VM28

VM28
Transient Heat Transfer in an Infinite Slab

Overview

Reference:	J. P. Holman, Heat Transfer, 4th Edition, McGraw-Hill Book Co., Inc., New York, NY, 1976, pg. 106.
Analysis Type(s):	Thermal Analysis (ANTYPE = 4)
Element Type(s):	2D 8-Node Thermal Solid Element (PLANE77)
Input Listing:	vm28.dat

Test Case

A semi-infinite solid is initially at temperature T_o. The solid is then suddenly exposed to an environment having a temperature T_e and a surface convection coefficient h. Determine the temperature distribution through the solid after 2000 seconds.

Figure 36: Infinite Slab Problem Sketch

Material Properties

Geometric Properties

k = 54 W/m°C

ρ = 7833 kg/m³

c = 465 J/kg-°C

a = 1 m

b = 0.1 m

T_o = 0°C

T_e = 1000°C

h = 50 W/m²-°C

Analysis Assumptions and Modeling Notes

The width b of 0.1 m is arbitrarily selected for the elements. The model length a (1 meter) is selected to model the infinite boundary such that no significant temperature change occurs at the inside end points (nodes 1, 13) for the time period of interest. The node locations are selected with a higher density near the surface to better model the transient behavior. The automatic time stepping procedure (AUTOTS,ON) is used with an initial integration time step of 10 sec (2000 sec/200 max. iterations = 10) to more closely model the thermal shock at the surface.

Results Comparison

Temperature °C	Target	Mechanical APDL	Ratio
@ Y = .9777 (Node 11)	140.0	140.2	1.002
@ Y = .9141 (Node9)	98.9	98.7	0.998
@ Y = .8134 (Node 7)	51.8	51.6	0.997
@ Y = .6538 (Node 5)	14.5	14.4	0.992