Axial Heat Conduction Research Articles

CFD analysis of high frequency miniature pulse tube refrigerators for space applications with thermal non-equilibrium model

High frequency, miniature, pulse tube cryocoolers are extensively used in space applications because of their simplicity. Parametric studies of inertance type pulse tube cooler are performed with different length-to-diameter ratios of the pulse tube with the help of the FLUENT (R) package. The local thermal non-equilibrium of the gas and the matrix is taken into account for the modeling of porous zones, in addition to the wall thickness of the components. Dynamic characteristics and the actual mechanism of energy transfer in pulse are examined with the help of the pulse tube wall time constant. The heat interaction between pulse tube wall and the oscillating gas, leading to surface heat pumping, is quantified. The axial heat conduction is found to reduce the performance of the pulse tube refrigerator. The thermal non-equilibrium predicts a higher cold heat exchanger temperature compared to thermal equilibrium. The pressure drop through the porous medium has a strong non-linear effect due to the dominating influence of Forchheimer term over that of the linear Darcy term at high operating frequencies. The phase angle relationships among the pressure, temperature and the mass flow rate in the porous zones are also important in determining the performance of pulse tuberefrigerator.

Conjugate forced convection and heat conduction in circular microchannels

The effects of axial heat conduction in the solid walls of microchannels of circular cross-sections are analyzed here. A systematic approach is adopted, with the aim of pointing out the influence of geometrical parameters and of solid wall thermal conductivity on microchannel heat transfer. The reliability of a commonly adopted criterium, based on the so-called axial conduction number, to assess the relevance of axial heat conduction is also discussed. Numerical simulations concern the simultaneously developing laminar flow of a constant property fluid in microchannels of different length, wall thickness and wall material, heated with a uniform heat flux at the outer surface, for different values of the Reynolds number. Moreover, since often in experimental tests the two end sections of the microchannel wall are not perfectly insulated, the effects of heat losses through these sections are also considered. A hybrid finite element procedure, which implies the step-by-step solution of the parabolized momentum equations in the fluid domain, followed by the solution of the energy equation in the entire domain, corresponding to both the solid and the fluid parts, is used for the numerical simulations.

Discussion: “Design Improvements to a Biomass Stirling Engine Using Mathematical Analysis and 3D CFD Modeling” (Mahkamov, K., 2006, ASME J. Energy Resour. Technol., 128, pp. 203–215)

Discussion: “Design Improvements to a Biomass Stirling Engine Using Mathematical Analysis and 3D CFD Modeling” (Mahkamov, K., 2006, ASME J. Energy Resour. Technol., 128, pp. 203–215)

Viscous dissipation effects on parallel plates with constant heat flux boundary conditions

This paper investigates basic analytical expressions for Nusselt number with the effect of viscous dissipation on the heat transfer between infinite fixed parallel plates, where the focus is on hydro-dynamically and thermally fully developed flow of a Newtonian fluid with constant properties, neglecting the axial heat conduction. Thermal boundary conditions considered are: both the plates kept at different constant heat fluxes, both the 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.

An experimental and numerical study of forced convection in a microchannel with negligible axial heat conduction

Experiments are conducted for laminar forced convection of water in a microchannel under partially-heated and fully-heated conditions on one wall with negligible axial heat conduction. The microchannel had a trapezoidal cross-sectional shape, with a hydraulic diameter of 155 μm and a heating length of 30 mm. Three-dimensional numerical simulations, based on the Navier–Stokes equations and energy equation, are obtained for forced convection of water in this microchannel under the same experimental conditions. It is found that the numerical predictions of wall temperatures and local Nusselt numbers are in good agreement with experimental data. This confirms that classical Navier–Stokes and energy equations are valid for the modeling of convection in a microchannel having a hydraulic diameter as small as 155 μm. For a microchannel with the same cross-sectional shape with one-wall heated and a heating length of 100 mm, numerical results show that the thermal entrance length is given by z = 0.15RePrD h, with the fully-developed Nusselt number approaching a constant value of 4.00.

