VM-WB-MECH-037

VM-WB-MECH-037
Cooling of a Spherical Body

Overview

Reference:

Kreith, F. (1959). Principles of Heat Transfer (2nd ed., pp. 143, ex. 4-5). Scranton, PA: International Textbook Co.

Solver(s):Ansys Mechanical
Analysis Type(s):Transient Thermal Analysis
Element Type(s):Plane

Test Case

Determine the temperature at the center of a spherical body, initially at a temperature T0, when exposed to an environment having a temperature Te for a period of 6 hours (21600 s). The surface convection coefficient is h.

  • Initial temperature, T0 = 65 °F

  • Surface temperature, Te = 25°F

  • Convection coefficient h = 5.5556e-4 BTU/s-ft2-°F

  • Time, t = 21600 seconds

  • Radius of the sphere ro = 2 in = 1/6 ft

Material PropertiesGeometric PropertiesLoading
K = (1/3) BTU/hr-ft-°F
ρ = 62 lb/ft3
c = 1.075 Btu/lb-°F
Quarter Circular lamina Radius = 0.16667 ft
Convection applied on Edge = 5.5556e-4 BTU/s-ft2-°F
Ambient Temperature for Convection = 25°F

Analysis Assumptions and Modeling Notes for Ansys Mechanical

Since the problem is axisymmetric, only a 2-D quarter model is used in Ansys Mechanical.

Figure 49: Schematic for Ansys Mechanical

Schematic for Ansys Mechanical Schematic for Ansys Mechanical 

Results Comparison for Ansys Mechanical

ResultsTargetMechanicalError (%)
Maximum Temperature (°F)2828.6882.457