VM98

VM98
Temperature Distribution Along a Tapered 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): 2D Thermal Solid Elements (PLANE55)
Input Listing: vm98.dat

Test Case

A tapered 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 138: Tapered Fin Problem Sketch

Tapered Fin Problem Sketch

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

Analysis Assumptions and Modeling Notes

The solution is based on a fin of unit depth (Z-direction). POST1 is used to extract results from the solution phase.

Results Comparison

Target[1]Mechanical APDLRatio
T, °F (at x/length = 0.0)1100.1100.1.000
T, °F (at x/length = 0.1)970.971.1.001
T, °F (at x/length = 0.2)850.854.1.004
T, °F (at x/length = 0.3)750.748.0.998
T, °F (at x/length = 0.4)655.653.0.997
T, °F (at x/length = 0.5)575.568.0.988
T, °F (at x/length = 0.6)495.492.0.994
T, °F (at x/length = 0.7)430.424.0.987
T, °F (at x/length = 0.8)370.364.0.984
T, °F (at x/length = 0.9)315.311.0.988
T, °F (at x/length = 1.0)265.267.1.006
q, Btu/hr5050.5109.1.012

  1. Based on graphical estimates.