Axial Heat Conduction Research Articles

Heat Transfer in the Slip Flow with Axial Heat Conduction in a Microchannel with Walls Having a Constant Temperature

The problem on thermally developed laminar slip gas flow with axial heat conduction in a microchannel (a micropipe or a parallel-plate microchannel) with walls having a constant temperature was solved analytically with the use of the self-adjoint formalism method involving the rearrangement of the energy equation for this flow into a system of two partial differential equations of the first order. The temperature distribution and Nusselt numbers in such a flow have been determined on the assumption that it is hydrodynamically fully developed in the region of the thermal entrance of a microchannel. The data obtained show that the heat transfer in this flow is substantially dependent on the axial heat conduction in it and its rarefaction.

Temperature-Sensitive Paint Applications in the Heat Transfer Analysis of 90° Elbow Microchannel Flow with Sharp and Curved Turns

ABSTRACTThis study presents the heat transfer analysis of 90° elbow microchannel flow with sharp and curved turn designs. Experimental technique of temperature-sensitive paint was adapted in the experiment for measuring both fluid and surface temperature. The detailed information of fluid and surface temperature data were successfully acquired with a microscope system at Reynolds number varying from 50.5 to 101.1. Micro heaters were fabricated and positioned underneath the microchannel to provide the constant heat flux boundary condition. The utilization of micro heaters can prevent the axial heat conduction. The Nusselt number contours were obtained in this study with sharp and curved corners, which can provide detailed information of localized region with high and low heat transfer. The experimental approach performed in this study could be applied in the future for micro heat exchanger or heat sink design with complex microchannel systems.

Low Reynolds numbers convective heat transfer enhancement in roughened microchannels

Abstract Heat transfer enhancement studies were conducted on a variety of roughened microchannels for a laminar flow at 3≦Re≦25 with DI water as the cooling fluid. Five different discrete roughened surfaces, which were circular, square, triangular, elliptical, and hexagonal in shape, were used in the test channels with a channel cross-sectional area aspect (height to width) ratio of 0.25. The smooth-surface channel had a length of 30 cm, width of 200 μm, and height of 50 μm, which creates the hydraulic diameter of 80 μm for the study. A constant heat flux of 1.25 W/cm2 was applied to the bottom of the channel through the ITO surface. Results of the cooling performance in terms of the enhancement factor compared to those of a smooth channel found that the square pin-fin roughened surfaces had the best transfer enhancement followed by the ellipse, circle, hexagon, and triangle as compared to that of a smooth surface. Furthermore, axial wall heat conduction was noted for both smooth and roughened channels.

An analytical full-scale model to predict thermal response in boreholes with groundwater advection

Borehole heat exchanger (BHE) is an important component in the ground coupled heat pump (GCHP) system. Based on the theories of composite medium line-source and the moving line-source, an analytical full time-scale model has been derived to predict the performance of BHE by considering the coupled effects of transient heat transfer in the borehole, the horizontal groundwater around the borehole and the axial heat conduction along the borehole. The full-scale model is validated by the experimental data and the numerical results. The validated model is applied to predict fluid temperature in the cases (i) with unit load, (ii) with annual building loads and (iii) with multiple boreholes. Based on the simulation results, the impacts of time length, axial conduction, groundwater flow and locations of boreholes are discussed in detail.

Gaseous Slip Flow Forced Convection in a Micropipe and Parallel-Plate Microchannel with a Piecewise Uniform Wall Heat Flux and Axial Heat Conduction

Gaseous Slip Flow Forced Convection in a Micropipe and Parallel-Plate Microchannel with a Piecewise Uniform Wall Heat Flux and Axial Heat Conduction

