Effect Of Axial Conduction Research Articles

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.

Pressure Work and Viscous Dissipation Effects on Heat Transfer in a Parallel–Plate Microchannel Gas Flow

ABSTRACTConvective heat transfer in a parallel plate microchannel gas flow is investigated analytically and numerically, considering the effects of viscous dissipation, pressure work, shear work, axial conduction and rarefaction. Analysis is performed with constant wall temperature and constant wall heat flux boundary conditions for both gas cooling and heating. The results presented demonstrate the significance of the combined effect of pressure work and viscous dissipation, shear work, rarefaction degree and axial conduction on microchannel convective heat transfer, in both the thermally developing and fully developed flow regions. Viscous dissipation and pressure work in a pressure-driven microchannel gas flow are of comparable magnitudes and may not be neglected from the energy equation. The shear work at the wall, which is effectively the combined effect of viscous dissipation and pressure work, needs to be included in the Nusselt number for better predictions of heat transfer.

On the role of axial wall conduction in mini/micro counterflow heat exchangers

Understanding the role of multi-dimensional conjugate heat transfer on the thermal efficiency of mini/micro counterflow heat exchangers is critical for the design of high efficient equipment. This topic is addressed here by considering a simple model with exact solution: the laminar counterflow parallel-plate heat exchanger. Using as starting point the eigenfunction series solution recently obtained by the authors, a thorough parametric study is carried out to investigate the role of the two dimensionless parameters involved in multi-dimensional wall conduction: the dimensionless wall thickness, Δw, and the dimensionless wall thermal resistance, κw-1. The analytical eigencondition is first presented and discussed, and the associated eigenvalue spectrum is analyzed using contour plots of the lowest-order eigenvalues in the (Δw,κw-1) plane. The complex task of determining the eigenvalues numerically is largely facilitated by approximate expressions obtained from the asymptotic analysis of the singularities that appear in the eigencondition. The fast evaluation of the eigenvalues makes it possible to obtain contour plots of the heat exchanger effectiveness in the (Δw,κw-1) plane, which exhibit distinguished regimes corresponding to limiting cases with and without axial and transverse wall conduction effects, with smooth transitions occurring for moderately small values of Δw and κw-1. The analysis provides conditions for neglecting axial and transverse wall conduction, and shows that an optimum wall conductivity always exists in heat exchangers with sufficiently thin walls.

Effects of pressure work, viscous dissipation, shear work and axial conduction on convective heat transfer in a microtube

This paper investigates the effects of viscous dissipation, pressure work, shear work, rarefaction and axial heat diffusion on convective heat transfer in a microtube gaseous flow. The problem is investigated numerically for the whole flow region using a finite difference scheme and the line Gauss-Seidel iterative technique. Exact solutions of the problem in terms of temperature distribution and Nusselt number variations are also derived under fully developed flow conditions. The microtube is assumed to be sufficiently long, so that fully developed conditions are established. The analysis presented demonstrate that the effect of the boundary shear work is significant and its contribution to heat transfer can be as high as that due to heat conduction close to the upper limit of the slip flow regime. As the shear work is a result of the combined effects of viscous dissipation and pressure work at the boundary, including these effects in the analysis leads to better predictions of heat transfer phenomena. Axial heat diffusion effect on Nusselt number and the thermal entrance length are also quantified.

Evaluation of axial conduction effects and heat losses in counter-flow microscale heat exchangers

A gas to gas counter flow micro Heat Exchanger (HE) made of an array of microchannels and fabricated using a combination of silicon and glass wafers is studied. A divergence of the experimental results from the classical heat exchanger theory is observed due to discernible axial conduction effects and heat loss to the environment. Hence, device performance is evaluated using a modified NTU approach that includes also non-negligible axial conduction effects due to the relatively thick and thermally conductive separating wall. This along with replacement of the adiabatic boundary conditions at the separating wall ends with proper temperature conditions enables to evaluate the heat losses to the environment and to reduce the average error between theoretical model and experimental data by 56%.

