A mathematical investigation of a heat transfer configuration
Solutions to heat transfer problems using Laplace transform
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Solutions to heat transfer problems using Laplace transform
Combined radiation and conduction heat transfer through various high-temperature, high-porosity, unbonded (loose) fibrous insulations was modeled based on first principles. The diffusion approximation was used for modeling the radiation component of heat transfer in the optically thick insulations. The relevant parameters needed for the heat transfer model were derived from experimental data. Semi-empirical formulations were used to model the solid conduction contribution of heat transfer in fibrous insulations with the relevant parameters inferred from thermal conductivity measurements at cryogenic temperatures in a vacuum. The specific extinction coefficient for radiation heat transfer was obtained from high-temperature steady-state thermal measurements with large temperature gradients maintained across the sample thickness in a vacuum. Standard gas conduction modeling was used in the heat transfer formulation. This heat transfer modeling methodology was applied to silica, two types of alumina, and a zirconia-based fibrous insulation, and to a variation of opacified fibrous insulation (OFI). OFI is a class of insulations manufactured by embedding efficient ceramic opacifiers in various unbonded fibrous insulations to significantly attenuate the radiation component of heat transfer. The heat transfer modeling methodology was validated by comparison with more rigorous analytical solutions and with standard thermal conductivity measurements. The validated heat transfer model is applicable to various densities of these high-porosity insulations as long as the fiber properties are the same (index of refraction, size distribution, orientation, and length). Furthermore, the heat transfer data for these insulations can be obtained at any static pressure in any working gas environment without the need to perform tests in various gases at various pressures.
As part of an investigation of the cooling characteristics of liquid-cooled engines, tests were conducted with an electrically heated single-tube heat exchanger to determine the heat-transfer characteristics of an-e-2 ethylene glycol and other ethylene glycol-water mixtures. Similar tests were conducted with water and commercial butanol (n-butyl alcohol) for check purposes. The results of tests conducted at an approximately constant liquid-flow rate of 0.67 pound per second (Reynolds number, 14,500 to 112,500) indicate that at an average liquid temperature 200 degrees f, the heat-transfer coefficients obtained using water, nominal (by volume) 30 percent-70 percent and 70 percent-30 percent glycol-water mixtures are approximately 3.8, 2.8, and 1.4 times higher, respectively, than the heat-transfer coefficients obtained using an-e-2 ethylene glycol.
The ability to solve the heat conduction equation is needed when designing materials to be used on vehicles exposed to extremely high temperatures; e.g. vehicles used for atmospheric entry or hypersonic flight. When using test and flight data, computational methods such as finite difference schemes may be used to solve for both the direct heat conduction problem, i.e., solving between internal temperature measurements, and the inverse heat conduction problem, i.e., using the direct solution to march forward in space to the surface of the material to estimate both surface temperature and heat flux. The completed research first discusses the methods used in developing a computational code to solve both the direct and inverse heat transfer problems using one dimensional, centered, implicit finite volume schemes and one dimensional, centered, explicit space marching techniques. The developed code assumed the boundary conditions to be specified time varying temperatures and also considered temperature dependent thermal properties. The completed research then discusses the results of analyzing temperature data measured while radiantly heating a carbon/carbon specimen up to 1920 F. The temperature was measured using thermocouple (TC) plugs (small carbon/carbon material specimens) with four embedded TC plugs inserted into the larger carbon/carbon specimen. The purpose of analyzing the test data was to estimate the surface heat flux and temperature values from the internal temperature measurements using direct and inverse heat transfer methods, thus aiding in the thermal and structural design and analysis of high temperature vehicles.
The most important heat-transfer process in the ash flow under consideration is heat convection. Besides the four important nondimensional parameters of isothermal ash flow (Pai et al., 1972), we have three additional important nondimensional parameters: the ratio of the specific heat of the gas, the ratio of the specific heat of the solid particles to that of gas, and the Prandtl number. We reexamine the one dimensional steady ash flow discussed by Pai et al. (1972) by including the effects of heat transfer. Numerical results for the pressure, temperature, density of the gas, velocities of gas and solid particles, and volume fraction of solid particles as function of altitude for various values of the Jeffreys number, initial velocity ratio, and two different gas species (steam and hydrogen) are presented.
