VM97

VM97
Temperature Distribution Along a Straight Fin

Overview

Reference: F. Kreith, Principles of Heat Transfer, 2nd Printing, International Textbook Co., Scranton, PA, 1959, pg. 57, ex. 2-13.
Analysis Type(s): Thermal Analysis (ANTYPE = 0)
Element Type(s):
4-Node Layered Thermal Shell Elements (SHELL131)
4-Node Layered Thermal Shell Elements (SHELL294)
Convection Link Elements (LINK34)
Input Listing: vm97.dat

VM97 requires a supplemental .cdb input file which is too long to include full input listings. This file must be downloaded and placed in your working directory for the test case to run properly. Additionally, the geometry and mesh should be regenerated.

Download link: MAPDL Test Case Files for 2024 R2

vm97_1.cdb

vm97_2.cdb

Test Case

A straight rectangular stainless steel cooling fin dissipates heat from an air-cooled cylinder wall. The wall temperature is Tw, the air temperature is Ta, and the convection coefficient between the fin and the air is h. Determine the temperature distribution along the fin and the heat dissipation rate q.

Figure 137: Straight Fin Problem Sketch

Straight Fin Problem Sketch

Material PropertiesGeometric PropertiesLoading
k = 15 Btu/hr-ft-°F
h = 15 Btu/hr-ft2-°F
t = 1 in = (1/12 ft)
= 4 in = (4/12) ft
Tw = 1100°F
Ta = 100°F

Analysis Assumptions and Modeling Notes

Convection from the tip of the fin is modeled with the two convection elements (LINK34). One half of the cross-sectional area is assigned to each element. The depth of the fin (Y-direction) is arbitrarily selected to be 1 foot. POST1 is used to extract results from the solution phase.

Results Comparison

SHELL131

Target[a]Mechanical APDLRatio
T, °F (at x/length = 0.0)1100.1100.1.00
T, °F (at x/length = 0.1)955.958.1.00
T, °F (at x/length = 0.2)835.838.1.00
T, °F (at x/length = 0.3)740.738.1.00
T, °F (at x/length = 0.4)660.655.0.99
T, °F (at x/length = 0.5)595.587.0.99
T, °F (at x/length = 0.6)535.532.1.00
T, °F (at x/length = 0.7)490.489.1.00
T, °F (at x/length = 0.8)460.456.0.99
T, °F (at x/length = 0.9)430.432.1.01
T, °F (at x/length = 1.0)416.417.1.00
q, Btu/hr5820.5840.1.00

[a] Based on graphical readings

SHELL294

 Target[a]Mechanical APDLRatio
T, °F (at x/length = 0.0)1100.1100.1.00
T, °F (at x/length = 0.1)955.958.1.00
T, °F (at x/length = 0.2)835.838.1.00
T, °F (at x/length = 0.3)740.738.1.00
T, °F (at x/length = 0.4)660.655.0.99
T, °F (at x/length = 0.5)595.587.0.99
T, °F (at x/length = 0.6)535.532.1.00
T, °F (at x/length = 0.7)490.489.1.00
T, °F (at x/length = 0.8)460.456.0.99
T, °F (at x/length = 0.9)430.432.1.01
T, °F (at x/length = 1.0)416.417.1.00
q, Btu/hr5820.5840.1.00