Моделирование обезвоживания открытых систем с помощью программы RELAP5

At present, there are many software tools that have positively proven themselves for carrying out computational analysis within the framework of assessing the safety of nuclear power utilization facilities. The RELAP5 code, which is intended for carrying out improved assessment of safety, is one of such tools. Initially, its use was limited to a numerical analysis of water-heated water-cooled apparatuses. At the same time, owing to extensive capabilities of the code and stable algorithms for solving hydraulic and thermophysical problems, its application field can be made significantly broader. However, the validity of such broadening should be justified both theoretically and by verification against relevant experimental data. The computational modeling results obtained using the RELAP5 code are given. A comparison between the calculated and experimental data on heating a system operating with low heat fluxes is presented. The results obtained from computations using the RELAP5 code are compared with the results of two experiments. In the first experiment, which was carried out at atmospheric pressure, water was heated in an open thermally insulated vessel. Due to evaporation, the water level in the vessel decreased, but water boiling did not occur. As soon as the water level dropped below the thermal element heated part, the element’s wall temperature showed a sharp increase. The classical approach that was applied to modeling using the RELAP5 code showed a significant discrepancy between the experimental and calculated data. After modifying the computational model, a more adequate agreement between the calculated and experimental results was obtained. In the second experiment, the dewatered system was heated at different heater power levels. With increasing the heater power in successive steps, its temperature changed accordingly. Based on the results from comparison of the calculated and experimental data, it has been shown that the axial heat conduction mechanism has a significant effect on the heating of a partially dewatered heating element, and a method for modeling the longitudinal heat flow along the thermal element in the computations carried out using the RELAP5 code is proposed. The possibility of using the RELAP5 code for simulating a dewatered system has been demonstrated. The verification materials presented in the article contain recommendations for constructing the analysis models of systems operating with low heat fluxes, e.g., spent fuel pools at nuclear power plants.

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.

LAMINAR HEAT TRANSFER WITH VISCOUS DISSIPATION FOR NEWTONIAN FLUIDS FLOWING IN PARALLEL HEATED PLATES WITH ONE PLATE MOVING

The paper investigates basic analytical expressions for Nusselt number with effect of viscous dissipation on the heat transfer between parallel heated plates with one plate moving, where the focus is on hydro-dynamically and thermally fully developed flow of Newtonian fluids with constant properties, neglecting the axial heat conduction in the fluids and through the walls. Thermal boundary conditions considered are: both plates kept at different constant heat fluxes, both plates kept at equal constant heat fluxes, and one plate insulated. From the analysis, new expressions for Nusselt numbers have been found, as a function of various definitions of the Brinkman number.

Numerical Investigation on Thermal Performance Design of Cryogenic Compact Heat Exchangers with Serrated-Fin Channels

Traditional empirical formulas of Colburn heat transfer factors will lead to a design deviation for cryogenic heat exchangers. This paper employs the computational fluid dynamics (CFD) technique to numerically study the thermal performance of cryogenic compact heat exchangers (CCHEs). To obtain more precise convective heat transfer coefficients, the heat transfer performance of CCHE with serrated fin channels is analyzed considering various cryogenic fluid properties, fin materials and the axial heat conduction (AHC), and a heat transfer deterioration rate is proposed to investigate the effect of AHC on the heat transfer performance of CCHEs. For the simulation design, a quasi-one-dimensional calculation model is developed to obtain the temperature and pressure fields of the whole heat exchanger using the previous CFD results of the finned channels to avoid the deviation caused by traditional empirical formulas. Finally, a case study for a CCHE in a practical system is designed and analyzed by the proposed approach. The results suggest that cryogenic conditions have a significant effect on the design performance of heat exchangers, especially when considering the influences of fluid properties, materials, and AHC. For different cryogenic fluids, accurate heat transfer factors should be selected for the design calculations, and materials with high thermal conductivity will increase the effect of AHC and deteriorate the performance of the CCHE.

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.