Local convective heat transfer coefficients were measured from a smooth NACA 0012 airfoil having a chord length of 0.533 m. Flight data were taken for the smooth airfoil at Reynolds numbers based on chord in the range 1.24 to 2.50 million and at various angles of attack up to 4 deg. During these flight tests, the freestream velocity turbulence intensity was found to be very low. Wind tunnel data were acquired in the Reynolds number range 1.20 to 4.52 million and at angles of attack from -4 to +8 deg. The turbulence intensity in the IRT was 0.5-0.7 percent with the cloud-generating sprays off. A direct comparison between the results obtained in flight and in the IRT showed that the higher level of turbulence intensity in the IRT had little effect on the heat transfer for the lower Reynolds numbers but caused a moderate increase in heat transfer at the higher Reynolds numbers. Turning on the cloud-generating spray nozzle atomizing air in the IRT did not alter the heat transfer. The present data were compared with leading-edge cylinder and flat plate heat transfer correlations that are often used to estimate airfoil heat transfer in computer codes.
Coaxial flow heat transfer - radiation integral evaluation for assumed temperature distributions
Pool boiling heat transfer improvements with enhanced surfaces have been extensively studied for various hydrofluorocarbon (HFC) refrigerants. However, there is a limited number of studies in the open literature that focus on the pool boiling heat transfer characteristics of hydrofluoroolefin (HFO) refrigerants on enhanced surfaces. This study aims to address this gap by analyzing the pool boiling behavior of HFO refrigerants, specifically R1234yf and R1234ze(E). Experiments were conducted on both plain surfaces and novel inverted trapezoid microgroove structures. Further, the experimental results indicate that the microgroove structures can improve heat transfer coefficients by up to 80% compared to plain surfaces. Additionally, the performance of R1234yf and R1234ze(E) was compared to that of R134. It was observed that R1234yf exhibited comparable performance to R134a, while R1234ze(E) showed slightly lower performance. To assess the influence of saturation temperature on pool boiling heat transfer, tests were conducted at different saturation temperatures of 15℃, 25℃, and 35℃. The findings revealed that the pool boiling heat transfer coefficient increases with rising saturation temperature.
The lack of accurate submodels for in-cylinder radiation and heat transfer has been identified as a key shortcoming in developing truly predictive, physics-based computational fluid dynamics (CFD) models that can be used to develop and design combustion systems for advanced high-efficiency, low-emissions engines. Measurements of wall boundary layers in engines show discrepancies of up to 100% with respect to standard CFD boundary layer models. And analysis of in-cylinder radiation based on the most recent spectral property databases and high-fidelity radiative transfer equation solvers has shown that at operating pressures and exhaust-gas recirculation levels typical of modern compression-ignition truck engines, molecular gas radiation (mainly carbon dioxide and water vapor) can be more important than soot particle radiation, and that a significant fraction of the emitted radiation (50% or more) can be reabsorbed before reaching the walls, thereby acting to redistribute energy in the combustion chamber. In this project, an integrated experimental and simulation approach has been used to generate new physical insight into in-cylinder heat-transfer processes in engines, and to develop computationally practicable CFD-based models that accurately represent the physics. New experimental data have been taken in an optically accessible single-cylinder research engine, and in a multi-cylinder production engine. Those data have provided new insight into the radiative environment in engines. New CFD models have been developed and validated for in-cylinder heat transfer, focusing mainly on radiative heat transfer and coupling between turbulent boundary layer wall heat transfer and radiative heat transfer. The CFD models have been developed and implemented in an open-source software framework that can be shared with other researchers. The models are compatible both with unsteady Reynolds-averaged Navier Stokes (URANS) formulations and with large-eddy simulations (LES) of in-cylinder processes in engines.
