An efficient bem solution for three‐dimensional transient heat conduction

1995 ◽  
Vol 5 (4) ◽  
pp. 327-340 ◽  
Author(s):  
Anil Gupta ◽  
John M. Sullivan ◽  
Hugo E. Delgado
Keyword(s):  
Heat Conduction ◽  
Three Dimensional ◽  
Transient Heat Conduction

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.

IG-DRBEM of three-dimensional transient heat conduction problems

2021 ◽  
Vol 128 ◽  
pp. 298-309
Author(s):  
Bo Yu ◽  
Geyong Cao ◽  
Yanpeng Gong ◽  
Shanhong Ren ◽  
Chunying Dong
Keyword(s):  
Heat Conduction ◽  
Three Dimensional ◽  
Transient Heat Conduction
Sign in / Sign up

Export Citation Format

Share Document