Simulation and Experiments of Active Greenhouse Heating System

This paper proposed an active greenhouse heating system which focused on the problem of crop growth under extreme cold weather. At the beginning, heat transfer process of heating system was analysed based on thermal equilibrium theory. Radial and axial heat conduction mathematical analysis model of temperature control system were established respectively. Then, numerical simulation of temperature distribution was carried out by means of finite element method (FEM) software. When the effective operation range (later referred to as Qf) was defined with soil temperature more than 15 °C at 20 cm underground, opening temperature of heating system should be no less than 28 °C. Simulation results show that an increase of air inlet temperature by 2 °C could extend axial effective operating range by 2.4 m–2.8 m. Later, field test was implemented in greenhouses which located in Changping district, Beijing. Finally, compared with simulation data, the field testing data shows that the perturbation law of heating system heat transfer process on shallow and deep layer soil temperature is consistent with theoretical analysis. The numerical simulation could help to guide the temperature control of greenhouse. DOI: 10.5755/j01.eie.25.2.23205

Transient conjugated heat transfer in thick walled pipes with axially periodic surface temperature in downstream region

Thermal entrance region transient conjugate heat transfer is investigated involving fluid axial heat conduction for laminar pipe flows. Constant outer wall temperature boundary condition is assumed in the upstream region of a thick walled, two regional pipe. In the downstream region, the outer wall temperature is considered changing spatially in a periodical manner. The problem is solved numerically by a finite difference method. A parametric analysis is conducted in order to determine the effects of Peclet number, wall thickness ratio, wall-to-fluid thermal conductivity ratio, wall-to-fluid thermal diffusivity ratio and axial frequency on heat transfer characteristics. It is seen that, the results are highly dependent on the parameter values and the most effective ones are the Peclet number and the wall thickness ratio. It is observed that heat is transferred towards upstream due to the axial conduction in the wall and in the fluid and with increasing values for high axial frequency.

Analysis of the heat transfer in the asynchronous intermittent laminar flow for mini channels in the recuperator for micro swing engines

A numerical investigation into conjugate heat transfer for a double-tube heat exchanger in mini-scale was conducted, with an asynchronous intermittent laminar flow imposed at the inlets. As a basic component of the micro recuperator for a micro swing engine, a mini double-tube exchanger under the same flow conditions was chosen as the physical model with consideration of variable fluid properties. Results indicate that, for the asynchronous intermittent pulsed flow, the axial wall heat conduction is much more serious and the periodic fluctuation of the solid wall temperature further worsens the heat transfer efficiency. Two dimensionless numbers R∗ and C¯∗ are proposed to evaluate the two adverse effects. Then, two key parameters involved in the design of the micro recuperator for the micro swing engine are studied, namely, wall thickness ratio δ/Dc and flow frequency. For certain flow frequencies, as the value of δ/Dc increases, the axial heat conduction is enhanced while the wall temperature fluctuation is reduced. For a given δ/Dc, the flow frequency dually affects the heat exchanger efficiency and the optimum frequency exists. The optimal value increases with the wall thickness ratio. These results lay a good foundation of the micro recuperator design for the micro swing engine.

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.

Capillary driven thermal and hydrodynamic characteristics of axial swallow-tailed micro-grooved heat pipe

ABSTRACTThermal and hydrodynamic models were developed for an axial swallow-tailed micro-grooved heat pipe and solved numerically. The axial heat conduction, the variation of the axial meniscus radius and the thin liquid film heat transfer in the evaporator and condenser sections were included in the proposed model. The results showed that the liquid film thickness increases along the axial direction of the microgrooves. The evaporation heat transfer coefficient of the liquid-vapor interface in the evaporator section is greater than the condensation heat transfer coefficient of the liquid-vapor interface in the condenser section. Additionally, the evaporation/condensation mass flow rates in the adiabatic section are not all zero. The wall, liquid and vapor temperatures are almost the same in the adiabatic section. In addition, an experimental study was performed to verify the heat transfer model in a heat pipe with axially swallow-tailed microgrooves. Moreover, in this paper, the obtained numerical results are accordant with the obtained experimental data.

