Heat Conduction From Circular Cylinders in Rarefied Gases

1965 ◽  
Vol 87 (4) ◽  
pp. 493-498 ◽  
Author(s):  
G. S. Springer ◽  
R. Ratonyi
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Transition Temperature ◽  
Cylindrical Surface ◽  
Temperature Jump ◽  
Circular Cylinders ◽  
Conductive Heat ◽  
Free Molecule ◽  
Thermal Accommodation ◽  
Concentric Cylinders

A method is presented for calculating the conductive heat transfer through gases contained between two concentric cylinders. The method of Lees and Liu is extended to include incomplete thermal accommodation at the inner cylindrical surface, and a comparison is made between the two methods. These results are then compared to those of the low pressure and temperature jump methods. On the basis of this analysis, limits are obtained for the free-molecule, transition, temperature jump, and continuum regimes.

EVALUATION OF COMBINED DELAUNAY TRIANGULATION AND REMESHING FOR FINITE ELEMENT ANALYSIS OF CONDUCTIVE HEAT TRANSFER

2004 ◽  
Vol 27 (4) ◽  
pp. 319-339 ◽  
Author(s):  
Sutthisak Phongthanapanich ◽  
Pramote Dechaumphai
Keyword(s):  
Heat Transfer ◽  
Finite Element ◽  
Heat Conduction ◽  
Steady State ◽  
Delaunay Triangulation ◽  
Transient Heat Conduction ◽  
Conductive Heat ◽  
Element Analysis ◽  
Adaptive Remeshing ◽  
Solution Accuracy

A finite element method is combined with the Delaunay triangulation and an adaptive remeshing technique to solve for solutions of both steady-state and transient heat conduction problems. The Delaunay triangulation and the adaptive remeshing technique are explained in detail. The solution accuracy and the effectiveness of the combined procedure are evaluated by heat transfer problems that have exact solutions. These problems include steady-state heat conduction in a square plate subjected to a highly localized surface heating, and a transient heat conduction in a long plate subjected to a moving heat source. The examples demonstrate that the adaptive remeshing technique with the Delaunay triangulation significantly reduce the number of the finite elements required for the problems and, at the same time, increase the analysis solution accuracy as compared to the results produced using uniform finite element meshes.

Design of an Experiment to Measure the Thermal Accommodation Coefficient Between Helium and Stainless-Steel in Concentric Cylinders

2015 ◽  
Author(s):  
Rachel Green ◽  
Mustafa-Hadj Nacer ◽  
Miles Greiner
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Stainless Steel ◽  
Temperature Difference ◽  
Rarefied Gas ◽  
Accommodation Coefficient ◽  
Theoretical Expression ◽  
Thermal Accommodation ◽  
Concentric Cylinders ◽  
Thermal Accommodation Coefficient

Heat transfer through a 1 mm gap between two concentric cylinders representing the gap between a fuel support basket and a canister is experimentally and numerically investigated. The objective of this work is to study rarefied gas heat transfer in a simple geometry, and to measure the thermal accommodation coefficient at the interface between stainless steel and rarefied helium. The thermal accommodation coefficient is used to characterize the interaction between gas molecules and wall at the molecular level. It is important to determine its value with precision for better determination of heat transfer at low pressure. The experimental procedure consists of measuring the temperature difference between the inner and outer cylinders as the pressure is decreased in the gap. By knowing the heat flux across the gap the thermal accommodation coefficient can be extracted from the theoretical expression relating the temperature difference to the radial heat flux. Three-dimensional simulations using the ANSYS/Fluent commercial code are conducted to assess on the design of the experimental apparatus. These simulations confirmed that the apparatus design is effective to study the heat transfer across rarefied gas and to determine the thermal accommodation coefficient for helium on stainless steel surface.

Exact Analytical Solution for Unsteady Heat Conduction in Fiber-Reinforced Spherical Composites Under the General Boundary Conditions

2015 ◽  
Vol 137 (10) ◽  
Author(s):  
A. Amiri Delouei ◽  
M. Norouzi
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Analytical Solution ◽  
Boundary Conditions ◽  
Laplace Transformation ◽  
Exact Analytical Solution ◽  
Function Technique ◽  
Conductive Heat ◽  
Fiber Reinforced ◽  
Legendre Series

The current study presents an exact analytical solution for unsteady conductive heat transfer in multilayer spherical fiber-reinforced composite laminates. The orthotropic heat conduction equation in spherical coordinate is introduced. The most generalized linear boundary conditions consisting of the conduction, convection, and radiation heat transfer is considered both inside and outside of spherical laminate. The fibers' angle and composite material in each lamina can be changed. Laplace transformation is employed to change the domain of the solutions from time into the frequency. In the frequency domain, the separation of variable method is used and the set of equations related to the coefficients of Fourier–Legendre series is solved. Meromorphic function technique is utilized to determine the complex inverse Laplace transformation. Two functional cases are presented to investigate the capability of current solution for solving the industrial unsteady problems in different arrangements of multilayer spherical laminates.

