Unsteady thermal conductivity of a sphere with boundary conditions of convection and a given temperature
Verification of the LIRA-FEM software / Unsteady thermal conductivity of a sphere with boundary conditions of convection and a given temperature / W.H.McAdams, Transmission de la chaleur, Paris, Dunod, 1961.
Type of analysis: unsteady thermal.
Source: W.H.McAdams, Transmission de la chaleur, Paris, Dunod, 1961.
Geometry::
D=0.2м
Material Characteristics:
Thermal conductivity coefficient: λ=48.822 Вт/м ° C
Specific heat capacity: Cp=669 Дж/кг ° C
Specific weight: ρ=7200 кг/м3
Boundary conditions:
convective heat transfer coefficient he=232,5 Вт/м2 ° C,
Ambient temperature: T e = 1000 ° C.
Initial temperature: T0 = 20 ° C.
The calculation method used to obtain the reference solution:
- calculation of coefficients.
- values according to the Gerni-Laurier diagram.
CALCULATION RESULTS:
|
Time(с) |
The desired value |
Analytical solution |
Analytical solution |
Uncertainty,% |
|
|
400 |
Surface temperature |
Т1 (0С) |
461 |
481 |
4.34 |
|
600 |
Т1 (0С) |
608 |
604 |
0.66 |
|
|
800 |
Т1 (0С) |
696 |
697 |
0.14 |
|
|
1000 |
Т1 (0С) |
774 |
768 |
0.78 |
|
|
1200 |
Т1 (0С) |
828 |
823 |
0.60 |
|
|
1400 |
Т1 (0С) |
868 |
864 |
0.46 |
|
|
1600 |
Т1 (0С) |
902 |
896 |
0.67 |
|
|
1800 |
Т1 (0С) |
923 |
921 |
0.22 |
|
|
2000 |
Т1 (0С) |
942 |
939 |
0.32 |
|
|
2200 |
Т1 (0С) |
956 |
954 |
0.21 |
|
|
2400 |
Т1 (0С) |
962 |
965 |
0.31 |
|
|
400 |
Temperature in the center |
Т2 (0С) |
334 |
329 |
1.50 |
|
600 |
Т2 (0С) |
500 |
487 |
2.60 |
|
|
800 |
Т2 (0С) |
618 |
607 |
1.78 |
|
|
1000 |
Т2 (0С) |
706 |
700 |
0.85 |
|
|
1200 |
Т2 (0С) |
774 |
770 |
0.52 |
|
|
1400 |
Т2 (0С) |
828 |
824 |
0.48 |
|
|
1600 |
Т2 (0С) |
872 |
866 |
0.69 |
|
|
1800 |
Т2 (0С) |
902 |
897 |
0.55 |
|
|
2000 |
Т2 (0С) |
923 |
921 |
0.22 |
|
|
2200 |
Т2 (0С) |
942 |
940 |
0.21 |
|
|
2400 |
|
956 |
954 |
0.21 |
|
Preview image: Array
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