Transient Conduction Heat Transfer

Analysis Characteristics

• Transient Heat Transfer
• Solid Medium
• Three Dimensional Conduction

Reference

Holman, J.P., Heat Transfer, 5th Edition, McGraw-Hill, 1981.

Problem Description

The Autodesk® CFD transient solver algorithms are verified by simulating transient heat conduction through a semi-infinite solid medium.

By analyzing conduction heat transfer (which is always highly accurate), we eliminate any potential flow inaccuracies, and effectively isolate the transient solver algorithm performance.

For this case, transient heat transfer in a 3-D steel block is modeled. We apply insulated boundary conditions on 2 dimensions so that the analytical expression for transient conduction in a semi-infinite solid can be used.

Geometry and Boundary Conditions

• Initial Condition: T(x,y,z,0) = 35 C.
• Boundary Conditions: T(x,y=0,z=10,t>0)=250 C.

Results

An analytic solution can be obtained by employing the Laplace transform technique. From the Holman reference, the analytical solution for transient conduction in a semi-infinite slab is:

From the properties in the above table and using 35 C as the initial temperature and 250 C as the boundary temperature, the temperature 2.5 cm from the boundary at t = 30 seconds is calculated:

The calculated temperature is 121.42 C.