Axial Heat Conduction Research Articles

Size effect on single-phase channel flow and heat transfer at microscale

The size effects on microscale single-phase fluid flow and heat transfer are reviewed and discussed. The physical mechanisms for the size effects on the microchannel flow and heat transfer were divided into two classifications: (a) The gas rarefaction effect occurs when the continuum assumption breaks down as the characteristic length of the flow becomes comparable to the mean free path of the molecules; (b) Variations of the predominant factors influence the relative importance of various phenomena on the flow and heat transfer as the characteristic length decreases, even if the continuum assumption is still valid. Due to the larger surface to volume ratio for microchannels, factors related to surface area have more impact to the microscale flow and heat transfer. Among them are: The surface friction induced flow compressibility in microchannels makes the fluid velocity profiles flatter and leads to higher friction factors and Nusselt numbers; The surface roughness of the microchannel is likely responsible for the early transition from laminar to turbulent flow and the increased friction factor and Nusselt number; The importance of viscous force in natural convection modifies the correlation between Nu and Ra for natural convection in a microenclosure and, other effects, such as the axial heat conduction in the channel wall, the channel surface geometry, and measurement errors as well, could lead to different flow and heat transfer behaviors from that at conventional scales.

The extended Graetz problem with piecewise constant wall heat flux for laminar and turbulent flows inside concentric annuli

In the present paper, the heat transfer characteristics in the thermal entrance region of concentric annuli have been analysed for laminar and turbulent internal flow. Axial heat conduction effects in the fluid have been taken into account. The present paper shows an exact analytical solution for the problem of a piecewise uniform wall heat flux. The obtained analytical solution for the extended Graetz problem is as simple and efficient to compute as the related solution of the parabolic problem. The obtained results show the effect of axial heat conduction in the fluid for a semi-infinite heated section as well as for a finite length of the heated section. It is shown, that for a finite length of the heated section, axial heat conduction effects might be important even for higher Peclet number.

Strategies for size reduction of microreactors by heat transfer enhancement effects

One of the likely aims of reactor miniaturization in the field of chemical production and energy generation is to increase the conversion to the desired product and the selectivity of the process through better control of heat and mass transfer. In addition to the effects related to miniaturization, a further increase of the transfer coefficients is achieved by applying microstructuring techniques. In this context, three different approaches for heat transfer enhancement in miniaturized reaction systems are presented. The ideas put forward rely on entrance flow effects, inertial flows in meandering channels, and suppression of axial heat conduction. Among these ideas the entrance flow effect, realized by an arrangement of microfins with a typical dimension of a few hundred micrometers, provides the most efficient heat transfer. It is found that a heat transfer enhancement of at least one order of magnitude can be achieved compared to unstructured channels. On this basis, a miniaturized heat-exchanger reaction system is investigated, where a kinetic model of an endothermic, heterogeneously catalyzed gas-phase reaction is used. The miniaturized heat-exchanger reactor, both with and without heat transfer enhancement, is subsequently benchmarked against conventional fixed-bed technology. It is shown that, for the reaction system under study, a substantial reduction of the required amount of catalyst can be achieved in microsystems.

Transient analysis of the conjugated heat transfer in circular ducts with a power-law fluid

The transient analysis of a conjugated heat transfer process in the thermal entrance region of a circular tube with a fully developed laminar power-law fluid flow, is studied. This conjugated heat transfer process is characterized by the simultaneous thermal interaction between the wall tube and the adjacent thermal boundary layer of the power-law fluid. We apply the quasi-steady approximation for the power-law fluid, identifying the suitable time scales of the process. Thus, the energy equation in the fluid is solved analytically using the well-known integral boundary layer technique. This solution is coupled to the transient energy equation for the solid where the axial heat conduction effects are taken into account. The governing equation is reduced to a integro-differential equation which is solved by muliple-scale analysis and a conventional numerical technique. The results for the temperature of the wall tube and the corresponding average temperature are plotted for differents parameters such as conduction parameter, α, the aspect ratios of the tube, ε and ε 0 and the index of power-law fluid, n.

