VM162

VM162
Cooling of a Circular Fin of Rectangular Profile

Overview

Reference:	P. J. Schneider, Conduction Heat Transfer, 2nd Printing, Addison-Wesley Publishing Co., Inc., Reading, MA, 1957, pg. 82, article 4-10.
Analysis Type(s):	Thermal Analysis (ANTYPE = 0)
Element Type(s):	3D 20-Node Thermal Solid Elements (SOLID90)
Input Listing:	vm162.dat

Test Case

A circular cooling fin of rectangular profile is attached to a cylindrical surface having a temperature T₁. Determine the temperature T₂ at the tip of the fin if the fin is surrounded by cooling air at temperature T_o having a convective film coefficient h.

Figure 227: Circular Fin Problem Sketch

Material Properties

Geometric Properties

h = 100 Btu/hr-ft²-°F

k = 15 Btu/hr-ft-°F

r₁ = 0.5 in = 0.04167 ft

r₂ = 0.75 in = 0.0625 ft

t = 0.0625 in = 0.005208 ft

T₁ = 100°F

T_o = 0°F

Analysis Assumptions and Modeling Notes

An arbitrary 5° sector is used to model the axisymmetric fin.

Results Comparison

	Target[1]	Mechanical APDL	Ratio
T₂, °F	53.22	52.37	.984
q, Btu/hr	102.05	101.70[2]	.997

Based on interpolation with Bessel function tables.
Obtained from the reaction heat flow summation of 1.41246 x 360°/5°.