Flush-Mounted Steady-Periodic Heated Film With Application to Shear-Stress Measurement

Surface-mounted heated films have been used for fluid-flow measurement for many years. Recently unsteady heating of such surface films has been explored experimentally. In this paper steady-periodic heating of a surface-mounted film is studied analytically. Wall effects and axial heat conduction in the fluid are included. The temperature is found as an exact integral expression constructed from separate Green’s function formulations in the fluid flow and in the solid wall that are matched at the fluid-solid interface. Results for temperature, obtained by quadrature, are reported for several flow speeds and several steady-periodic frequencies. The results show that steady-periodic heating has potential for shear-stress measurement because the heating frequency may be tuned to maximize the temperature response at the shear stress of interest. Thermal calibration of these sensors is discussed, and simulated calibration curves are given.

Axial heat conduction effects in the entrance region of circular ducts

This paper describes the transport of thermal energy within a small distance after an abrupt wall temperature change in a circular duct. In general, the axial conduction becomes significant when the Peclet number is small. The results indicate that the inclusion of axial conduction in the fluid substantially increases the wall heat flux at near the thermal inlet location. The exact series solution leads to a modified Graetz type problem. This exact solution is augmented by an asymptotic solution describing the wall heat flux near the thermal entrance location.

Axial heat conduction effects in the entrance region of parallel plate ducts

Exact series solutions for the computation of temperature in parallel plate channels and circular passages are well known. The inclusion of the contribution of axial conduction leads to a set of modified Graetz type problems for these fluid passages. The emphasis of this paper is the study of the asymptotic variations of wall heat flux values adjacent to the thermal entrance location for parallel plate ducts. The acquired results show interesting variations for different values of the Peclet number near the thermal entrance location. This study reports the unique variations of the wall heat flux values near the location where the wall temperature changes as the Peclet number changes.

Parametric Study of Solid-Phase Axial Heat Conduction in Thermally Integrated Microchannel Networks

A parametric study is presented to highlight design challenges of thermally integrated microchannel networks for portable chemistry and/or fuels reforming. One-dimensional modeling analysis of heat transfer in a two-fluid system is presented for the case of (i) two nonreacting fluids (heat exchanger), (ii) a single exothermic reacting fluid and a second nonreacting fluid (regenerative combustor), and (iii) one exothermic reacting fluid and a second endothermic reacting fluid (heat exchanger reactor). In each case, the influence of solid-phase thermal conductivity and thermal packaging upon thermal efficiency, reaction conversion, and steady-state multiplicity is investigated. Results demonstrate the importance of both packaging and solid-phase axial thermal conduction upon system performance, with optimal performance obtained using low thermal conductivity substrates. Modeling analysis predicts steady-state multiplicity when employing low thermal conductivity materials, illustrating the need for future de...

Theoretical and Experimental Methods for the Sensible Effectiveness of Air-to-Air Energy Recovery Wheels

This paper compares a new theoretical method with three other methods to determine the sensible effectiveness of energy wheels. The methods in this study include a new theoretical transient response prediction method, the standard steady state test method, a simulation or correlation method, and a transient response test method. The fully developed flow theoretical model includes sensible effectiveness corrections for effects due to entrance, axial heat conduction, carryover due to wheel rotation, phase change of water vapor, and flow channel variations due to manufacturing tolerances. All of these effectiveness correction factors are presented as dimensionless ratios that will be convenient to use for designers of energy wheels and HVAC systems. Comparison of the four methods shows agreement for typical summer and winter operating conditions. It is concluded that the new transient theoretical correction method gives a sensible effectiveness that is as least as accurate as the test methods. Only the transient theoretical model and simulations correctly predict the effects of controlled wheel speeds.

Axial heat conduction in a moving semi-infinite fluid

This paper considers the steady state conduction of heat from a wall to a fluid moving at a uniform velocity. The wall is heated by a step change in temperature. Although this appears to be a classical heat conduction problem, its application to various convective heat transfer problems is new. The mathematical procedure leads to the computation of the temperature field and the heat transfer coefficient. In the presence of a step change in the wall temperature, it is shown that the Stanton number is a function of the Peclet number alone. The acquired analytical results show that, near the thermal entrance location, heat conduction dominates and the local heat flux becomes independent of velocity. This phenomenon applies to classical convection problems in various-shaped ducts.

