Issue 70

A. Chulkov et alii, Frattura ed Integrità Strutturale, 70 (2024) 177-191; DOI: 10.3221/IGF-ESIS.70.10

The numerical simulation of 3D heat conduction problems yields temporal evolutions at all surface points of a solid body subjected to uniform or uneven heating. The model used represents a rectangular plate containing air-filled parallelepiped like defects. A visual presentation of the model is shown in Fig. 1. The example of calculated temperature distributions is given in Fig. 2.

Figure 1 : TNDT 3D numerical model.

The general mathematical formulation of the 3D model of non-adiabatic heat conduction in a multilayer body with defects accepted in ThermoCalc-3D is as follows (Fig. 1):

2

2

2

T x y z 

( , , , ) 



( , , , ) 



( , , , ) 



( , , , ) 

T x y z

T x y z

T x y z

x   i 

y   i 

z   

i

i

i

i

(5)

i

2

2

2









x

y

z

(   



i

layers

defects

1 76 (36

40

)

(6)

0)  

T

T

i

in

( , , T x y z 



0, ) 

1 z   K

1



( , , ) 

 

[ ( , , , ) 



Q x y

h T x y z

T

(7)

]

F

amb

1



z

( , , T x y z L  

, ) 

z

3

z m



 

[ ( , , , ) 



(8)

K

h T x y z

T

]

R

amb

3



z



( , , , ) 

i T x y z x T x y z 



  

0   

0, x y

, L x L y

L

0 for

0 ;

y

x

y

(9)



( , , , ) 

i



0,   

0 ; x L y L x L    , 0

y

0 for

x

y

x



y

T x y z 

( , , , ) 

T x y z 

( , , , ) 

q

g



i

i

1

( , , , ) T x y z     and

T x y z



1 j   K  i

(10)

( , , , )

K

j

i

i

1

i





q

q

j

j

181