# 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.

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:

2nd material:

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

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