A comparative study of H2-air premixed flame in micro combustors with different physical and boundary conditions

A numerical study of H2-air premixed combustion in the micro channels with a detailed chemical reaction mechanism is performed by solving the two-dimensional fully elliptic governing equations of continuity, momentum, energy and species, coupled with the energy equation in the solid wall. A reference case is defined as the combustion in a cylindrical tube with 0.8 mm inner diameter and 8 mm length with a non-slip wall and a uniform velocity profile at the inlet plane. Different physical and boundary conditions have been applied in order to investigate their respective effects on the flame temperature. The conditions studied in the current paper include the combustor size and geometry, inlet velocity profile, axial heat conduction in the solid wall and slip-wall and temperature jump at the gas–solid interface. It is noted that effects of Knudsen number (slip-wall and temperature jump) on the thermal and fluid field are not very significant in a d = 0.4 mm micro combustor. Furthermore, the qualitative effects of Knudsen number on the flame temperature are analysed. The results of this paper indicate that these various boundary and physical conditions have effects on the flame temperature to different extent and should be carefully monitored when applied for different applications.

Closure to “Discussion: ‘Design Improvements to a Biomass Stirling Engine Using Mathematical Analysis and 3D CFD Modeling’ ” (2007, ASME J. Energy Resour. Technol., 129, pp. 278, 279, 280)

Closure to “Discussion: ‘Design Improvements to a Biomass Stirling Engine Using Mathematical Analysis and 3D CFD Modeling’ ” (2007, ASME J. Energy Resour. Technol., 129, pp. 278, 279, 280)

An analytical solution to non-axisymmetric heat transfer with viscous dissipation for non-Newtonian fluids in laminar forced flow

Forced convection heat transfer in a non-Newtonian fluid flow inside a pipe whose external surface is subjected to non-axisymmetric heat loads is investigated analytically. Fully developed laminar velocity distributions obtained by a power-law fluid rheology model are used, and viscous dissipation is taken into account. The effect of axial heat conduction is considered negligible. The physical properties are assumed to be constant. We consider that the smooth change in the velocity distribution inside the pipe is piecewise constant. The theoretical analysis of the heat transfer is performed by using an integral transform technique – Vodicka’s method. An important feature of this approach is that it permits an arbitrary distribution of the surrounding medium temperature and an arbitrary velocity distribution of the fluid. This technique is verified by a comparison with the existing results. The effects of the Brinkman number and rheological properties on the distribution of the local Nusselt number are shown.

Numerical investigation of wall heat conduction effects on catalytic combustion in split and continuous monolith tubes

The optimum length of a monolith tube is one for which near-hundred percent conversion is attained, and at the same time, the catalyst over the entire length of the tube is utilized. In practice, the length is adjusted by stacking monolith plugs end-to-end. In this study, the repercussions of such a practice are investigated numerically with the goal to determine if a tube of length 2 L demonstrates the same behavior as two tubes of length L each, stacked end-to-end. Catalytic combustion of methane–air mixture on a platinum catalyst is considered. The studies are conducted using a multi-step reaction mechanism involving 24 surface reactions between 19 species. Two different materials are considered for the walls of the monolith tube, namely silicon carbide and cordierite. Both steady state and transient simulations are performed. Results indicate that the ignition and blowout limits can be significantly different between split and continuous tubes when the wall is made up of a high thermal conductivity material, such as silicon carbide. For steady state combustion, for both wall materials, the point of attachment of the flame to the wall is altered by splitting the tube—the effect being more pronounced for silicon carbide and at relatively high Reynolds numbers. These results imply that axial heat conduction, or lack thereof due to thermal contact resistance, through the walls of the monolith results in thermal non-equilibrium between the solid and fluid phase, and subsequently affects ignition and flame stability in catalytic combustion.

