VM-WB-MECH-007

VM-WB-MECH-007
Thermal Stress in a Bar with Temperature Dependent Conductivity

Overview

Reference:	Any basic Heat Transfer book
Solver(s):	Ansys Mechanical
Analysis Type(s):	Nonlinear Thermal Stress Analysis
Element Type(s):	Solid

Test Case

A long bar has thermal conductivity that varies with temperature. The bar is constrained at both ends by frictionless surfaces. A temperature of T °C is applied at one end of the bar (End A). The reference temperature is 5°C. At the other end, a constant convection of h W/m² °C is applied. The ambient temperature is 5 °C. Advanced mesh control with element size of 2 m is applied.

Find the following:

Minimum temperature
Maximum thermal strain in z direction (on the two end faces)
Maximum deformation in z direction
Maximum heat flux in z direction at z = 20 m

Temperature at a distance z from rear face is given by:

Thermal strain in the z-direction in the bar is given by:

Deformation in the z-direction is given by:

Heat flux in the z-direction is given by:

Material Properties

Geometric Properties

E = 2 x 10¹¹ Pa

ν = 0

α = 1.5 x 10^-5 / °C

k = 0.038 * (1 + 0.00582 * T) W/m °C

Length = 20 m

Width = 2 m

Breadth = 2 m

Rear face temperature T = 100 °C

Film Coefficient h = 0.005 W/m² °C

Ambient temperature = 5 °C

Reference temperature = 5 °C

Temperature (°C)

Conductivity (W/m °C)

3.91 x 10^-2

800

0.215

Analysis Assumptions and Modeling Notes for Ansys Mechanical

The following figure shows the finite element model in Ansys Mechanical:

Figure 7: Ansys Mechanical Schematic

Results Comparison for Ansys Mechanical

Results	Target	Mechanical	Error (%)
Minimum Temperature (°C)	38.02	38.014	-0.017
Maximum Thermal strain (z = 20) (m/m)	0.000495	0.0004952	0.041
Maximum Thermal strain (z = 0) (m/m)	0.001425	0.001425	0.000
Maximum Z Deformation (m)	0.00232	0.002341	0.914
Maximum Z Heat Flux (z = 20) (W/m²)	0.165	0.16507	0.042