EXPERIMENTAL VALIDATION OF LMTD METHOD FOR MICROSCALE HEAT TRANSFER

The s ingle phase fluid flow and heat transfer characteristic has been investigated experimentally. Experiments were conducted to cover transition zone for the Reynolds numbers ranging from 100 to 4800 by fused silica and stainless steel microtubes having diameters of 103-180 µm. The applicability of the Logarithmic Mean Temperature Difference (LMTD) method was revealed and an experimental method was developed to calculate the heat transfer coefficient. Moreover the scaling effects in micro scale such as axial conduction, viscous heating and entrance effects were discussed. The heat transfer coefficients were compared with data obtained by the correlations available in the literature in the study. The Nusselt numbers of microtube flows do not accord with the conventional results when the Reynolds number was lower than 1000. After that, the Nusselt number approaches the conventional theory prediction. On the aspect of fluid characteristics, the friction factor was well predicted with conventional theory and the conventional friction prediction was valid for water flow through microtube with a relative surface roughness less than about 4 %.

Numerical simulation of subcooled flow boiling under conjugate heat transfer and microgravity condition in a vertical mini channel

In this study, subcooled flow boiling in a vertical mini channel is simulated using Color Function Volume Of Fluid (CF-VOF) in micro gravity condition. The continuous surface force model and Lee model are used for analyzing surface tension forces and mass transfer via interface, respectively. The Newtonian flow equations are solved using the finite volume method, which is based on the Pressure Implicit with Splitting of Operators (PISO) algorithm. The existing OpenFOAM two phase solver i.e. interFoam was developed by adding energy equation and the source terms corresponding phase change. Moreover, in order to increasing the accuracy of the simulation, the effect of axial conduction is taken into account by applying the conjugate heat transfer model. The validation of developed solver and mathematical model indicates a proper compliance with experimental data of technical literature. Results show variation in flow patterns and heat transfer coefficients in the micro gravity (gravity level of ±0.05g) condition comparing with the normal gravity condition. Moreover, it is found that some imperative parameters such as heat flux and mass flux affect aforementioned patterns and coefficients. In addition, simulation results show that the size of bubbles formed in the micro gravity condition is larger than the bubbles in normal gravity condition and the variation in the size of bubbles increases the heat transfer coefficient in the micro gravity (%22) compared to the normal gravity condition.

Transient conjugate heat transfer in a circular microchannel involving rarefaction, viscous dissipation and axial conduction effects

Transient conjugate heat transfer of a hydrodynamically developed and thermally developing laminar flow in a circular microchannel is investigated considering the effects of rarefaction, viscous dissipation and axial conduction. The problem is solved numerically by a finite difference method based on Patankar’s (1980) control volume approach. Momentum and energy equations are solved with the boundary conditions of the first degree velocity slip and temperature jump. The problem depends on four parameters. These are the Peclet number (Pe), the Knudsen number (Kn), the Brinkman number (Br) and the wall thickness ratio (d′). The results obtained showed that heat transfer characteristics are significantly affected by these parameters and that in micro channel flows, the fluid’s rarefaction effects, viscous dissipation and axial conduction should not be ignored.

Laminar counterflow parallel-plate heat exchangers: An exact solution including axial and transverse wall conduction effects

Multilayered, counterflow, parallel-plate heat exchangers are studied theoretically and numerically. The analysis, carried out for constant property fluids, assumes a fully developed laminar flow with moderately large Peclet numbers in the flow channels, so that longitudinal conduction can be neglected in the fluids in first approximation. By way of contrast, both axial and transverse conduction effects are fully accounted for in the heat conducting plates, making the analysis relevant to the design of mini- and micro-heat exchangers. The exact solution for the temperature field is obtained in terms of eigenfunction expansions involving infinite sets of both positive and negative eigenvalues. Based on previous results, the eigenfunctions are expressed in terms of Whittaker functions, leading to an analytical eigencondition that provides the eigenvalues numerically. Making use of a newly defined orthogonality condition, the expansion coefficients are determined through an infinite system of linear equations that must be truncated to a sufficiently large number of terms to obtain a numerical solution of the problem. The exact solution for the temperature field provides analytical expressions for the interfacial and bulk temperatures, local heat-transfer rates, overall heat-transfer coefficient, Nusselt numbers, and outlet bulk temperatures of both fluids. Numerical results evaluated using a moderate number of terms in the series are compared against finite difference solutions of the problem and against previous results reported in the literature, showing excellent agreement in both cases. The exact solution presented here may be used as a benchmark case for computational heat transfer codes, and enables future spectral and parametric studies of the problem.

