VM96

VM96
Temperature Distribution in a Short, Solid Cylinder

Overview

Reference: P. J. Schneider, Conduction Heat Transfer, 2nd Printing, Addison-Wesley Publishing Co., Inc., Reading, MA, 1957, pg. 134, fig. 6-7.
Analysis Type(s): Thermal Analysis (ANTYPE = 0)
Element Type(s): 3D 10-Node Tetrahedral Thermal Solid Elements (SOLID87)
Input Listing: vm96.dat

Test Case

A short, solid cylinder is subjected to the surface temperatures shown. Determine the temperature distribution within the cylinder

Figure 135: Short, Solid Cylinder Problem Sketch

Short, Solid Cylinder Problem Sketch

Material PropertiesGeometric PropertiesLoading
k = 1.0 Btu/hr-ft-°F
r =  = 0.5 ft
Ttop = 40°F
Tbot = Twall = 0°F

Analysis Assumptions and Modeling Notes

Since the problem is axisymmetric, the entire cylinder geometry is not required. An angle Θ = 45° is arbitrarily chosen. Postprocessing is used to print temperatures at the centerline in geometric order. A finer mesh density (than required for reasonable results) is used to produce a smooth isosurface plot.

Results Comparison

At CenterlineTargetMechanical APDLRatio
z = 0.0 ftT, °F0.00.0--
z = 0.125 ftT, °F6.86.81.007
z = 0.25 ftT, °F15.615.40.985
z = 0.375 ftT, °F26.826.60.991
z = 0.5 ftT, °F40.040.01.00

Figure 136: Temperature Isosurface Display with Annotation

Temperature Isosurface Display with Annotation