VM112

VM112
Cooling of a Spherical Body

Overview

Reference: F. Kreith, Principles of Heat Transfer, 2nd Printing, International Textbook Co., Scranton, PA, 1959, pg. 143, ex. 4-5.
Analysis Type(s): Thermal Analysis (ANTYPE = 4)
Element Type(s): 2D 8-Node Thermal Solid Elements (PLANE77)
Input Listing: vm112.dat

Test Case

See VM111 for test case description, geometric and material properties, and loading.

Figure 159: Spherical Body Problem Sketch

Spherical Body Problem Sketch

Analysis Assumptions and Modeling Notes

Since the problem is axisymmetric, only a one-element sector is needed. A small angle Θ = 15° is used for approximating the circular boundary with a curved-side element. Nodal coupling is used to ensure circumferential symmetry. Automatic time stepping is used. The initial integration time step (6/40 = 0.15 hr) is based on  δ2/4 α, where δ is the element characteristic length (0.0555 ft) and α is the thermal diffusivity (k/γc = 0.005 ft2/hr). POST1 is used to extract results from the solution phase.

Results Comparison

Time = 6 hr.Target[1]Mechanical APDLRatio
T, °F28.029.01.035

  1. Based on graphical estimates.