Effect of axial conduction and viscous dissipation on heat transfer for laminar flow through a circular pipe

Summary The effect of viscous dissipation and axial conduction on heat transfer for laminar forced convection flow through a circular pipe was studied. Constant wall temperature boundary condition was imposed on the circular pipe and the flow is assumed to be hydrodynamically developed and thermally developing. Numerical solutions were obtained to observe the variations of non-dimensional bulk mean temperature, Nusselt number and wall heat from (or) to the fluid for Brinkman numbers ±1.0, ±0.5, ±0.2, 0.0 and Peclet numbers 10, 50, 100, 300 and 500. It was found that the heat generated by viscous dissipation was higher for higher Brinkman number and it delays the thermal entrance development of the fluid. The effect of axial conduction becomes negligible when the value of Peclet number crosses hundred.

A molecular dynamics simulation of nanoscale convective heat transfer with the effect of axial heat conduction

ABSTRACTEffective heat dissipation from nano-fluidic devices is sometimes necessary to ensure their performance and lifespan. In the molecular dynamics simulation of nanoscale convective heat transfer, thermostats cannot be directly applied to the fluid because of the non-uniform temperature distribution. Periodic boundary is typically utilised, but unrealistic axial heat conduction exists when there is a temperature difference between the outlet and images of inlet atoms. In this paper, the effect of axial conduction caused by periodic boundary is investigated through the Péclet number (Pe). Taking viscous dissipation into consideration, the magnitude of outlet thermal diffusion is observed to decrease with increasing Pe. The local average temperature of fluid changes in an exponential form except in the region close to the outlet. Results show that the contribution of outlet axial conduction to the local average temperature is less than 2.0% when Pe > 10. The main reason is that the magnitude of fluid velocity and viscous heat dissipation in nanochannels is much larger than that in macro-channels at the same Péclet number.

Numerical modeling of recuperative cryogenic matrix heat exchangers and the experimental validation

The recuperative matrix heat exchanger (MHE) has advantages of large specific surface area, compactness, high effectiveness, and low flow resistance, which make it promising for applications in Joule-Thomson cryocooler and reverse Brayton cryocooler. In this study, a numerical model is developed to predict the thermal performance of MHEs. The effects of axial conduction of both inner and outer walls as well as radial heat conduction through mesh-screens and the heat leakage are considered. The temperature distribution over the fluids and mesh screens in MHEs can be determined using this model. The model is validated by analytical solution of effectiveness-NTU method and the results of the experimental tests on two MHEs with different structures at cryogenic temperature. Using the proper correlations for heat transfer coefficients, the relative deviations of the ineffectiveness predictions from experimental results are below 13.2% in the mass flow range of 0.4 g/s – 2.1 g/s. The numerical results show that the axial conduction of inner and outer walls has similar effects on the thermal performance of MHEs. The increase of axial conduction can substantially lower the effectiveness of the MHEs at mass flow rates below 1 g/s, while the influence of the number of transfer unit (NTU) on the MHE effectiveness becomes dominant at mass flow rates above 1 g/s.

Shear work, viscous dissipation and axial conduction effects on microchannel heat transfer with a constant wall temperature

Convective heat transfer in a microchannel rarefied gas flow with a constant wall temperature boundary condition is investigated numerically. The boundary shear work, viscous dissipation and axial conduction are all included in the study. An analytical solution is also derived for the fully developed flow condition including the boundary shear work. The proper thermal boundary condition considering the sliding friction at the wall is implemented. A comparative study is performed to quantify the effect of the shear work on heat transfer in the entrance – and the fully developed – regions of the microchannel for both gas cooling and heating. The results demonstrate that the effect of shear work on heat transfer is significant and it increases with increasing both the Knudsen number and Brinkman number. Neglecting the shear work in a microchannel slip flow leads to over- or under estimation of the Nusselt number considerably. For a fully developed flow in a microchannel with constant wall temperature boundary condition, the contribution of the shear work to heat transfer can be around 55% in the vicinity of the upper limit of the slip flow regime, regardless of how small the non-zero Brinkman number can be. Including the shear work is therefore crucial in the analysis of microchannel heat transfer and should not be neglected.

