scholarly journals THE PROCESS OF HEAT TRANSFER IN TWO-LAYERED CYLINDRICAL BODY

Author(s):  
U. V. Vidin ◽  
R. V. Kazakov ◽  
V. S. Zlobin

Determination of thermal regimes of composite cylindrical bodies by analytical methods leads to the appearance of complex characteristic equations, the solution of which is the determination of eigenvalues. The article considers a relatively simple approximate analytical method for determining the eigenvalues of characteristic equations for a two-layer cylindrical body under boundary conditions of the third kind. This method can also be easily used in more complex formulations of heat conduction problems.

Author(s):  
Koji Nishi ◽  
Tomoyuki Hatakeyama ◽  
Shinji Nakagawa ◽  
Masaru Ishizuka

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.


1959 ◽  
Vol 81 (2) ◽  
pp. 121-127 ◽  
Author(s):  
L. S. Han

Three cases of laminar heat transfer with linear heat input in long rectangular channels have been treated by the method of orthogonal trigonometric series. The boundary conditions of the first two problems are those of laminar and slug flows with two opposite faces as secondary extended surfaces. A new fin parameter K defined as (wkm/bkf) has been shown to be the important factor in governing the Nusselt number. The third case discussed is the combined effects of free and forced-convection in vertical rectangular tubes.


2013 ◽  
Vol 17 (2) ◽  
pp. 581-589 ◽  
Author(s):  
Jordan Hristov ◽  
Ganaoui El

Simple 1-D semi-infinite heat conduction problems enable to demonstrate the potential of the fractional calculus in determination of transient thermal impedances under various boundary conditions imposed at the interface (x=0). The approach is purely analytic and very effective because it uses only simple semi-derivatives (half-time) and semi-integrals and avoids development of entire domain solutions. 0x=


1983 ◽  
Vol 105 (3) ◽  
pp. 317-320 ◽  
Author(s):  
S. K. Hati ◽  
S. S. Rao

The optimum design of an one-dimensional cooling fin is considered by including all modes of heat transfer in the problem formulation. The minimum principle of Pontryagin is applied to determine the optimum profile. A new technique is used to solve the reduced differential equations with split boundary conditions. The optimum profile found is compared with the one obtained by considering only conduction and convection.


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