This study is the culmination of a long-term collaborative effort between researchers from the Purdue University Boiling and Two-Phase Flow Laboratory (PU-BTPFL) and the NASA Glenn Research Center to investigate gravitational effects on flow boiling and flow condensation. The science and design concepts for this large-scale effort were initiated in 2011 and included several studies detailing various aspects of two-phase fluid physics in both Earth gravity and microgravity, culminating in construction of the large-scale experimental facility named “Flow Boiling and Condensation Experiment (FBCE)”. The experiment was launched to the International Space Station (ISS) in August 2021. Following the successful installation of FBCE, equipped with the Flow Boiling Module (FBM), onboard the ISS and completion of several safety checks, flow boiling experiments were performed for five months from February 2022 until July 2022. This resulted in a large flow boiling database covering broad ranges of operating parameters and heating configurations spanning several research objectives. This study investigates microgravity flow boiling of n-perfluorohexane with subcooled inlet in a single-side-heated rectangular channel of dimensions 114.6-mm heated length, 2.5-mm heated width, and 5.0-mm height. Key operating parameters investigated are mass velocity (199.90 – 3200.13 kg/m 2 s), inlet subcooling (0.10 – 45.76°C), and inlet pressure (113.30 – 164.29 kPa). Images and image sequences acquired via high-speed-video are presented to elucidate the interfacial flow physics. To analyze and explain the effects of various parameters in microgravity, heat transfer results are presented as flow boiling curves, streamwise profiles of wall temperature and heat transfer coefficient, and parametric trends of local and averaged heat transfer coefficient. Mass velocity and inlet subcooling significantly influenced most of the aforementioned aspects of flow boiling, whereas effects of inlet pressure were comparatively insignificant. Although the data and observed flow physics might be different, the parametric effects and trends in microgravity are similar to vertical upflow in Earth gravity. Some cases, especially low mass velocities, high heat fluxes, and large degrees of inlet subcooling, experienced temporally anomalous flow behaviors caused by two-phase flow instabilities manifesting as flow reversals and resulted in deviations in overall trends. Severe thermodynamic non-equilibrium is observed throughout the channel. Overall, FBCE’s ISS experiments were successful for subcooled inlet with single-sided heating of rectangular channel, and the collected data well established the various effects on flow boiling physics in highly controlled long-term microgravity conditions.
Superposition techniques are used to calculate the rate of heat transfer from a flat plate to a turbulent incompressible boundary layer for several cases of variable surface temperature. The predictions of a number of these calculations are compared with experimental heat- transfer rates, and good agreement is obtained. A simple computing procedure for determining the heat-transfer rates from surfaces with arbitrary wall-temperature distributions is presented and illustrated by two examples. The inverse problem of determining the temperature distribution from an arbitrarily prescribed heat flux is also treated, both experimentally and analytically.
Superposition techniques are used to calculate the rate of heat transfer from a flat plate to a turbulent incompressible boundary layer for several cases of variable surface temperature. The predictions of a number of these calculations are compared with experimental heat-transfer rates, and good agreement is obtained. A simple computing procedure for determining the heat-transfer rates from surfaces with arbitrary wall-temperature distributions is presented and illustrated by two examples. The inverse problem of determining the temperature distribution from an arbitrarily prescribed heat flux is also treated, both experimentally and analytically.
Internal heat source effect on heat transfer for turbulent liquid metal flow between parallel plates
The NASA Glenn Research Center General Multi-Block Navier-Stokes Convective Heat Transfer Code, Glenn-HT, has been used extensively to predict heat transfer and fluid flow for a variety of steady gas turbine engine problems. Recently, the Glenn-HT code has been completely rewritten in Fortran 90/95, a more object-oriented language that allows programmers to create code that is more modular and makes more efficient use of data structures. The new implementation takes full advantage of the capabilities of the Fortran 90/95 programming language. As a result, the Glenn-HT code now provides dynamic memory allocation, modular design, and unsteady flow capability. This allows for the heat-transfer analysis of a full turbine stage. The code has been demonstrated for an unsteady inflow condition, and gridding efforts have been initiated for a full turbine stage unsteady calculation. This analysis will be the first to simultaneously include the effects of rotation, blade interaction, film cooling, and tip clearance with recessed tip on turbine heat transfer and cooling performance. Future plans call for the application of the new Glenn-HT code to a range of gas turbine engine problems of current interest to the heat-transfer community. The new unsteady flow capability will allow researchers to predict the effect of unsteady flow phenomena upon the convective heat transfer of turbine blades and vanes. Work will also continue on the development of conjugate heat-transfer capability in the code, where simultaneous solution of convective and conductive heat-transfer domains is accomplished. Finally, advanced turbulence and fluid flow models and automatic gridding techniques are being developed that will be applied to the Glenn-HT code and solution process.
