VM100

VM100
Heat Conduction Across a Chimney Section

Overview

Reference:F. Kreith, Principles of Heat Transfer, 2nd Printing, International Textbook Co., Scranton, PA, 1959, pg. 102, ex. 3-4.
Analysis Type(s):Thermal Analysis (ANTYPE = 0)
Element Type(s):2D Thermal Solid Elements (PLANE55)
Input Listing:vm100.dat

Test Case

Determine the temperature distribution and the rate of heat flow q per foot of height for a tall chimney whose cross-section is shown in Figure 140: Heat Conduction Across a Chimney Section Problem Sketch. Assume that the inside gas temperature is Tg, the inside convection coefficient is hi, the surrounding air temperature is Ta, and the outside convection coefficient is ho.

Figure 140: Heat Conduction Across a Chimney Section Problem Sketch

Heat Conduction Across a Chimney Section Problem Sketch

Material PropertiesGeometric PropertiesLoading
k = 1.0 Btu/hr-ft-°F
hi = 12 Btu/hr-ft2-°F
ho = 3 Btu/hr-ft2-°F
a = 4 ft
b = 1 ft

Analysis Assumptions and Modeling Notes

Due to symmetry, a 1/8 section is used. The finite element model is made the same as the reference's relaxation model for a direct comparison. The solution is based on a fin of unit depth (Z-direction). POST1 is used to obtain results from the solution phase.

Results Comparison

Target[1]Mechanical APDLRatio
T, °F (at Node 1)93.793.61.00
T, °F (at Node 2)56.356.81.01
T, °F (at Node 3)22.222.10.99
T, °F (at Node 4)93.293.21.00
T, °F (at Node 5)54.654.91.01
T, °F (at Node 6)21.421.10.98
T, °F (at Node 7)87.687.81.00
T, °F (at Node 8)47.547.71.01
T, °F (at Node 9)18.317.30.95
T, °F (at Node 11)29.627.60.93
T, °F (at Node 12)11.712.51.07
T, °F (at Node 15)4.75.01.07
q, Btu/hr775.2773.5[2]1.00

  1. Based on a numerical relaxation method.

  2. From heat rates at elements 1 and 3 multiplied by 8.

Figure 141: Temperature Contour Display

Temperature Contour Display