VM95

VM95
Heat Transfer from a Cooling Spine

Overview

Reference: F. Kreith, Principles of Heat Transfer, 2nd Printing, International Textbook Co., Scranton, PA, 1959, pg. 48, eq. 2-44, 45.
Analysis Type(s): Heat Transfer Analysis (ANTYPE = 0)
Element Type(s):
3D Conduction Bar Elements (LINK33)
Convection Link Elements (LINK34)
3D Thermal Solid Elements (SOLID70)
Input Listing: vm95.dat

Test Case

A cooling spine of square cross-sectional area A, length , and conductivity k extends from a wall maintained at temperature Tw. The surface convection coefficient between the spine and the surrounding air is h, the air temperature is Ta, and the tip of the spine is insulated. Determine the heat conducted by the spine q and the temperature of the tip T .

Figure 134: Cooling Spine Problem Sketch

Cooling Spine Problem Sketch

Material PropertiesGeometric PropertiesLoading
k = 25 Btu/hr-ft-°F
h = 1 Btu/hr-ft2-°F
A = 1 in2 = (1/144) ft2
= 8 in = (2/3) ft
b = 1 in = (1/12) ft
Ta = 0°F
Tw = 100°F

Analysis Assumptions and Modeling Notes

The problem is solved first using conducting line elements (LINK33) and convection elements (LINK34) and then using conducting solid elements (SOLID70). The surface convection area is 4 in2 (4/144 ft2) per inch of length.

In the first case, the convection elements at the end are given half the surface area of the interior convection elements. Nodes 11 through 19 are given arbitrary locations.

In the second case, coupled nodal temperatures are used to ensure symmetry.

Unit conversions are done by input expressions. POST1 is used to process results from the solution phase.

Results Comparison

 TargetMechanical APDLRatio
LINK33 and LINK34 Tlength, °F68.59468.6181.000
q, Btu/hr17.50417.5281.001
SOLID70 Tlength, °F68.59468.6181.000
q, Btu/hr17.50417.5281.001