Analysis of solid-phase axial heat conduction upon hot-spot formation in a one-dimensional microreactor

A generalized one-dimensional model of a non-isothermal, monolithic microreactor is developed to investigate the impact of solid-phase axial heat conduction upon hot-spot formation. The model consists of a pair of first-order differential equations describing an exothermic reacting fluid which exchanges heat with the solid-phase that comprises the monolithic microreactor. Solid-phase axial heat conduction and exchange with an isothermal coolant is described by an additional second-order ordinary differential equation, with boundary conditions accounting for the possibility of conductive heat losses to adjacent fluid distribution manifolds. Criticality analysis is performed using both the explicit Van Welsenaure and Froment (VWF) criteria and implicit Morbidelli and Varma (MV) criteria. Results indicate that the VWF criteria applied to the limiting case of negligible axial heat conduction provides a reliable, albeit conservative, criteria for hot-spot prevention. Additionally, MV criteria applied to the case of sufficiently high axial heat conduction yields criteria for ensuring hot-spot formation. Analysis using MV criteria indicates that the introduction of mild solid-phase axial heat conduction promotes hot-spot formation so long as heat losses to manifolds is minimal.

Effect of radial heat conduction on effective thermal conductivity of carbon nanotube bundles

The effect of the radial heat conduction on the effective thermal conductivity of carbon nanotube (CNT) bundles is studied by the nonequilibrium molecular dynamics (NEMD) method. The hexagonal CNT bundle consists of seven (10, 10) single-walled carbon nanotubes (SWCNTs). The radial heat conduction is induced by creating the vacancy defects in some segments of the constituent CNTs. Combined with the temperature differences and the inter-tube thermal resistances at the different segments, the radial heat flow in the CNT bundle is calculated. The maximum percentage of the radial heat flow is less than 7% with the presence of four defective CNTs, while the resultant decrement of the effective thermal conductivity of the bundle is about 18%. The present results indicate that the radial heat flow can significantly diminish the axial heat conduction in the CNT bundles, which probably explains the smaller effective thermal conductivity in the CNT assemblies compared to that of the individual CNTs.

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.

A novel method based on thermal conductivity for material identification in scrap industry: An experimental validation

Fast, accurate and reliable identification and sorting of materials is still a challenge in recycling sector. Scrap metals are often classified through density and colour, which cause notable financial burdens to the companies in most cases. Within the scope of this research, a novel method based on thermal conductivity is presented for material identification in scrap industry. The unit consists of a constant heat flux source and a cooling system, in which axial heat conduction is enabled and radial heat transfer is eliminated. For the steady-state conditions, temperature gradient across the sample metals is measured along with the constant heat flux value, and the thermal conductivity of the samples is determined via the Fourier’s heat conduction law. Copper, brass and stainless steel samples are considered in this research to verify the accuracy of the results. For a reliable and scientific approach, three independent sets of experiments are conducted, and the results are evaluated in terms of accuracy and consistency. Experimental thermal conductivity values of the said samples are compared with the reported data in literature and a good accordance is achieved. Error in measurements is calculated to be 1.37, 3.31 and 4.46% for copper, brass and stainless steel sample, respectively which is acceptable. The tests are repeated with highly sensitive probes for aluminium sample, and the measurement error is calculated to be 0.56%.

Thermal calculation of heat exchangers with simplified consideration of axial wall heat conduction

The usual thermal design and rating methods [1, 2] for heat exchangers neglect axial wall heat conduction in the separating walls and external shells of recuperators and in the solid matrix of regenerators. This may lead to undesirable undersizing. In this paper a simplified model is developed for the fast estimation of axial wall conduction effects in counterflow, parallel flow and mixed-mixed cross-flow recuperators. The dispersion model [3] is used to describe the performance deterioration of the exchanger with an effective fluid dispersion Peclet number for the correction of the heat transfer coefficients or mean temperature difference. The method is tested against analytical and numerical calculations for counterflow and parallel flow with good results. It is also shown how the method can be adapted to thermal regenerators and the related thermal calculation methods [1, 2]. An alternative approach is suggested for the consideration of lateral heat conduction resistance in the solid matrix.