gas–wall interface. The analytical solution is compared with available calculations. The results show that the thermal characteristics in the heating region are significantly affected by the axial heat conduction, rarefaction effects, and finite length of the heating region.

Influence of flow non-uniformity on the dynamic behaviour of three-fluid cross-flow compact heat exchanger

The flow uniformity at any cross-section along the flow is highly influenced due to different practical limitations such as improper header/distributor design, manufacturing defect etc. Hence, the compact three-fluid heat exchanger with cross-flow arrangement is numerically investigated with non-uniform flow at the entrance of central fluid for four feasible flow arrangements (C1,2,3,4) for turbulent flow regime. The experiments are conducted to validate the numerical solutions obtained from Implicit Finite Difference scheme. The dynamic response of the cross-flow three-fluid heat exchanger is analysed with step and sinusoidal perturbation at the entry and both the cooling and heating efficacy of the heat exchanger is discussed. The model is made more realistic by incorporating the dispersive axial heat conduction effect within the fluids as well as at the inlet section of heat exchanger (Dankwert's boundary condition) and wall longitudinal heat conduction in the conducting walls. Four cases of flow non-uniformity (P, Q, R and S), which resemble the most realistic and possible case of non-uniform flow in the heat exchangers are selected for present study. It is learnt that case P and case Q offers the maximum and the minimum augmentation or deterioration in the efficacy of heat exchanger when non-uniform flow exists only in central fluid. The impact of flow non-uniformity on the performance of heat exchanger is more significant in turbulent flow regime than laminar. The analysis is further extended for the flow non-uniformity in all the three fluid streams simultaneously and for certain combinational case of U (uniform flow), P and Q. It is found that flow non-uniformity drastically affects the heat exchanger's efficacy and the upshot of axial dispersion causes more deterioration in the thermal performance than that by longitudinal heat conduction.

The Effect of Axial Conduction of the Wall on Temperature Conditions and Effectiveness of Heat Exchangers with Parallel Flow of Heat Carriers

The effect of heat conduction in the wall on temperature distribution along a heat exchanger with parallel flow of heat carriers and on heat exchanger effectiveness has been investigated. The problem was solved based on a system of one-dimensional (cross-section averaged) energy equations for two heat carriers and the heat conduction equation for the wall. The wall ends were assumed to be heat insulated. The system was solved using the finite-difference technique. For the special cases, the system was solved analytically. The parameter determining the effect of the wall axial conduction on the heat exchanger effectiveness and the value of this parameter at which this effect can be neglected have been found. This dimensionless parameter is proportional to the heat transfer coefficient, thermal resistance of the wall, and square of the heat-exchanger length to the tube wall thickness ratio. Besides the parameter describing the effect of axial heat conduction, the solution depends on the number of heat transfer units and the ratios of thermal equivalents of the heat carriers and heat transfer coefficients on the hot and cold sides. For a cocurrent flow of the heat carriers, the best result is attained when the value of these two ratios is 1. In this case, the effectiveness of the heat exchanger does not change as compared to that with no effect of the axial heat conduction of the wall. For a countercurrent heat exchanger, the effect of axial heat conduction on the heat exchanger effectiveness is at a minimum when the ratios of thermal equivalents of the heat carriers and heat transfer coefficients on the cold and hot sides are equal. The estimations based on the results of calculations demonstrate that, in case of microchannel heat removal, the effect of axial heat conduction in the heat exchanger wall can considerably reduce the heat exchanger effectiveness.

Thermal performance evaluation method of multistream plate fin heat exchanger

Multistream plate fin heat exchangers (MSPFHEs) are vital components of large cryogenic systems. A computer program is developed for layer by layer analysis of thermal performance of MSPFHEs and is validated against the published experimental results. Cross layer conduction between the streams in non-adjacent layers and heat transfer between the streams in consecutive layers are computed using analytical formulation. This avoids the need of fin discretisation along its height. Heat exchanger is discretised along the flow direction to take care of the effects of axial heat conduction and material property variation. Finite difference method (FDM) is used to convert the energy balance equations into a system of linear algebraic equations, which are solved iteratively. The developed computational method is found to be of adequate accuracy, capturing all the effects and can be used for MSPFHE design for cryogenic systems.

