VM93

VM93
Temperature Dependent Conductivity

Overview

Reference:	F. Kreith, Principles of Heat Transfer, 2nd Printing, International Textbook Co., Scranton, PA, 1959, pg. 25, ex. 2-2
Analysis Type(s):	Thermal Analysis (ANTYPE = 0)
Element Type(s):	3D Conduction Bar Elements (LINK33)
Input Listing:	vm93.dat

Test Case

The conductivity of an 85% magnesia insulating material is given by k(T) = C₀ + C₁ T for 100°F T 300°F. Determine the rate of heat flow q between these temperatures for a slab of thickness t.

Figure 132: Conductivity Problem Sketch

Material Properties

Geometric Properties

C₀ = 0.031 Btu/hr-ft-°F

C₁ = 0.000031 Btu/hr-ft-°F²

t = 3 in = 0.25 ft

T₁ = 300°F

T₂ = 100°F

Analysis Assumptions and Modeling Notes

A 1 ft² area is used for the conduction element.

Results Comparison

	Target[1]	Mechanical APDL	Ratio
q, Btu/hr	29.760	29.760	1.000

Solution recalculated.