VM-LSDYNA-SOLVE-029

Overview

Reference:

Kreith, F. (1976) Principles of heat transfer (3rd ed.). Harper and Row.

p.59: equation 2-44a. p.60: equation 2–45.

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. Advanced mesh control is applied with element size of 0.025'. Figure 105 shows the external forces and supports for each case. The goal is to find the heat conducted by the spine and the temperature of the tip.

This test case also appears in the Workbench Verification Manual. See VM-WB-MECH-008.

Figure 105: Schematic of the steel cooling spine

Material Properties	Geometric Properties	Loading
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

Material Properties

Geometric Properties

Loading

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

Analysis Assumptions and Modeling Notes

A solid model and a steady-state thermal analyses are used (ATYPE=0 in *CONTROL_THERMAL_SOLVER), and LS-DYNA performs a thermal analysis by using SOLN=1 in the *CONTROL_SOLUTION keyword.

Figure 106: Problem setup for steel cooling spine

Figure 107: Mesh model

Results Comparison

The LS-DYNA results are nearly identical to the theoretical results.

Results	Target	LS-DYNA Solver	Error (%)
Scenario 1: Directional Deformation in Y-direction (m)	79.0344	78.97	0.081
Scenario 2: Directional Deformation in Y-direction (m)	6.364 x10^-3	6.362 x 10^-3	0.031