Approximate Solutions of Canonical Heat Conduction Equations

1990 ◽  
Vol 112 (4) ◽  
pp. 836-842 ◽  
Author(s):  
B. D. Vujanovic´ ◽  
S. E. Jones
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Heat Conduction ◽  
Integral Method ◽  
Approximate Solutions ◽  
Boundary Layer Theory ◽  
Variational Procedure ◽  
Nonlinear Heat Conduction ◽  
One Dimensional ◽  
The Third

We consider three analytical methods for finding the approximate solutions of one-dimensional, transient, and nonlinear heat conduction problems based upon the canonical equations of heat transfer. The first method can be considered as a generalization or refinement of the integral method. The second is an iterative method similar to that of Targ utilized in boundary layer theory. The third method is a variational procedure introduced in the spirit of Gauss’ variational principle of least constraint.

Microprocessor Silicon Die Temperature Prediction by Simplified Boundary Conditions

2015 ◽  
Author(s):  
Koji Nishi ◽  
Tomoyuki Hatakeyama ◽  
Shinji Nakagawa ◽  
Masaru Ishizuka
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Boundary Conditions ◽  
Thermal Resistance ◽  
Hot Spot ◽  
Three Dimensional ◽  
Thermal Design ◽  
Target Temperature ◽  
One Dimensional ◽  
Thermal Network

The thermal network method has a long history with thermal design of electronic equipment. In particular, a one-dimensional thermal network is useful to know the temperature and heat transfer rate along each heat transfer path. It also saves computation time and/or computation resources to obtain target temperature. However, unlike three-dimensional thermal simulation with fine pitch grids and a three-dimensional thermal network with sufficient numbers of nodes, a traditional one-dimensional thermal network cannot predict the temperature of a microprocessor silicon die hot spot with sufficient accuracy in a three-dimensional domain analysis. Therefore, this paper introduces a one-dimensional thermal network with average temperature nodes. Thermal resistance values need to be obtained to calculate target temperature in a thermal network. For this purpose, thermal resistance calculation methodology with simplified boundary conditions, which calculates thermal resistance values from an analytical solution, is also introduced in this paper. The effectiveness of the methodology is explored with a simple model of the microprocessor system. The calculated result by the methodology is compared to a three-dimensional heat conduction simulation result. It is found that the introduced technique matches the three-dimensional heat conduction simulation result well.

scholarly journals A Useful Equation for Gas Turbine Design

2018 ◽  
Vol 140 (03) ◽  
pp. S52-S53
Author(s):  
Lee S. Langston
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Gas Turbine ◽  
Rankine Cycle ◽  
Combined Cycle ◽  
Brayton Cycle ◽  
Nonlinear Superposition ◽  
Transient Conditions ◽  
One Dimensional ◽  
Turbine Design

This article presents three different gas turbine phenomena and design cases. The sketch in the article shows a schematic of a combined cycle powerplant consisting of a Brayton cycle (gas turbine) whose exhaust provides energy to a Rankine cycle (steam turbine). Frequently, one can use simple but exact one-dimensional (1D) heat conduction solutions to estimate the heat loss or gain of gas turbine components under transient conditions. These easy-to-use solutions are found in most undergraduate heat transfer texts. The article suggests that those three widely different gas turbine phenomena and design cases all have the simple, nonlinear superposition form.

Comparison of Pin Surface Heat Transfer in Arrays of Oblong and Cylindrical Pin Fins

2013 ◽  
Vol 136 (4) ◽  
Author(s):  
Kathryn L. Kirsch ◽  
Jason K. Ostanek ◽  
Karen A. Thole
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Boundary Layer Separation ◽  
Diameter Ratio ◽  
Pin Fin ◽  
The Third ◽  
Spacing Effects ◽  
Pin Fins ◽  
Turbine Airfoils ◽  
Pin Fin Arrays

Pin fin arrays are most commonly used to promote convective cooling within the internal passages of gas turbine airfoils. Contributing to the heat transfer are the surfaces of the channel walls as well as the pin itself. Generally the pin fin cross section is circular; however, certain applications benefit from using other shapes such as oblong pin fins. The current study focuses on characterizing the heat transfer distribution on the surface of oblong pin fins with a particular focus on pin spacing effects. Comparisons were made with circular cylindrical pin fins, where both oblong and circular cylindrical pins had a height-to-diameter ratio of unity, with both streamwise and spanwise spacing varying between two and three diameters. To determine the effect of relative pin placement, measurements were taken in the first of a single row and in the third row of a multirow array. Results showed that area-averaged heat transfer on the pin surface was between 30 and 35% lower for oblong pins in comparison to cylindrical. While heat transfer on the circular cylindrical pin experienced one minimum prior to boundary layer separation, heat transfer on the oblong pin fins experienced two minimums, where one is located before the boundary layer transitions to a turbulent boundary layer and the other prior to separation at the trailing edge.

Nonlinear Inverse Heat Conduction With a Moving Boundary: Heat Flux and Surface Recession Estimation

1999 ◽  
Vol 121 (3) ◽  
pp. 708-711 ◽  
Author(s):  
V. Petrushevsky ◽  
S. Cohen
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Fourier Series ◽  
Heat Conduction ◽  
Moving Boundary ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Variable Order ◽  
Inverse Heat Conduction ◽  
One Dimensional

A one-dimensional, nonlinear inverse heat conduction problem with surface ablation is considered. In-depth temperature measurements are used to restore the heat flux and the surface recession history. The presented method elaborates a whole domain, parameter estimation approach with the heat flux approximated by Fourier series. Two versions of the method are proposed: with a constant order and with a variable order of the Fourier series. The surface recession is found by a direct heat transfer solution under the estimated heat flux.

Numerical Investigation of Heat Transfer Characteristics of Debris Bed After Severe Accident of SFR Based on 1-D Heat Conduction Model

2018 ◽  
Author(s):  
Mengwei Zhang ◽  
Bin Zhang ◽  
Jianqiang Shan
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Transfer Process ◽  
Severe Accident ◽  
Heat Transfer Characteristics ◽  
Conduction Model ◽  
One Dimensional ◽  
The Core ◽  
Transfer Characteristics ◽  
Core Catcher

Nuclear reactor severe accidents can lead to the release of a large amount of radioactive material and cause immense disaster to the environment. Since the Fukushima nuclear accident in Japan, the severe accident research has drawn worldwide attention. Based on the one-dimensional heat conduction model, a DEBRIS-HT program for analyzing the heat transfer characteristics of a debris bed after a severe accident of a sodium-cooled fast reactor was developed. The basic idea of the DEBRIS-HT program is to simplify the complex energy transfer process in the debris bed to a simple one-dimensional heat transfer problem by solving the equivalent thermal conductivity in different situations. In this paper, the DEBRIS-HT program code is prepared by using the existing model and compared with the experimental results. The results show that the DEBRIS-HT program can correctly predict the heat transfer process in the fragment bed. In addition, the heat transfer characteristics analysis program is also used to model the core catcher of the China fast reactor. Firstly, the dryout heat flux when all of molten core dropped on the core catcher was calculated, which was compared with the result of Lipinski’s zero dimensional model, and the error between two values is only 11.2%. Then, the temperature distribution was calculated with the heat power of 15MW.

Sign in / Sign up

Export Citation Format

Share Document