In this issue:
UK Modelling Workshop
Convective Cooling of Surfaces
GEO-SLOPE International is pleased to announce that the next UK Geotechnical Modelling workshop will be held May 21-23, 2007 in Ironbridge, England. The workshop is a well attended event where GEO-SLOPE clients from around the world gather to learn, enhance and fine-tune their numerical modelling skills under the guidance of GEO-SLOPE personnel.
See the UK 2007 Training page for a registration form and additional details on the workshop.
Convective
Cooling of SurfacesConvective heat transfer is a process in which heat is removed from a body by fluid that flows over the body's surface. The fluid can be water or air, as in the case of cooling systems in automobiles. TEMP/W is formulated with a special boundary condition that lets you remove heat from an object (soil or other) at a rate dependent on the object temperature, the fluid temperature and the rate of movement of the fluid.
The convective heat transfer boundary condition option can be used for many types of thermal analysis. Originally implemented for use in artificial ground freezing, the feature is used in this example to illustrate the rate of cooling of a heated Pyrex tile.
Problem Definition
A tile of Pyrex material that is 200 mm square and 10 mm thick emerges from a curing process at a uniform temperature of 140°C. The back side of the tile is insulated while the upper surface is exposed to ambient air temperature at 25°C. The ambient air may be still or moving past the tile at a rate of 10 m/s. The objective is to determine how long it takes the tile to cool to 40°C, a low enough value that it can be removed from the conveyor system without damage.
Figure 1 Tile cooling problem
definition and material properties
Solution
The TEMP/W program is used to compute the amount of heat removed from the object
based on the difference between the tile and air temperatures according to
Where:
Q = the total heat flux,
h = the convective heat transfer coefficient,
A
= the area in contact with the flowing fluid,
Ttile = the tile surface
temperature, and
Tfluid = the bulk temperature of the flowing fluid.
As heat is removed, the tile surface temperature drops and on subsequent time steps, the rate of heat loss reduces until the system comes to equilibrium.
The adaptive time stepping routine is used to help ease the solution between defined time steps as it is assumed there will be a high thermal gradient as cooling progresses. This option will limit the time steps if those specified are too large for any given time step.
A comparison of the TEMP/W solution with a closed form analytical solution is presented in Figure 2. The TEMP/W solution was obtained for node 128 of the defined mesh, which is located at the base of the tile where it is in contact with the insulation.
Figure 2 Comparison of TEMP/W
with closed form analytical solution
You can also show the heat flow towards the cooler air surface in TEMP/W for any time step, as illustrated in Figure 3.
Figure 3 Heat flow due to
convective cooling of tile surfaces
The convective heat transfer boundary condition type is ideally suited to modeling the heat transfer process that exists in artificial ground freezing or other situations where hot or cold pipe lines are buried. Other special boundary conditions available in TEMP/W include thermosyphons and transient boundary functions of temperature or flux versus time.
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