VM101

VM101
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 Thermal Solid Elements (SOLID70)
Input Listing:	vm101.dat

Test Case

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

Figure 142: Short Solid Cylinder Problem Sketch

Material Properties

Geometric Properties

k = 1.0 Btu/hr-ft-°F

r =

= 6 in = 0.5 ft

T_Top = 40°F

T_Bot = T_Wall = 0°F

Analysis Assumptions and Modeling Notes

Since the problem is axisymmetric only a sector (one element wide) is modeled. A small angle Θ=10° is used for approximating the circular boundary with a straight-sided element. Note that circumferential symmetry is automatically ensured due to default adiabatic boundary conditions. POST1 is used to report centerline and mid-radius temperatures to compare results.

Results Comparison

		Target[1]	Mechanical APDL	Ratio
T, °F (centerline)	Node 11	6.8	7.4	1.09
	Node 21	15.6	16.4	1.05
	Node 31	26.8	27.4	1.02
T, °F (mid-radius)	Node 13	5.2	5.3	1.02
	Node 23	12.8	13.0	1.02
	Node 33	24.0	24.8	1.03

Based on a graphical estimate.

Figure 143: Temperature Contour Display