Laminar Heat Transfer With Viscous Dissipation and Fluid Axial Heat Conduction for Modified Power Law Fluids Flowing in Parallel Plates With One Plate Moving

Using the fully developed laminar velocity distributions obtained by applying the modified power-law model proposed by Irvine and Karni, the thermal-entrance-region heat transfer of non-Newtonian fluids flowing in parallel plates with one plate moving is investigated taking into account both viscous dissipation and fluid axial heat conduction for two kinds of thermal boundary conditions, namely, constant temperature and constant heat flux at the moving wall. The energy equation subject to a constant temperature at upstream infinity, fully developed temperature profile at downstream infinity and the appropriate thermal boundary conditions at the upper and lower walls is numerically solved by the finite difference method as an elliptic type problem. The effects of the moving plate velocity, rheological properties, Brinkman number and Peclet number on the temperature distribution and Nusselt numbers are discussed for both Newtonian and pseudoplastic fluids

H113 単層カーボンナノチューブの接触熱抵抗

Molecular dynamics simulations of heat transfer between nanotubes in a bundle of 7 SWNTs were performed. Initially, whole system was kept at 300 K for 100 ps. Then, the temperature of only the center SWNT was suddenly heated up to 1000 K and temperature control was stopped. By monitoring the temperature of each SWNT, heat transfer from the center nanotube to surrounding nanotubes were calculated. We found that this heat transfer rate was well characterized by the thermal boundary resistance (TBR) between nanotubes. TBR value was estimated to be 1.0×(10)^<-7> m^2K/W. We have defined a length scale that can express the amount of TBR in comparison to the axial heat conduction. The estimated length was about 1μm.

Size effect on microscale single-phase flow and heat transfer

The present discussion will focus on the size effect induced by the variation of dominant factors and phenomena in the flow and heat transfer as the device scale decreases. Due to the larger surface to volume ratio for microchannels and microdevices, factors related to surface effects have more impact to microscale flow and heat transfer. For example, surface friction induced flow compressibility makes the fluid velocity profiles flatter and leads to higher friction factors and Nusselt numbers; surface roughness is likely responsible for the early transition from laminar to turbulent flow and the increased friction factor and Nusselt number; the relative importance of viscous force modifies the correlation between Nu and Ra for natural convection in a microenclosure and, other effects, such as channel surface geometry, surface electrostatic charges, axial heat conduction in the channel wall and measurement errors, could lead to different flow and heat transfer behaviors from that at conventional scales.

A Numerical Investigation of the Heat Transfer in a Parallel Plate Channel With Piecewise Constant Wall Temperature Boundary Conditions

For turbulent flows in ducts, streamwise heat conduction effects within the flow can be important for low Prandtl number fluids (liquid metals). The paper presents a numerical investigation of the influence of axial heat conduction within the flow on the heat transfer for hydrodynamically fully developed flow. The calculations have been carried out for a semi-infinite heated section as well as for a heated section of finite length. Additionally, by considering different models for calculating the turbulent heat flux, the normally used assumption that the eddy diffusivity in axial and normal direction are the same was investigated.

Performance study of a partitioned thermally stratified storage tank in a solar powered absorption air conditioning system

Accurate modeling of solar heating or cooling with storage generally requires an accounting of the stratification within such storage tank, since overall system performance is significantly affected by the storage temperature distribution. In this study, a simple one-dimensional multi-node approach, taking into account of the axial heat conduction between nodes, has been used to theoretically analyze temperature stratification in the thermal storage tank. The results indicate that, for less collector area, the heat removal factor plays a major role in increasing the system performance, than the thermal stratification. Also, an optimum ratio of tank volume over collector area exists for a solar powered absorption air conditioning system. This paper also reviews the state of the art on different kinds of variable inlet design, and a simple new inlet design (partitioning the tank) has been introduced to effect better thermal stratification in storage tank.

Critical analysis of heat transfer experiments in microchannels

Calculations using a standard CFD (Computational Fluid Dynamics) software were performed to investigate heat transfer characteristics in microchannels. The results were compared with published experimental data using dimensional analysis. To identify deviations between micro- and macroscale the computations took into account effects which are often neglected in macroscopic heat transfer devices, like axial heat conduction in the channel walls and entrance effects in the flow and temperature fields. The calculations indicate that analysis of experimental data has to be reconsidered taking into account these well known effects.

