Analysis of Transient Heat Conduction in Complex Shaped Composite Materials

1988 ◽  
Vol 110 (2) ◽  
pp. 110-112 ◽  
Author(s):  
Seiichi Nomura ◽  
A. Haji-Sheikh
Keyword(s):  
Temperature Field ◽  
Heat Conduction ◽  
Composite Materials ◽  
Analytical Procedure ◽  
Three Dimensional ◽  
Transient Heat Conduction ◽  
Temperature Fields ◽  
Finite Region ◽  
Symbolic Algebra ◽  
The Galerkin Method

This paper addresses a generalized analytical procedure for transient heat conduction in composite materials of two- and three-dimensional finite region. The Galerkin method is employed to obtain temperature field in closed form with the utilization of symbolic algebra software such as REDUCE or MACSYMA. It is found from illustrative examples that the proposed method yields accurate and effective predictions of temperature fields for which purely numerical methods such as finite element or finite difference are not suitable.

scholarly journals Impact of Tunnel Temperature Variations on Surrounding Rocks in Cold Regions

2019 ◽  
Author(s):  
Qingyang Yu ◽  
Chao Zhang ◽  
Zhenxue Dai ◽  
Chao Du ◽  
Mohamad Reza Soltanian ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Temperature Field ◽  
Temperature Distribution ◽  
Three Dimensional ◽  
Temperature Fields ◽  
Insulation Layer ◽  
Cold Regions ◽  
Ambient Temperatures ◽  
Temperature Conditions ◽  
Layer Control

Temperature is an important factor in designing and maintaining tunnels, especially in cold regions. We present three-dimensional numerical simulations of tunnel temperature fields at different temperature conditions. We study the tunnel temperature field in two different conditions with relatively low and high ambient temperatures representing winter and summer of northeast China. We specifically study how these temperature conditions affect tunnel temperature and its migration to surrounding rocks. We show how placing an insulation layer could affect the temperature distribution within and around tunnels. Our results show that the temperature field without using an insulation layer is closer to the air temperature in the tunnel, and that the insulation layer has shielding effects and could plays an important role in preventing temperature migration to surrounding rocks. We further analyzed how thermal conductivity and thickness of insulation layer control the temperature distribution. The thermal conductivity and thickness of insulation layer only affect the temperature of the surrounding rocks which are located at distances below ~20 m from the lining.

A New Method for Thermal Analysis of Die Casting

1993 ◽  
Vol 115 (2) ◽  
pp. 284-293 ◽  
Author(s):  
M. R. Barone ◽  
D. A. Caulk
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Problem ◽  
Die Casting ◽  
Three Dimensional ◽  
Transient Heat Conduction ◽  
Steady Solution ◽  
Cavity Surface ◽  
Varying Coefficients ◽  
Transient Heat Conduction Problem ◽  
Time Varying Coefficients

A new approach is developed for solving the initial value, steady periodic heat conduction problem in steady-state die casting. Three characteristics found in nearly all die casting processes are exploited directly: The casting is thin compared with its overall size, its thermal conductivity is high compared with that of the mold, and the cycle time is short compared with the start-up transient of the process. Under these conditions, it is reasonable to neglect the transverse temperature gradients in the casting and assume that all die temperatures below a certain depth from the cavity surface are independent of time. The transient die temperatures near the cavity surface are represented by a polynomial expansion in the depth coordinate, with time-varying coefficients determined by a Galerkin method. This leads to a set of ordinary differential equations on the cavity surface, which govern the transient interaction between the casting and the die. From the time-averaged solution of these equations, special conditions are derived that relate the transient solution near the cavity surface to the three-dimensional steady solution in the die interior. With these conditions, the steady temperatures in the bulk of the die can be determined independently of the explicit surface transients. This reduces the effort of solving a complex transient heat conduction problem to little more than finding a steady solution alone. The overall approach provides a general analytical tool, which is capable of predicting complex thermal interactions in large multicomponent dies.

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