Theoretical Two-Dimensional Modeling of Gas Conduction Between Finite Parallel Plates in High Vacuum

2012 ◽  
Vol 134 (5) ◽  
Author(s):  
Taishan Zhu ◽  
Wenjing Ye
Keyword(s):  
Heat Transfer ◽  
High Vacuum ◽  
Finite Size ◽  
Direct Simulation Monte Carlo ◽  
Free Molecule ◽  
Mems Devices ◽  
Parallel Plates ◽  
Thermal Accommodation ◽  
Representative Model ◽  
Gas Conduction

A theoretical approach based on gaskinetic theory is described and applied for the modeling of steady-state free-molecule gaseous heat conduction within a diffusive enclosure. With a representative model of microelectromechanical system (MEMS) devices with integrated heaters, the heat transfer between the heated component and its gaseous ambient enclosed in a high vacuum is studied in detail. A molecular simulation based on the direct simulation Monte Carlo (DSMC) method is also employed to validate the theoretical solutions and to study the effects of incomplete thermal accommodation. The impacts of the finite size of the heated beam as well as the gap between the beam and a substrate on the heat transfer are investigated to examine the appropriateness of the common assumptions employed in the modeling of Pirani sensors. Interesting phenomena that are unique in the free-molecule regime are observed and discussed. These studies are valuable to the design of MEMS devices with microheaters.

Heat Transfer and Forces for Free-Molecule Flow on a Concave Cylindrical Surface

1964 ◽  
Vol 86 (1) ◽  
pp. 1-9 ◽  
Author(s):  
E. M. Sparrow ◽  
V. K. Jonsson ◽  
T. S. Lundgren ◽  
T. S. Chen
Keyword(s):  
Heat Transfer ◽  
Wall Temperature ◽  
Cylindrical Surface ◽  
High Speed ◽  
Angle Of Attack ◽  
Accommodation Coefficient ◽  
Free Molecule ◽  
Adiabatic Wall ◽  
The Difference ◽  
Molecule Flow

An analysis has been carried out to determine the local and overall heat-transfer rates, the adiabatic wall temperature, and the forces exerted when a high-speed, free-molecule flow is incident on a concave cylindrical surface. The flow may impinge on the surface at an arbitrary angle of attack. Additionally, the thermal accommodation coefficient may be arbitrary, and the degree of concavity of the surface may be varied at will from a semicircular cross section to a relatively flat circular arc. The concavity causes molecules to interreflect back and forth between surface elements. Even with the interreflections, the heat-transfer rate continues to depend linearly on the difference between the wall temperature and the adiabatic wall temperature. The interreflections are found to have a greater effect on both the heat transfer and the force results as the accommodation co-efficient decreases and as the degree of concavity and the angle of attack increase.

Numerical Calculations of Heat Conduction Between Soot Aggregates and the Surrounding Gas in the Free-Molecular Regime Using the DSMC Method

2005 ◽  
Author(s):  
Fengshan Liu ◽  
Min Yang ◽  
David R. Snelling ◽  
Gregory J. Smallwood
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Direct Simulation Monte Carlo ◽  
Interaction Model ◽  
Numerical Calculations ◽  
Hard Sphere Model ◽  
Sphere Diameter ◽  
Free Molecular Regime ◽  
Thermal Accommodation ◽  
Maxwell Gas

Numerical calculations were conducted to calculate the heat conduction rate between soot (carbon) aggregates of different sizes and the surrounding gas in the free-molecular regime using the direct simulation Monte Carlo method. This method is based on simulation of the trajectories of individual molecules and calculation of the heat transfer at each of the molecule/molecule collisions and the molecule/particle collisions. Soot aggregates of known fractal dimension and pre-factor are first numerically generated using a cluster-cluster aggregation algorithm. Effect of incomplete thermal accommodation was accounted for by employing the Maxwell gas-surface interaction model. Gas collisions were treated using the simple hard sphere model. Numerical results were obtained for aggregate sizes between 10 and 228 primary particles and the thermal accommodation coefficient between 0.1 and 1. A simple scaling for the heat transfer equivalent sphere diameter was also presented for incorporation into a laser-induced incandescence model.

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