VM-WB-MECH-032

VM-WB-MECH-032
Radial Flow due to Internal Heat Generation in a Copper Disk - Axisymmetric Model

Overview

Reference:	Any basic Heat Transfer book
Solver(s):	Ansys Mechanical
Analysis Type(s):	Axisymmetric Analysis
Element Type(s):	2D Structural Solid

Test Case

A copper disk with thickness t and radii R_i and R_o is insulated on the flat faces. It has a heat-generating copper coaxial cable (of radius R_i) passing through its center. The cable delivers a total heat flow of Q to the disk. The surrounding air is at a temperature of T_o with convective film coefficient h. To get accurate results, set the advanced mesh control element size to 0.002 m.

Find the disk temperature and heat flux at inner and outer radii.

Figure 43: Schematic

Material Properties

Geometric Properties

E = 1.1 x 10¹¹ Pa

ν = 0.34

Thermal conductivity k = 401.0 W/m-°C

R_i = 10 mm

R_o = 60 mm

t = 8 mm

Q = 100 W (Internal Heat Generation = 39788735.77 W/m³)

Film coefficient h = 1105 W/m²-°C

Surrounding temperature T_o = 0°C

Analysis Assumptions and Modeling Notes for Ansys Mechanical

Because the geometry and loading are symmetric about the y-axis, the above problem can be analyzed as an axisymmetric problem in Ansys Mechanical.

Figure 44: Axisymmetric Model

Results Comparison for Ansys Mechanical

Results	Target	Mechanical	Error (%)
Maximum Temperature (°C)	38.9	38.896	-0.010
Minimum Temperature (°C)	30	30.007	0.023
Maximum Heat Flux (W/m²)	198943	197840	-0.554
Minimum Heat Flux (W/m²)	33157	33151	-0.018