Stationary heat propagation along the radius of an inhomogeneous hollow ball under boundary conditions of the third kind (convection)

Verification of the LIRA-FEM software / Stationary heat propagation along the radius of an inhomogeneous hollow ball under boundary conditions of the third kind (convection) / Société Bançajse des Mécaniciens, Commission Validation des progiciels de calcul de. Structures, groupe de travail Thermique (2D et 3D) et thermoélasticité, Pan‘s, 1989.



Stationary heat propagation along the radius of an inhomogeneous hollow ball under boundary conditions of the third kind (convection)

Type of analysis: stationary thermal.

 

Source: Société Bançajse des Mécaniciens, Commission Validation des progiciels de calcul de. Structures, groupe de travail Thermique (2D et 3D) et thermoélasticité, Pan‘s, 1989.

Geometry:



Ri=0.3м

Rm=0.35м

Re=0.37м

 

Material Characteristics:

Thermal conductivity coefficient: λ1=40 Вт/м ° C

Thermal conductivity coefficient: λ2=20 Вт/м ° C.

 

Boundary conditions:

 

The inner radius of the sphere:

convective heat transfer coefficient hi=150,0 Вт/м2 ° C,

set temperature on the convection elements =70°С.

 

The outer radius of the sphere:

convective heat transfer coefficient he=200,0 Вт/м2 ° C,

set temperature on the convection elements = -9°С.

 

The calculation method used to obtain the reference solution:

1st material:

 12_1.png

2nd material:

 12_2.png

 

where, ϕ – heat flux (1W = 1 J/s);

         φ is the heat flux density (W/m2 = 1 J/(s m2).

 

CALCULATION RESULTS:

R(м)

The desired value

Analytical solution

Calculation results (LIRA-SAD)

Uncertainty,%

0.30

Тi (0С)

25.06

24.93

0.52

0.35

Тm(0С)

17.84

17.84

0.06

0.37

Тe (0С)

13.16

13.24

0.53

[0.30÷0.37]

ϕ (W)*

7623.36

7511.43

1.47


test10_12 - типы конечных элементов заданная температура значение температуры в узлах.png

test10_12 значение теплового потока в узлах суммарный тепловой поток.PNG

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