Experimental data on pressure distribution and heat transfer on a turbine airfoil were obtained over a range of Reynolds numbers from 0.75 to 7.5 million and a range of turbulence intensities from 1.8 to about 15 percent. Fundamental heat transfer and pressure distribution data are obtained over a wide range of high Reynolds numbers and to extend the heat transfer data base to include the range of Reynolds numbers encountered in the SSME turbopump turbines. The results obtained indicated that Reynolds number and turbulence intensity have a large effect on both the transition from laminar to turbulent flow and the resulting heat transfer. For a given turbulence intensity, heat transfer for all Reynolds numbers at the leading edge can be correlated with the Frossling number developed for lower Reynolds numbers. For a given turbulence intensity, heat transfer for the airfoil surfaces downstream of the leading edge can be approximately correlated with a dimensionless parameter. Comparison of the experimental results were also made with a numerical solution from a 2D Navier-Stokes code.
Practical application of flow boiling to ground- and space-based thermal management systems hinges on the ability to predict the systems heat removal capabilities under expected operating conditions. Research in this field has shown that the heat transfer coefficient within two-phase heat exchangers can be largely dependent on the experienced flow regime. This finding has inspired an effort to develop mechanistic heat transfer models for each flow pattern which are likely to outperform traditional empirical correlations. As a contribution to the effort, this work aimed to identify the heat transfer mechanisms for the slug flow regime through analysis of individual Taylor bubbles.An experimental apparatus was developed to inject single vapor Taylor bubbles into co-currently flowing liquid HFE 7100. The heat transfer was measured as the bubble rose through a 6 mm inner diameter heated tube using an infrared thermography technique. High-speed flow visualization was obtained and the bubble film thickness measured in an adiabatic section. Experiments were conducted at various liquid mass fluxes (43-200 kgm2s) and gravity levels (0.01g-1.8g) to characterize the effect of bubble drift velocityon the heat transfer mechanisms. Variable gravity testing was conducted during a NASA parabolic flight campaign.Results from the experiments showed that the drift velocity strongly affects the hydrodynamics and heat transfer of single elongated bubbles. At low gravity levels, bubbles exhibited shapes characteristic of capillary flows and the heat transfer enhancement due to the bubble was dominated by conduction through the thin film. At moderate to high gravity, traditional Taylor bubbles provided small values of enhancement within the film, but large peaks in the wake heat transfer occurred due to turbulent vortices induced by the film plunging into the trailing liquid slug. Characteristics of the wake heat transfer profiles were analyzed and related to the predicted velocity field. Results were compared and shown to agree with numerical simulations of colleagues from EPFL, Switzerland.In addition, a preliminary study was completed on the effect of a Taylor bubble passing through nucleate flow boiling, showing that the thinning thermal boundary layer within the film suppressed nucleation, thereby decreasing the heat transfer coefficient.
An electrochemical heat transfer device for a hot water tank utilizes an electrochemical hydrogen compressor to pump hydrogen into and out of a tank having a metal hydride forming alloy therein. The absorption of hydrogen by the metal hydride forming alloy is exothermic, produces heat, and the desorption of the hydrogen from the metal hydride forming alloy is endothermic and draws heat in. An electrochemical hydrogen compressor may be configured between to tanks and pump hydrogen back and forth to form a heat transfer device, such as a hot water heater. A heat transfer device may be coupled with the tank or may comprise the outer surface of the tank to transfer heat to an object or to the surroundings. A closed loop may be configured having two tanks and one or two electrochemical hydrogen compressors to pump the hydrogen in a loop around the system.
A computational approach to modeling transient, compressible fluid flow with heat transfer in long, narrow ducts is presented. The primary application of the model is for analyzing fluid flow and heat transfer in solid propellant rocket motor nozzle joints during motor start-up, but the approach is relevant to a wide range of analyses involving rapid pressurization and filling of ducts. Fluid flow is modeled through solution of the spatially one-dimensional, transient Euler equations. Source terms are included in the governing equations to account for the effects of wall friction and heat transfer. The equation solver is fully-implicit, thus providing greater flexibility than an explicit solver. This approach allows for resolution of pressure wave effects on the flow as well as for fast calculation of the steady-state solution when a quasi-steady approach is sufficient. Solution of the one-dimensional Euler equations with source terms significantly reduces computational run times compared to general purpose computational fluid dynamics packages solving the Navier-Stokes equations with resolved boundary layers. In addition, conjugate heat transfer is more readily implemented using the approach described in this paper than with most general purpose computational fluid dynamics packages. The compressible flow code has been integrated with a transient heat transfer solver to analyze heat transfer between the fluid and surrounding structure. Conjugate fluid flow and heat transfer solutions are presented. The author is unaware of any previous work available in the open literature which uses the same approach described in this paper.