VM-WB-MECH-008

VM-WB-MECH-008
Heat Transfer from a Cooling Spine

Overview

Reference:	Kreith, F. (1976). Principles of Heat Transfer (3rd ed.). Harper and Row. (Equation 2-44a, p. 59; Equation 2–45, p. 60).
Solver(s):	Ansys Mechanical
Analysis Type(s):	Linear Static Thermal Analysis
Element Type(s):	Solid

Test Case

A steel cooling spine of cross-sectional area A and length L extend from a wall that is maintained at temperature T_w. The surface convection coefficient between the spine and the surrounding air is h, the air temperature is T_a, and the tip of the spine is insulated. Apply advanced mesh control with element size of 0.025'.

Find the heat conducted by the spine and the temperature of the tip.

Figure 8: Schematic

Material Properties

Geometric Properties

E = 4.177 x 10⁹ psf

ν = 0.3

Thermal conductivity k = 9.71 x 10^-3 BTU/s ft °F

Cross section = 1.2" x 1.2"

L = 8"

T_w = 100°F

T_a = 0°F

h = 2.778 x 10^-4 BTU/s ft² °F

Results Comparison for Ansys Mechanical

Results	Target	Mechanical	Error (%)
Temperature of the Tip (°F)	79.0344	78.9674	-0.085
Heat Conducted by the Spine (Heat Reaction) (BTU/s)	6.364 x10^-3	6.3614 x 10^-3	-0.041