Validation Case: Heat Transfer Through Encased Rod

This article is part of the series of FEA validation cases performed using OnScale Solve.

In this case, a copper rod encased in stainless steel has an applied temperature at each side of the rod. The aim of this FEA analysis is to determine the temperature distribution across the copper rod. 

The FEA model and the resulting comparison of the simulation results against the analytical calculations validates the use of following conditions for linear static thermal analysis in Solve: 

• Temperature

Geometry

Download the geometry here or use Onshape to access the geometry used for this analysis: 

Geometry Dimensions:

• Stainless Steel Parts
  • Thickness dimension (L_ss) = 0.01 m
• Copper Part
  • Thickness dimension (L_cu) = 0.02 m

Material

• Stainless Steel
  • Thermal Conductivity (k) = 17 W/mK
• Copper
  • Thermal Conductivity (k) = 372 W/mK

Physics

• Temperature
  • 400 °C on Part 1 Face 3 
  • 100 °C on Part 3 Face 2

Note, all side walls are adiabatic (Heat flux = 0).

Meshing

OnScale Solve generated the mesh automatically and the meshing statistics, at the time of writing this document, are as follows:

Mesh Quality: Medium

Reference Solution

Conservation of energy requires that the steady state heat flux through all three layers must be the same, therefore:

Where k is the thermal conductivity and L is the length of the layer. The total difference in temperature (300°C) can be given as:

Rearranging equation 1 and substituting into equation 2 gives:

Solving for the ΔT_cu yields temperature difference across the copper part to be 13.12 °C and ΔTss to be 143.44 °C.

The top and bottom surface temperature of the copper part can be calculated to be:

T_cu, top = 400°C – ΔTss = 256.56 °C

T_cu, bot = T_cu, top – ΔT_cu = 243.44 °C

Results Comparison

The table below compares the values obtained using the analytical methods described above and the FEA analysis performed using OnScale Solve.

Result Quantity	Analytical	OnScale Solve
Tcu, top (°C)	256.56	256.56
Tcu, bot (°C)	243.44	243.44
ΔTcu (°C)	13.12	13.12

Note, probe capability through SimAPI was used to extract the temperature values from the model.