Stationary heat propagation in an inhomogeneous rod under boundary conditions of the third kind (convection)

Verification of the LIRA-FEM software / Stationary heat propagation in an inhomogeneous rod under boundary conditions of the third kind (convection) / Société Fançajse 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 in an inhomogeneous rod under boundary conditions of the third kind (convection)

Type of analysis: stationary thermal.

 

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

Geometry:

Rod AB: l1=0.05m

BC rod: l2=0.02m

Sectional area of ​​the rod: S=1m2

 

Material characteristics:

 

Rod AB: λ1=0.75W/m0C

Rod BC: λ2=1W/m0C

 

Boundary conditions:

 

Convection at ends A and B:

 

End point A: set temperature on convection elements = -20.0°C,

convective heat transfer coefficient hA=20.0 W/m2 ° C.

 

End point B: set temperature for convection elements =193.0 ° C,

convective heat transfer coefficient hс = 10.0 W/m2 ° C,

 

Calculation method used to obtain the reference solution:

 

    8_1.png

 

 

where, ϕ – heat flux (1W = 1 J/s);

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

 

CALCULATION RESULTS:

Dot

Desired value

Analytical solution

Calculation results (LIRA-SAPR)

Error,%

А

(0С)

25

25

0

B

(0С)

85

85

0

С

(0С)

103

103

0

[А÷С]

φ (W/m2)*

900

900

0

test10_8 - типы конечных элементов заданная температура значение температуры в узлах.png

test10_8 значение теплового потока в узлах.png

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