Steady-State Temperature Solution for a Heat-Generating Circular Cylinder Cooled by a Ring of Holes

1964 ◽  
Vol 86 (4) ◽  
pp. 531-536 ◽  
Author(s):  
J. C. Rowley ◽  
J. B. Payne
Keyword(s):  
Heat Conduction ◽  
Steady State ◽  
Circular Cylinder ◽  
Heat Conduction Equation ◽  
Series Solution ◽  
Concentric Circle ◽  
Optimum Location ◽  
Shape Factors ◽  
Steady State Temperature ◽  
Temperature Solution

A series solution is presented to the heat-conduction equation for a heat-generating circular cylinder pierced axially by a ring of equal holes spaced uniformly on a concentric circle. The solution is based upon a class of potential functions previously defined by Howland. Typical nondimensional curves for peak and average temperatures and optimum location of the ring of holes for uniform convective cooling are presented. In addition, some shape factors or conductances for the geometry are given.

Analytical Solution to Steady-State Heat-Conduction Problems With Irregularly Shaped Boundaries

1971 ◽  
Vol 93 (4) ◽  
pp. 449-454 ◽  
Author(s):  
D. M. France
Keyword(s):  
Heat Conduction ◽  
Steady State ◽  
Analytical Solution ◽  
Least Squares ◽  
Series Solution ◽  
Point Matching ◽  
State Heat ◽  
Temperature Heat ◽  
Steady State Heat ◽  
Least Squares Approach

A method of obtaining an analytical solution to two-dimensional steady-state heat-conduction problems with irregularly shaped boundaries is presented. The technique of obtaining the coefficients to the series solution via a direct least-squares approach is compared to the “point-matching” scheme. The two methods were applied to problems with known solutions involving the three heat-transfer boundary conditions, temperature, heat flux, and convection coefficient specified. Increased accuracy with substantially fewer terms in the series solution was obtained via the least-squares technique.

Study on Radial Temperature Distribution of Aluminum Dispersed Nuclear Fuels: U3O8-Al, U3Si2-Al, and UN-Al

2018 ◽  
Vol 4 (3) ◽  
Author(s):  
Jayangani I. Ranasinghe ◽  
Ericmoore Jossou ◽  
Linu Malakkal ◽  
Barbara Szpunar ◽  
Jerzy A. Szpunar
Keyword(s):  
Thermal Conductivity ◽  
Heat Conduction ◽  
Steady State ◽  
Temperature Gradient ◽  
Heat Conduction Equation ◽  
Conduction Equation ◽  
Temperature Profiles ◽  
Nuclear Fuels ◽  
State Heat ◽  
Steady State Heat

The understanding of the radial distribution of temperature in a fuel pellet, under normal operation and accident conditions, is important for a safe operation of a nuclear reactor. Therefore, in this study, we have solved the steady-state heat conduction equation, to analyze the temperature profiles of a 12 mm diameter cylindrical dispersed nuclear fuels of U3O8-Al, U3Si2-Al, and UN-Al operating at 597 °C. Moreover, we have also derived the thermal conductivity correlations as a function of temperature for U3Si2, uranium mononitride (UN), and Al. To evaluate the thermal conductivity correlations of U3Si2, UN, and Al, we have used density functional theory (DFT) as incorporated in the Quantum ESPRESSO (QE) along with other codes such as Phonopy, ShengBTE, EPW (electron-phonon coupling adopting Wannier functions), and BoltzTraP (Boltzmann transport properties). However, for U3O8, we utilized the thermal conductivity correlation proposed by Pillai et al. Furthermore, the effective thermal conductivity of dispersed fuels with 5, 10, 15, 30, and 50 vol %, respectively of dispersed fuel particle densities over the temperature range of 27–627 °C was evaluated by Bruggman model. Additionally, the temperature profiles and temperature gradient profiles of the dispersed fuels were evaluated by solving the steady-state heat conduction equation by using Maple code. This study not only predicts a reduction in the centerline temperature and temperature gradient in dispersed fuels but also reveals the maximum concentration of fissile material (U3O8, U3Si2, and UN) that can be incorporated in the Al matrix without the centerline melting. Furthermore, these predictions enable the experimental scientists in selecting an appropriate dispersion fuel with a lower risk of fuel melting and fuel cracking.

Modified Quadrature Method for Solving BIEs of Steady-State Anisotropic Heat Conduction Problems

2014 ◽  
Vol 687-691 ◽  
pp. 1354-1358
Author(s):  
Xin Luo ◽  
Jin Huang
Keyword(s):  
Integral Equation ◽  
Heat Conduction ◽  
Steady State ◽  
Heat Conduction Equation ◽  
Numerical Solutions ◽  
Trapezoidal Rule ◽  
Conduction Equation ◽  
Quadrature Method ◽  
Singular Kernels ◽  
Anisotropic Heat Conduction

In this paper, steady-state anisotropic heat conduction equation can be converted into the first kind integral equation, then modified quadrature formula based on trapezoidal rule is used to deal the integrals with singular kernels. In addition, Sidi transformation is applied to remove the singularities at concave points in concave polygons. This technique improves the accuracy of numerical solutions of the heat conduction equation. Numerical results show the convergence rate of the proposed method is the order three.

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