VM92

VM92
Insulated Wall Temperature

Overview

Reference: F. Kreith, Principles of Heat Transfer, 2nd Printing, International Textbook Co., Scranton, PA, 1959, pg. 32, ex. 2-5.
Analysis Type(s): Thermal Analysis (ANTYPE = 0)
Element Type(s):
Convection Link Elements (LINK34)
3D Conduction Bar Elements (LINK33)
Input Listing: vm92.dat

Test Case

A furnace wall consists of two layers, firebrick and insulating brick. The temperature inside the furnace is Tf and the inner surface convection coefficient is hi. The ambient temperature is Ta and the outer surface convection coefficient is ho. Neglect the thermal resistance of the mortar joints and determine the rate of heat loss through the wall q, the inner surface temperature Ti, and the outer surface temperature To.

Figure 131: Insulated Wall Temperature Problem Sketch

Insulated Wall Temperature Problem Sketch

Material PropertiesGeometric PropertiesLoading
k1 = 0.8 Btu/hr-ft-°F
k2 = 0.1 Btu/hr-ft-°F
hi = 12 Btu/hr-ft2-°F
ho = 2 Btu/hr-ft2-°F
1 = 9 in = 0.75 ft
2 = 5 in = 5/12 ft
Tf = 3000°F
Ta = 80°F

Analysis Assumptions and Modeling Notes

A 1 ft2 area is used for the convection and conduction elements. Nodes 1 and 5 are given arbitrary locations. Feet units are input as (inches/12) for convenience. POST1 is used to extract results from the solution phase.

Results Comparison

Target[1]Mechanical APDLRatio
q, Btu/hr513.513.1.001
Ti , °F2957.2957.1.000
To , °F336.337.1.002

  1. Rounded-off values (normalized)