Analytical solution of thermally developing microtube heat transfer including axial conduction, viscous dissipation, and rarefaction effects

The solution of extended Graetz problem for micro-scale gas flows is performed by coupling of rarefaction, axial conduction and viscous dissipation at slip flow regime. The analytical coupling achieved by using Gram–Schmidt orthogonalization technique provides interrelated appearance of corresponding effects through the variation of non-dimensional numbers. The developing temperature field is determined by solving the energy equation locally together with the fully developed flow profile. Analytical solutions of local temperature distribution, and local and fully developed Nusselt number are obtained in terms of dimensionless parameters: Peclet number, Knudsen number, Brinkman number, and the parameter Kappa accounting temperature-jump. The results indicate that the Nusselt number decreases with increasing Knudsen number as a result of the increase of temperature jump at the wall. For low Peclet number values, temperature gradients and the resulting temperature jump at the pipe wall cause Knudsen number to develop higher effect on flow. Axial conduction should not be neglected for Peclet number values less than 100 for all cases without viscous dissipation, and for short pipes with viscous dissipation. The effect of viscous heating should be considered even for small Brinkman number values with large length over diameter ratios. For a fixed Kappa value, the deviation from continuum increases with increasing rarefaction, and Nusselt number values decrease with an increase in Knudsen number.

Analysis of operating modes of a ground source heat pump with short helical heat exchangers

This study focuses on different operating modes of a ground source heat pump system in residential buildings. Ground coupling was made using a closed loop system consisting of a helical shaped pipe installed at a shallow depth. Few studies have examined this particular ground heat exchanger.The analysis was carried out using a detailed numerical model capable of considering the geometry of the helical ground heat exchanger as well as the effects of axial thermal conduction and the weather at ground level, variables which cannot be ignored when shallow depths are being investigated. Field measurements were used to validate the model before it was utilized. In addition, the simulation tool considered the entire ground source heat pump system, including both the borehole field and the heat pump.The energy efficiency of the heat pump in three operating modes (continuous daytime, continuous nighttime, and intermittent mode) over a ten year period was analysed. The simulations were performed in two different climatic zones maintaining the daily energy load of the building unmodified. Finally, the effect of the grouting material of the helical ground heat exchanger and of the diameters of both the borehole and the helix on the system’s energy performance was also investigated. Results indicated that the seasonal energy efficiency of the heat pump was approximately the same for the three operating modes and that energy efficiency was nearly constant during the day when the system was operating on an hourly intermittent basis. When the borehole diameter was smaller, the reduction in the heat exchange surface needed to be balanced by a thermally enhanced grouting material.

The extended Graetz problem for a gaseous slip flow in micropipe and parallel-plate microchannel with heating section of finite length: Effects of axial conduction, viscous dissipation and pressure work

Abstract The extended Graetz problem for a gaseous slip flow through a micropipe and a parallel-plate microchannel, with an isothermal heating section of finite length, is analytically investigated. The simultaneous effects of the axial heat conduction, viscous dissipation and pressure work are all taken into account and discussed. The solution obtained is based on a powerful method using self-adjoint formalism, resulting from a decomposition of energy equation into a system of the first-order partial differential equations. This solution, which is applicable for finite and semi-infinite heating section, represents an improvement and extension of those obtained in the earlier works, by considering the slip boundary conditions at the fluid–wall interface for the velocity and temperature. This extension has been done by using a new matrix operator of three dimensions and a suitable scalar product between two vectors in the Hilbert space. The analytical results are compared for simplified limiting cases with available analytical and numerical calculations and a good agreement is found. The results of the effects of different dimensionless parameters involved in the problem, namely Peclet, Knudsen, Brinkman numbers and the length of the heating section, on the heat transfer characteristics are illustrated and discussed. Furthermore, some useful correlations of these characteristics are provided for some values of Peclet number. It is shown particularly that for non-zero values of Brinkman number, when the heat flow is established, the sum of the enthalpy and the energy which results from the friction and pressure work is conserved through cross-sections of microchannels, and the heat transfer is mainly governed by the shear work at the wall. Among the most important applications of this analytical solution is its potential to simulate an isothermal hot film sensor of finite size, mounted on the wall of microchannel, which can be serve to measure a heat flux between the gas and wall and hence heat transfer coefficient in the slip flow regime.

