Analysis Characteristics
- Steady-state
- 2D internal flow
- Laminar
- Incompressible
- Forced convection
Reference
Holman, J.P., Heat Transfer, 5th Edition, McGraw-Hill, 1981.
Problem Description
A circular cylinder with an infinitely long axis (thus approximated as 2D) is immersed in a laminar flow with a Reynolds number of 50 (based on the diameter of the cylinder). The cylinder wall has a fixed temperature 100 K higher than the fluid bulk temperature. This model is analyzed to verify the fluid flow and heat transfer modeling capabilities of Autodesk Simulation CFD.
Accuracy is assessed by comparing two expressions for Nusselt number. One is an experimental correlation and the other is an analytical derivation. The experimental correlation is extracted from Holman (1981):
The subscript “e” indicates experimental. The analytical derivation is:
The subscript “a” indicates analytical.
- Q is the heat flux into the fluid (in watts)
- L and D are the length (unit length into the page) and diameter of the cylinder
- k is the conductivity of the fluid, h is the film coefficient
- Tcyl is the fixed temperature of the cylinder
- Tin is the bulk temperature of the incoming fluid.
Geometry and Boundary Conditions
Results
Using Re=50 (based on cylinder diameter), Q=17.08 watts, Pr=6.97, and the known geometry and boundary condition data, the following results are computed:
| Benchmark | 2013: Build 20120131 | % Error | 2014: Build 20130102 | % Error |
| Nue = 8.29 | Nua = 8.268 | 0.257 | Nua = 8.229 | 0.735 |
