VM192

VM192
Cooling of a Billet by Radiation

Overview

Reference:

R. Siegel, J. R. Howell, Thermal Radiation Heat Transfer, 2nd Edition, Hemisphere Publishing Corporation, 1981, pg. 229, problem 21.

Analysis Type(s):

Transient Analysis (ANTYPE = 4)

Element Type(s):

3D Thermal Solid Elements (SOLID70)

3D Thermal Surface Effect Elements (SURF152)

Input Listing:

vm192.dat

Test Case

A carbon steel billet is initially at a temperature T_Band is supported in such a manner that it loses heat by radiation from all its surfaces to surroundings at temperature T_E. Determine the temperature T_B of the billet at the end of 3.7 hours.

Figure 295: Cooling of a Billet by Radiation Problem Sketch

Material Properties	Geometric Properties	Loading
C = 0.11 Btu/lb-°R ρ = 487.5 lb/ft³ ε = emissivity = 1.0 Stefan-Boltzmann constant = 0.1712x10^-8 Btu/hr-ft²-R⁴	a = 2 ft b = 4 ft	T_E = 70°F (530°R) T_B = 2000°R (at t = 0)

Material Properties

Geometric Properties

C = 0.11 Btu/lb-°R

ρ = 487.5 lb/ft³

ε = emissivity = 1.0

Stefan-Boltzmann constant = 0.1712x10^-8 Btu/hr-ft²-R⁴

a = 2 ft

b = 4 ft

T_E = 70°F (530°R)

T_B = 2000°R (at t = 0)

Analysis of Assumptions and Modeling Notes

The billet is modeled using a single SOLID70 element overlaid with a SURF152 element on each of its faces. The surface elements have a common extra node representing the surrounding space. An arbitrary value is selected for the billet conductivity. The form factor from the billet to surrounding space is input as unity.

Results Comparison

Time = 3.7 hr	Target	Mechanical APDL	Ratio
T_B, °R	1000.0	1007.8	1.008