Experimental and numerical studies of liquid flow and heat transfer in microtubes

Experimental and numerical studies were conducted to reveal the flow and heat transfer characteristics of liquid laminar flow in microtubes. Both the smooth fused silica and rough stainless steel microtubes were used with the hydraulic diameters of 50–100 μm and 373–1570 μm, respectively. For the stainless steel tubes, the corresponding surface relative roughness was 2.4%, 1.4%, 0.95%. The experiment was conducted with deionized water at the Reynolds number from 20 to 2400. The experimental data revealed that the friction factor was well predicted with conventional theory for the smooth fused silica tubes. For the rough stainless steel tubes, the friction factor was higher than the prediction of the conventional theory, and increased as the surface relative roughness increased. The results also confirmed that the conventional friction prediction was valid for water flow through microtube with a relative surface roughness less than about 1.5%. The experimental results of local Nusselt number distribution along the axial direction of the stainless steel tubes do not accord with the conventional results when Reynolds number is low and the relative thickness of the tube wall is high. The numerical study reveals that the large ratio of wall thickness over tube diameter in low Reynolds number region causes significant axial heat conduction in the tube wall, leading to a non-linear distribution of the fluid temperature along the axial direction. The axial heat conduction effect is gradually weakened with the increase of Reynolds number and the decrease of the relative tube wall thickness and thus the local Nusselt number approaches the conventional theory prediction.

Experimental investigation on heat transfer characteristics of water flow in a narrow annulus

Experiments are carried out to investigate the convection heat transfer characteristics of water flow in a narrow annulus. The experiments include three flow directions, which are horizontal flow, upward flow and downward flow. Experimental results show that the heat transfer characteristics of single-phase water flow in the narrow annulus are different from those in circular tubes. The transition from the laminar to turbulent heat transfer in the narrow annulus is earlier than that in circular tubes. When the Reynolds number is lower than 150, the axial heat conduction has an important influence on the overall heat transfer and the heat transfer deteriorates here. Two techniques, i.e. measuring wall temperature and separating coefficient, were adopted in processing the experimental data. The results obtained by these two data processing techniques are different, especially when the Reynolds number is lower than 400. The differences between these two techniques are analyzed.

Effect of developing flow and thermal regime on momentum and heat transfer in micro-scale heat sink

A developing micro-channel heat transfer and fluid flow has been investigated experimentally in rectangular micro-channels of D h = 440 μm, having water as a working fluid. Infrared technique was used to design and built a micro-channel test section that incorporate internal fluid temperature measurements. The new method that provides information about the fluid temperature distribution inside the channel and provides validation for the methods used to determine the local and average Nusselt numbers. The experimental results have been compared with theoretical predictions from the literature and results obtained by numerical modeling of the present experiment. The experimental results of pressure drop and heat transfer confirm that including the entrance effects, the conventional theory is applicable for water flow through micro-channels. These results differ from the conclusions of several researches. It was shown that data presented by some researches can be due to entrance effects. The present results highlight the importance of accounting for common phenomena that are often negligible for standard flows such as accounting for profile of inlet velocity, axial heat conduction, effect of the design inlet and outlet manifolds. This paper, to the best of knowledge, is the first presentation on the method of the bulk fluid temperature measurements along micro-channel using IR technique, and calculation of the local heat transfer coefficient based on the local heat flux and the local temperature difference between the heated wall and the bulk fluid temperature.

Axial Symmetric Stationary Heat Conduction Analysis on Functional Gradient Materials by Triple-Reciprocity BEM

Homogeneous heat conduction can be easily solved by means of the boundary element method. However, domain integrals are generally necessary to solve the heat conduction problem in the functional gradient materials (FGM). This paper shows that the axial symmetric stationary heat conduction problem in the functional gradient materials can be solved approximately without a domain integral by the triple-reciprocity boundary element method. In this method, the distribution of domain effects is interpolated by integral equations. A new computer program is developed and applied to several problems.

The effect of wall conduction for the extended Graetz problem for laminar and turbulent channel flows

Axial heat conduction effects within the fluid can be important for duct flows if either the Prandtl number is relatively low (liquid metals) or if the dimensions of the duct are small (micro heat exchanger). In addition, axial heat conduction effects in the wall of the duct might be of importance. The present paper shows an entirely analytical solution to the extended Graetz problem including wall conduction (conjugate extended Graetz problem). The solution is based on a selfadjoint formalism resulting from a decomposition of the convective diffusion equation into a pair of first order partial differential equations. The obtained analytical solution is relatively simple to compute and valid for all Péclet numbers. The analytical results are compared to own numerical calculations with FLUENT and good agreement is found.