Cooling performance of a nanofluid flow in a heat sink microchannel with axial conduction effect

In this work, the forced convection of a nanofluid flow in a microscale duct has been investigated numerically. The governing equations have been solved utilizing the finite volume method. Two different conjugated domains for both flow field and substrate have been considered in order to solve the hydrodynamic and thermal fields. The results of the present study are compared to those of analytical and experimental ones, and a good agreement has been observed. The effects of Reynolds number, thermal conductivity and thickness of substrate on the thermal and hydrodynamic indexes have been studied. In general, considering the wall affected the thermal parameter while it had no impact on the hydrodynamics behavior. The results show that the effect of nanoparticle volume fraction on the increasing of normalized local heat transfer coefficient is more efficient in thick walls. For higher Reynolds number, the effect of nanoparticle inclusion on axial distribution of heat flux at solid–fluid interface declines. Also, less end losses and further uniformity of axial heat flux lead to an increase in the local normalized heat transfer coefficient.

Radiation and heat generation effects on viscous Joule heating MHD-conjugate heat transfer for a vertical flat plate

Conjugate heat transfer formed by the coupling effect of conduction inside and free convection flow along the flat plate is analyzed. The Joule heating effect because of considered magnetohydrodynamics (MHD) along with viscous dissipation, heat generation, and radiation phenomena are included in the investigation. The converted dimensionless partial differential equations representing the aforementioned flow characteristics are transformed into nonlinear equations with the help of a stream function with similarity variable. Finally, a numerical solution is carried out using the implicit finite difference method to analyze the flow behaviors in terms of velocity, temperature, skin friction coefficient, heat transfer rate, and surface temperature. A complete parametric analysis is done on the numerical results to show the effects of the radiation parameter, magnetic parameter, Eckert number, heat generation parameter, conjugate conduction parameter, and Prandtl number. It is found that thermal radiation, viscous Joule heating, and internal heat generation in the presence of axial conduction effects have a significant effect on MHD natural convection flow and thermal fields.

Effect of flow maldistribution and axial conduction on compact microchannel heat exchanger

When a compact microchannel heat exchanger is operated at cryogenic environments, it has potential problems of axial conduction and flow maldistribution. To analyze these detrimental effects, the heat exchanger model that includes both axial conduction and flow maldistribution effect is developed in consideration of the microchannel heat exchanger geometry. A dimensionless axial conduction parameter (λ) is used to describe the axial conduction effect, and the coefficient of variation (CoV) is introduced to quantify the flow maldistribution condition. The effectiveness of heat exchanger is calculated according to the various values of the axial conduction parameter and the CoV. The analysis results show that the heat exchanger effectiveness is insensitive when λ is less than 0.005, and effectiveness is degraded with the large value of CoV. Three microchannel heat exchangers are fabricated with printed circuit heat exchanger (PCHE) technology for validation purpose of the heat exchanger model. The first heat exchanger is a conventional heat exchanger, the second heat exchanger has the modified cross section to eliminate axial conduction effect, and the third heat exchanger has the modified cross section and the cross link in parallel channel to mitigate flow maldistribution effect. These heat exchangers are tested in cryogenic single-phase, and two-phase environments. The third heat exchanger shows the ideal thermal characteristic, while the other two heat exchangers experience some performance degradation due to axial conduction or flow maldistribution. The impact of axial conduction and flow maldistribution effects are verified by the simulation results and compared with the experimental results.

Two-Dimensional Variable Property Conjugate Heat Transfer Simulation of Nanofluids in Microchannels

Laminar two-dimensional forced convective heat transfer of CuO-water and Al2O3-water nanofluids in a horizontal microchannel has been studied numerically, considering axial conduction effects in both solid and liquid regions and variable thermal conductivity and dynamic viscosity. The results show that using nanoparticles with higher thermal conductivities will intensify enhancement of heat transfer characteristics and slightly increases shear stress on the wall. The obtained results show more steep changes in Nusselt number for lower diameters and also higher values of Nusselt number by decreasing the diameter of nanoparticles. Also, by utilizing conduction number as the criterion, it was concluded from the results that adding nanoparticles will intensify the axial conduction effect in the geometry considered.