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Examples of these types of thermal systems include heat treatment andsintering furnaces, curing ovens, heated enclosures for process instruments, fermentation vats, and material property test chambers.
To maintain a uniform temperature in such situations, all the sourcesof heat gain and loss must be considered. Often the supporting structure for the container is a significant heat loss path. Heating the supports will help, but unless the temperature at the support is independently controlled, the temperature uniformity can be degraded for variations in boundary conditions or set-point temperatures. An independentzone of temperature control at a support, or thermal anchor, can be used to control the temperature of the support at its interface with thecontainer which can substantially improve the temperature uniformityinside the container.
Model Geometry
To help illustrate theconcept, a simplified model of a cylindrical container supported at one end can be used. In this simplified model, the container is assumedto be vertical and includes a central tube that may be used to injector remove the material inside the temperature controlled volume, or sample volume, inside the cylindrical container. The model assumes thatthe container is partially filled with material representing a sample, charge, work product or other substance that must be maintained at uniform temperature. A relatively large mass representing the structureand any associated machinery is included at the top end of the cylinder. Features representing electric heaters are positioned on the outside circumference of the cylindrical container and are constructed to allow several power distribution configurations for analysis. Figure 1provides a cut-away illustration of the geometry used for analysis.
The thermal analysis of this geometry includes consideration ofconduction between the various parts of the model as well as convective and radiant heat loss to the environment. A two-dimensional, axi-symmetric, finite element, steady state representation of the model is used for thermal analysis to illustrate the model’s thermal behavior. The thermal boundary condition at the bottom of the cylindrical container has been selected to approximate a well-insulated surface to simplify the model for easy understanding of the concepts. These concepts canthen be easily generalized to more complicated geometries and boundary conditions. The set-point temperatures for the cases studied are fixed at specific sensor locations so that valid comparisons can be made.Mention of the sensor location used is made in the paragraphs corresponding to each case.
Case 1 Uniform Heat Distribution
The first case examined assumes a uniform distribution of power (heat generation rate) over the surface area covered by the heater. A common misconception is that a uniform power distribution will produce a uniform temperature distribution. Figure 2 shows that the uniform distributionof power does not produce uniform temperature.
An intuitive understanding of the cause of the non-uniformity of temperature can be gained by recognizing that a significant portion of the heat flows upward along the container wall and therefore must be replaced by the heater. Since the heater is designed for uniform heat generation, the replacement heat must be generated over the entire surface area covered bythe heater. This replacement heat must flow (by conduction, convection or radiation) from the heater to other locations.
No heat will flow until a temperature difference first exists. Therefore, replacement heat generated away from the location of the heat loss will result in a temperature gradient. Figure 2 shows that the temperature distribution inside the container is expected to range over a 34oC interval(sample volume temperatures range from about 81oC to 115oC). This ispoor result considering that the set point is 100oC (at a virtual sensor location between the heater and the container and 0.138m from the bottom of the container shown as sensor location #1 in Figure 1). Notethat the color scales for the views within figure 2 are different andare displayed to the right of each temperature map.
Figure 3 shows a plot of temperature versus the position along a vertical centerline in the model for the various cases discussed here. The horizontalaxis of the plot represents the vertical dimension in meters from thebottom of the container to various locations in the model. The vertical axis of the plot is the temperature of the corresponding locations in the model.
The curve corresponding to case 1 in figure 3 islabeled Uniform Heat Generation, 100oC Set-Point. Since the containeris assumed to be partially filled with heated material (see the samplevolume labeled in Figure 2), an abrupt change in the slope of the temperature curve occurs as the vertical centerline crosses the boundarybetween the heated material and the airspace above this material. A similar abrupt change in slope exists at the boundary between the airspace and the large mass representing the structure and machinery. Theseabrupt changes in slope are the result of discontinuities in the material properties in adjacent regions (between the sample and the air, for example).
Case 2 Heater Zoned for 100oC Set-Point
The second case examined includes a heater designed to produce power that isdistributed between two areas, or zones, such that temperature uniformity is optimized at a set-point of 100C. These two areas are labeled “top heater zone” and “bottom heater zone” in figure 1. As in the firstcase, the set-point temperature is measured at sensor location #1.
Since a significant fraction of the heat loss flows upward by conduction along the container wall, the top heater zone must produce somewhat more heat per unit area than the remainder of the heater in order to maintain uniformity within the temperature controlled sample volume. Optimizing the heat generated in the top 2” (0.05m) of heated area for temperature uniformity yields a temperature distribution as shown in figure 4.
As evidenced by the range of temperature in thesample volume in figure 4, temperature uniformity can theoretically be controlled accurately for the system modeled. Temperature variationin the sample volume from the temperature at sensor location #1 is nowless than 0.25oC. It should be noted again that the model has been selected so that the attachment of the container is a major source of heat loss and that other potential heat sinks, such as the bottom of thecontainer and the central sample injection tube, have been minimized.If these other potential heat sinks were significant, additional zones of heat generation, with varying power density, would potentially beneeded to achieve similar temperature uniformity. The effects of sensor and controller error are also neglected here.
The plot in Figure 3 shows that the temperature uniformity is well maintained for the sample volume (i.e. the first 0.21 m) for the curve corresponding tocase 2 labeled “Power Distribution for 100C”.
Conclusion
Many variations on the general “heated container system” are possible in laboratory and industrial applications. Maintaining tight control ofthe temperature in all locations within the heated container requiressystem designs that compensate for heat losses in a manner that preserves temperature uniformity. If this compensation must accommodate anysignificant range of boundary conditions or changes in set-point temperature, one or more adjustable sources of heat, such as the thermal anchors described here, may be needed to preserve temperature uniformity over the range of conditions. By Mark Everly, Principal Systems Engineer for Watlow.
Many processes require that a volume of materialinside a tank, bottle, vessel, oven or furnace, be held at a uniform temperature. Often this temperature must also be selectable, accommodating various set-point temperatures as well as multiple boundary conditions.
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