Stationary heat propagation in a plate (ring section) under boundary conditions of the third kind (convection)

Verification of the LIRA-FEM software / Stationary heat propagation in a plate (ring section) under boundary conditions of the third kind (convection) / Аналитическое решение: Société Fançajse des Mécaniciens, Commission Validation des progiciels de calcul de Structures, groupe de travail Thermique (2D et 3D) et thermoélasticité, Pan‘s, 1989.

Problems of stationary and non-stationary heat conduction

Stationary heat propagation in a plate (ring section) under boundary conditions of the third kind (convection)

Type of analysis: stationary thermal.

Source: 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:

Inner radius: R_i=0.3m

Outer radius: R_e=0.391m

Length: L

Material characteristics:

λ=40W/m⁰C

Boundary conditions:

Cylinder inner radius:

convective heat transfer coefficient h_i=150.0 W/m2 °C,

set temperature for convection elements < /span> =500°С.

Outer radius of the cylinder:

convective heat transfer coefficient h_e=142.0 W/m2 °C,

set temperature for convection elements =20°C.

Calculation method used to obtain the reference solution:

CALCULATION RESULTS:

R(m)	Desired value	Analytical solution	Calculation results (LIRA-SAPR)	Uncertainty,%
0.30	Т (⁰С)	272.27	272.1	0.062
0.391	Т (⁰С)	205.05	204.71	0.166

Preview image: Array

Note: To build the scheme we used FE1509 - quadrangular FE of heat conduction, 1555 - two-node FE of convective heat transfer. Number of nodes:98. Number of elements:147.

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Stationary heat propagation in a plate (ring section) under boundary conditions of the third kind (convection)

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