scholarly journals Transient thermal conduction with variable conductivity using the Meshless Local Petrov–Galerkin method

2016 ◽  
Vol 272 ◽  
pp. 676-686 ◽  
Author(s):  
N.P. Karagiannakis ◽  
G.C. Bourantas ◽  
A.N. Kalarakis ◽  
E.D. Skouras ◽  
V.N. Burganos
Author(s):  
Natasha L. Smith ◽  
Brandon S. Field

This paper describes an integrated laboratory project between separate heat transfer and machine design courses. The project was structured around a Jominy end quench hardenability test. Most of the students participating were simultaneously enrolled in both classes. In the heat transfer class, students were required to model one-dimensional, transient thermal conduction for an end quench geometry of 4140 steel. In machine design, students applied their theoretical temperature profiles to a continuous cooling transformation curve (CCT) of 4140 steel to predict microstructure and matched the theoretical cooling rates with hardenability curves from literature to predict hardness. In laboratory, students then performed an end quench test in accordance with ASTM A255 on four steel rods. By combining activities across the two courses, students developed an appreciation for the interconnectivity of material within the engineering curriculum, and learned that practical applications typically require they employ knowledge from a variety of sources.


1987 ◽  
Vol 61 (1) ◽  
pp. 74-80 ◽  
Author(s):  
A. N. Burgess ◽  
K. E. Evans ◽  
M. Mackay ◽  
S. J. Abbott

2020 ◽  
Vol 12 (01) ◽  
pp. 2050005
Author(s):  
Xiaofei Hu ◽  
Xing Ding ◽  
Tinh Quoc Bui ◽  
Weian Yao

Numerical modeling of mechanical behavior of cracks under transient thermal conduction involves solving an initial value problem (IVP) and two boundary value problems (BVPs). Both of the BVPs have a singularity issue. Drawbacks such as numerical error accumulation and high computational expense of existing numerical approaches should be overcome. This contribution intends to build a unified framework with highly efficiency and accuracy for the numerical modeling of cracks under thermal shock. The precise integration method (PIM) and the symplectic analytical singular element (SASE) have been demonstrated to be favorable alternatives for each problem, i.e., the PIM for solving the IVP and SASE for the BVP. However, it is found that these two methods cannot be combined directly. In order to incorporate the SASEs into the PIM, the existing SASEs are reformulated for the thermal shock cracks analysis. Details of the mathematical derivations are provided. The validity of the proposed method is demonstrated through numerical examples.


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