VM-WB-MECH-035

VM-WB-MECH-035
Thermal Stress in a Bar With Radiation

Overview

Reference: Any Basic Heat transfer and Strength of Materials book
Solver(s): Ansys Mechanical
Analysis Type(s): Coupled Analysis (Static Thermal and Static Stress)
Element Type(s): Solid

Test Case

Heat of magnitude 2500 W and Heat Flux of magnitude 625 W/m2 is flowing through a long bar (2 x 2 x 20) m in an axial direction, and radiating out from the other face having emissivity 0.3; Ambient temperature is maintained at 20 °C. Find the following:

  • Temperatures on End Faces.

  • Thermal strain and Directional deformation and Normal Stress in Z direction if both the end faces have frictionless supports and Reference temperature of 22°C.

Analysis

(Heat flowing through body) Q = (Heat Flow) + (Heat Flux * Area) = 5000 W.

(Heat flowing through body) = (Heat Conducted through body) = (Heat Radiated out of the Surface); that is, Q = Qr =QC = 5000 W.

Heat Radiated out of the body gives T2 = 260.16 °C.

Heat Conducted through the body gives T1 = 673.38 °C.

Thermal strain is given by:

The compressive stress introduced is given by:

Temperature at a distance z from the face with higher temperature is given by:

Only half-length is considered for calculating deformation, since deformation is symmetric:

Material PropertiesGeometric PropertiesLoading
E = 2.0 x 1011 Pa
v = 0
α = 1.2 x 10-5 1/°C
k = 60.5 W/m°C
Part 1: 2 m x 2 m x 2 m
Part 2: 2 m x 2 m x 5 m
Part 3: 2 m x 2 m x 10 m
Part 4: 2 m x 2 m x 3 m
Heat Flow = 2500W on Part 4
Heat Flux = 625 W/m2 on Part 4
Radiation = 20 °C, 0.3

Analysis Assumptions and Modeling Notes for Ansys Mechanical

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

Figure 47: Schematic in Ansys Mechanical

Schematic in Ansys Mechanical

Results Comparison for Ansys Mechanical

ResultsTargetMechanicalError (%)
Temperature on Part 4 (°C)673.38673.490.016
Temperature on Part 1 (°C)260.16260.15-0.004
Maximum Thermal Strain (m/m)7.81656 x 10-3 7.8179 x 10-3 0.017
Minimum Thermal Strain (m/m)2.85792 x 10-3 0.0028578-0.004
Normal Stress in Z direction (Pa)-1.067448 x 109 -1.0183 x 109 -4.6
Directional Deformation in Z direction (m)-0.0123966-0.0125721.4