Verification of Analytical Test Based Thermohydraulic Systems Codes for One- and Two-Phase Liquid-Metal Flows

This work is devoted to the development of a system of analytical tests for verification of the thermohydraulic codes used in modeling the flow of one- and two-phase flows of liquid metals. The change of temperature in constant and variable flow of coolant, effect of axial heat conduction of the coolant on the temperature distribution, development of natural circulation in a closed loop, motion of a two-phase mixture under gravity, and fluctuations of the gas volume and distribution of the true process steam content in the presence of boiling/condensation are studied. The developed system of tests was used to verify the HYDRA-IBRAE/LM thermohydraulic code and the thermohydraulic module of the SOKRAT-BN code. The computational errors in the individual thermohydraulic parameters are obtained.

Convective heat transfer for a gaseous slip flow in micropipe and parallel-plate microchannel with uniform wall heat flux: effect of axial heat conduction

Thermally developing laminar slip flow through a micropipe and a parallel plate microchannel, with axial heat conduction and uniform wall heat flux, is studied analytically by using a powerful method of self-adjoint formalism. This method results from a decomposition of the elliptic energy equation into a system of two first-order partial differential equations. The advantage of this method over other methods, resides in the fact that the decomposition procedure leads to a selfadjoint problem although the initial problem is apparently not a self-adjoint one. The solution is an extension of prior studies and considers a first order slip model boundary conditions at the fluid-wall interface. The analytical expressions for the developing temperature and local Nusselt number in the thermal entrance region are obtained in the general case. Therefore, the solution obtained could be extended easily to any hydrodynamically developed flow and arbitrary heat flux distribution. The analytical results obtained are compared for select simplified cases with available numerical calculations and they both agree. The results show that the heat transfer characteristics of flow in the thermal entrance region are strongly influenced by the axial heat conduction and rarefaction effects which are respectively characterized by Peclet and Knudsen numbers.

Fully Developed Laminar Forced Convection in a Circular Duct for Herschel–Bulkley Fluids With Viscous Dissipation and Axial Heat Conduction

The asymptotic behavior of laminar forced convection in a circular duct for a Herschel–Bulkley fluid of constant properties is analyzed. The viscous dissipation and the axial heat conduction effects in the fluid are both considered. The asymptotic bulk and mixing temperature field, and the asymptotic values of the bulk and mixing Nusselt numbers are determined for every boundary condition, enabling a fully developed region. In particular, it is proved that whenever the wall heat flux tends to zero, the asymptotic Nusselt number is zero. The obtained results are compared to other existing solutions in the literature for Newtonian and non-Newtonian cases.

Numerical simulation of AP1000 LBLOCA with SCDAP/RELAP 4.0 code

ABSTRACTThe risk of large-break loss of coolant accident (LBLOCA) is that core will be exposed once the accident occurs, and may cause core damages. New phenomena may occur in LBLOCA due to passive safety injection adopted by AP1000. This paper used SCDAP/RELAP5 4.0 to build the numerical model of AP1000 and double-end guillotine of cold leg is simulated. Reactor coolant system and passive core cooling system were modeled by RELAP5 modular. HEAT STRUCTURE component of RELAP5 was used to simulate the fuel rod. The reflood option in RELAP5 was chosen to be activated or not to study the effect of axial heat conduction. Results show that the axial heat conduction plays an important role in the reflooding phase and can effectively shorten reflood process. An alternative core model is built by SCDAP modular. It is found that the SCDAP model predicts higher maximum peak cladding temperature and longer reflood process than RELAP5 model. Analysis shows that clad oxidation heat plays a key role in the reflood. From the simulation results, it can be concluded that the cladding will keep intact and fission product will not be released from fuel to coolant in LBLOCA.

Axial heat conduction effects in the thermal entrance region for flows in concentric annular ducts: Correlations for the local bulk-temperature and the Nusselt number at the outer wall

Streamwise heat conduction in the flow can affect the heat transfer in ducts. This is mainly relevant for flows with small Prandtl numbers or in micro-channels. In both situations the Péclet number is small, so axial heat conduction in the fluid cannot be neglected. In literature analytical solutions of this so called extended Graetz problem are well documented. In the present paper correlations are developed for the local bulk-temperature and the local Nusselt number at the outer wall in the thermal entrance region of concentric annular ducts. Correlations are given for laminar and turbulent fully-developed flow and different thermal boundary conditions. The correlations also consider the effect of different ratios of the inner radius to the outer radius of the annular ducts.