Heat transfer by laminar Hartmann's flow in thermal entrance region with uniform wall heat flux: the Graetz problem extended

Thermally developing laminar Hartmann flow through a parallel plate channel, with prescribed transversal uniform magnetic field, including both viscous dissipation, Joule heating and axial heat conduction with uniform heat flux, is studied analytically by using a functional analysis method. The analytical expressions for the developing temperature and local Nusselt number in the entrance region are obtained in the general case. However, the solution obtained could be applied to any developed flow with heat generation. Applications to Hagen-Poiseuille and Hartmann flows are made. The associated eigenvalues problem is solved analytically to obtain explicit forms of the eigenfunctions, which correspond to Mathieu's functions. Results show that the effects of viscous and Joule dissipation can be neglected for liquid metal, even for large values of Hartmann number M, for which the corresponding Brinkman number Br is very small. Therefore, the heat transfer characteristics in the entrance region are only influenced by Peclet and Hartmann numbers. Results show that as long as M increases, the heat transfer increases until a certain saturation is reached, for which the effect of magnetic field on Nusselt number vanishes completely. Finally, a practical empirical expression for local Nusselt number is proposed in terms of axial distance ξ and Hartmann number M.

Approche analytique de la convection forcée des fluides de Bingham dans un tube

The asymptotic behaviour of laminar forced convection for Bingham fluid in a circular tube subjected to an axially varying wall heat flux is studied analytically. The effect of viscous dissipation is taken into account while the axial heat conduction in the fluid is considered as negligible. The asymptotic temperature profile and the asymptotic Nusselt number are determined for various axial wall heat flux distributions which yield a thermally developed region. The results obtained show a diminution in asymptotic Nusselt number when the Brinkman number and the dimensionless radius of the plug flow region increase. Comparisons with the results in the literature for Newtonian fluids show the validity of the present analysis. To cite this article: R. Khatyr et al., C. R. Mecanique 330 (2002) 69–75.

Boundary condition effects on the flow stability in a toroidal thermosyphon

The toroidal thermosyphon is widely used in solar water systems, nuclear reactors and geothermal energy systems, etc. The flow stability has been the main research topic but little attention was paid to the influence of boundary conditions. An experiment was performed on a copper torus. The Lorenz-like chaotic flow was not observed in clear contrast to that in the usual glass torus. Numerical simulation showed that the axial heat conduction in the tube wall deformed the heat flux distribution. A one-dimensional model generally formulated the boundary condition effects on the Hopf bifurcation. The model suggested that the metal wall could efficiently eliminate temperature perturbation, decrease the driving force and hence stabilize the global flow. The model was also used to analyze the effect of torus tilt angle on flow stability, whose conclusion agreed with previous experiment.

Heat transfer by laminar Hartmann flow in thermal entrance region with a step change in wall temperatures: the Graetz problem extended

Thermally developing laminar Hartmann flow through a parallel-plate channel, including both viscous dissipation, Joule heating and axial heat conduction with a step change in wall temperatures, has been studied analytically. Expressions for the developing temperature and local Nusselt number in the entrance region are obtained in terms of Peclet number Pe, Hartmann number M, Brinkman number Br, under electrically insulating wall conditions, χ=−1 and perfectly conducting wall conditions, χ=0. The associated eigenvalue problem is solved by obtaining explicit forms of eigenfunctions and related expansion coefficients. We show that the nonorthogonal eigenfunctions correspond to Mathieu's functions. We propose a new asymptotic solution for the modified Mathieu's differential equation. The asymptotic eigenfunctions for large eigenvalues are also obtained in terms of Pe and M. Results show that the heat transfer characteristics in the entrance region are strongly influenced by Pe, M, Br and χ.

Conjugated heat transfer in circular ducts with a power-law laminar convection fluid flow

This work deals with the study of the steady-state analysis of conjugated heat transfer process for the thermal entrance region of a developed laminar-forced convection flow of a power-law fluid in a circular tube. A known uniform heat flux is applied at the external surface of the tube. The energy equation in the fluid is solved analytically using the integral boundary layer approximation by neglecting the heat generation by viscous dissipation and the axial heat conduction in the fluid. This solution is coupled to the Laplace equation for the solid, where the axial heat conduction effects are taken into account. The governing equations are reduced to an integro-differential equation which is solved by analytical and numerical methods. The results are shown for different parameters such as conduction parameter, α, the aspect ratio of the tube, ε and the index of power-law fluid, n.

Constant-Wall-Temperature Nusselt Number in Micro and Nano-Channels1

We investigate the constant-wall-temperature convective heat-transfer characteristics of a model gaseous flow in two-dimensional micro and nano-channels under hydrodynamically and thermally fully developed conditions. Our investigation covers both the slip-flow regime 0⩽Kn⩽0.1, and most of the transition regime 0.1&lt;Kn⩽10, where Kn, the Knudsen number, is defined as the ratio between the molecular mean free path and the channel height. We use slip-flow theory in the presence of axial heat conduction to calculate the Nusselt number in the range 0⩽Kn⩽0.2, and a stochastic molecular simulation technique known as the direct simulation Monte Carlo (DSMC) to calculate the Nusselt number in the range 0.02&lt;Kn&lt;2. Inclusion of the effects of axial heat conduction in the continuum model is necessary since small-scale internal flows are typically characterized by finite Peclet numbers. Our results show that the slip-flow prediction is in good agreement with the DSMC results for Kn⩽0.1, but also remains a good approximation beyond its expected range of applicability. We also show that the Nusselt number decreases monotonically with increasing Knudsen number in the fully accommodating case, both in the slip-flow and transition regimes. In the slip-flow regime, axial heat conduction is found to increase the Nusselt number; this effect is largest at Kn=0 and is of the order of 10 percent. Qualitatively similar results are obtained for slip-flow heat transfer in circular tubes.

The extended Graetz problem with piecewise constant wall heat flux for pipe and channel flows

Heat transfer in the thermal entrance region of a pipe or a parallel plate channel has been analysed for laminar and turbulent internal flow taking into account axial heat conduction effects in the fluid. The present paper shows an analytical solution for the problem of a piecewise uniform wall heat flux. The obtained exact analytical solutions for the extended Graetz problem are as simple and efficient to compute as the related solutions of the parabolic problem. The obtained results show the effect of axial heat conduction in the fluid for a semi-infinite as well as for a finite length of the heated sections.

The single-blow transient testing technique for plate–fin heat exchangers

A new model of the single-blow problem is proposed, considering the lateral heat conduction resistance along the fins, the axial heat conduction along the separating plates and the axial thermal dispersion in the fluid. For plate–fin heat exchangers made up of stainless steel, the effect of the lateral heat conduction resistance along the fins can usually not be neglected. This effect is taken into account by solving the temperature dynamics in the fluid, separating plates and fins simultaneously. The axial dispersion model is used to take flow maldistribution in plate–fin heat exchangers into account. The effect of the axial heat conduction in separating plates is also considered. The governing equation system is solved by means of Laplace transform and numerical inverse transform algorithms. The investigation confirms: for plate–fin heat exchangers of aluminium the effect of the lateral heat conduction resistance of fins can usually be neglected because of their high fin efficiency. However, the assumption of uniform porous medium is not valid if the plate–fin heat exchangers are made up of stainless steel. In such a case the heat conduction resistance of fins has significant influence on the outlet fluid temperature variation.

Temperature gradients in the laser‐heated diamond anvil cell

A semianalytic heat transfer model reproduces the temperature distributions measured inside the laser‐heated diamond cell and constrains the temperature dependence of the thermal conductivity of dielectric mineral samples at high pressures and temperatures. Both axial and radial heat conduction determine the observed temperature distributions obtained from the TEM00 (Gaussian) and TEM01* laser modes. Measurements on the high‐pressure perovskite‐dominated assemblage of peridotite are consistent with the expected T−1 dependence of thermal conductivity at 45 GPa and temperatures between 1500 and 3800 K.

Analysis of the conjugate effect of wall and flow parameters on pipe flow heat transfer

A combined numerical and analytical solution procedure is proposed to examine the conjugate heat transfer for laminar flow in a pipe. This simple and rather general procedure has the capability of handling the constant temperature, the constant heat flux, and the convection heat transfer boundary conditions of the pipe outer surface without detailed program modification. The results of the present work and fully analytical solution are compared to test the proposed solution procedure. The general trend of predicted results is in agreement with the analytical solution, but the quantitative differences between them is considered to be acceptable from the numerical point of view. Variation in the local Nusselt number and in the the wall and local mean fluid temperature across the axial direction is strongly dependent on the pipe wall thermal conductivity and the boundary condition at the outer surface of the pipe wall. Two non-dimensional numbers, the thermal conductivity ratio ks/ kf and the Biot number, are found to be controlling parameters for the effect of wall axial heat conduction on the heat transfer characteristics.