ME-442 Final Project maj 1, y

Heat Transfer and Finite Element Analysis on a Circular Electric Hot Plate

Kristopher Saladin, and Samuel Mir

Abstract

Analysis using the finite element theory is a current and well proven method for breaking large problems down into smaller, more manageable parts. It has been utilized in complex structural problems and is very capable of performing additional studies such as heat transfer analysis and fluid flow mechanics. The program used in this course, COMSOL, is an industry standard tool for engineers and allows the freedom of ‘experimentation’ due to its basic interface.

Introduction

The task was to understand the stress, deformation, and temperature distribution of a typical hot plate with an applied load and find alternate (improved) designs based on the outcome. Three cases were chosen: Case 1: cylindrical shaped hot plate made of cast iron. Case 2: cylindrical shaped hot plate made of glass. Case 3: Improved geometry hot plate made of the “best” material (this turned out to be cast iron). The circular geometry of the electric hot plate allowed for modeling in an axis-symmetric space. After some research, average dimensions of a typical plate were 3.0 in. radius and 0.5 in. thick (units were converted to meters before input). The temperature ranges were based on the quality of the device, in our case a 600K max temperature was used. Ambient temperature was set to 273.15K (32°F), and the load applied was a 10lb beaker of water (this load on a 3 in. radius plate equaled a 1.57 Pa pressure load).

Application

Using the model wizard, stated above, the choice of modeling space was 2D axis-symmetric. From this, both ‘Heat Transfer in Solids’ as well as ‘Solid Mechanics’ modules were needed. And since we were only interested in the maximum temperature case, a stationary solution set was chosen. The boundary conditions listed in the introduction were used in a Bezier polygon geometry instead of a rectangular geometry for the purpose of easily altering the design after analyses. For cases 1&2, a cylindrical plate was used (shown below in figure 1a); for case 3, the edge was changed to reduce deformation and increase cooling surface area (figure 1b). Additional conditions were used to model a realistic scenario better. These included: a 600k temperature applied to element 1, surface to ambient radiation applied to element 2, natural

convective heat flux (air cooling) applied to element 2, and a boundary load applied to element 3 (stated in introduction). Element 1 was of course fixed, to model the hot plate sitting on an apparatus.

(a) (b)

Figure (1) – a) Cylindrical Hot Plate b) Improved Hot Plate Prototype

Results

Case 1 – Cast Iron Cylindrical PlateResults from the cast iron cylindrical plate were taken on the entire 3D structure (recall this had previously been 2D axis-symmetric). As previously mentioned; von mises stress, total displacement, and temperature distribution were all analyzed.

Shown in figure (2) is the von mises stress analysis. The maximum stress shown in

the figure was 3.34 Nm2

located around the edges of the plate. You will also notice, the geometry has been flattened a bit by the pressure force applied to the top.

1 1

2 23 3

4 4

Figure (3) shows the total displacement. Cast iron is known to be very rigid, inexpensive, and resistant to forces and heat expansion. Compare this to something like aluminum, which is much higher quality, more expensive, but expands and contracts with temperature much more. This would cause a large problem in designs for heated surfaces with excessive loads applied. The maximum displacement here had a value of 1.68 x10−13m and was again located on the edges of the plate. The symmetry of the geometry as well as the forces applied allows for a symmetrical displacement. This however, does not simulate a realistic scenario because during use of a hot plate, beakers are not always put on the exact center of the plate.

The temperature distribution is shown in Figure (4). In this case, not much can be said about the temperature distribution. The size of the plate is so small, unless a forced convective cooling is applied, there is little to no change in temperature. However, not every hot plate is designed to be heated from the bottom. If the heat source was located in the center, temperature would radiate outwards to the edges, much like a fin, and have greater distribution/cooling. The max temperature for this plate was set to 600K. With natural convective heat flux and surface to ambient radiation applied, the minimum temperature calculated would only be 598K. Again this is on the edge (element 2) where the boundary conditions are applied for cooling. No cooling was applied to the top surface (element 3)

because the beaker is sitting on it. A more accurate model would take into account the conduction heat transfer through the cast iron plate into the glass beaker (this was not done due to complexity).

Figure (2) – Von Mises Stress (Nm2

) in Cast Iron Cylindrical Plate

Figure (3) – Total Displacement (m) for a Cast Iron Cyl. Plate

Case 2 – Glass Cylindrical PlateAs the material of the cylindrical plate was changed from cast iron to glass, physical properties changed as well. Typically, glass is not known to be used in this fashion due to its brittle structure. The structure of glass makes it so that it’s not good at relieving stress. If an excess or stress acts on the glass it will form cracks at surface deformations. For this experiment excess stress weren’t applied to the plate, however, this could present an issue in real world application.

Figure (5) shows the von mises stress values. The maximum stress for a glass plate with the same geometry was 3.78 Nm2

compared to the previous, 3.34 in cast

iron. Given by the properties of glass, this makes sense. From the figure, the stress distribution was similar if not the exact same as cast iron, concentrating the most stress to the edges of the plate.

The total displacement for the glass plate is shown in Figure (6). Again, the change in material did not change the area of displacement. Max displacement was concentrated towards the edge of the plate, with a value of

Figure (4) – Temp. Distribution (K) for a Cast Iron Cylindrical Plate

Figure (5) – Von Mises Stress (Nm2

) in a Glass Cylindrical

Plate

Figure (6) – Total Displacement (m) for a Glass Cylindrical Plate

3.35 x10−13m. This was almost double what the displacement for cast iron was (again illustrated by the properties of glass).

Figure (7) shows the temperature distribution for the glass model. The distribution, again, is similar if not exact to the cast iron model. This is again because the cooling is only applied to the outside edge (element 2). In this case, glass was shown to have a much better cooling ability, with a minimum temperature at the edge of 526K. This was not ideal because keeping the entire hot plat at a consistent temperature leads to the hot plate providing a more accurate temperature while heating.

Case 3 – Cast Iron Improved PlateThe results from cases 1&2 showed similar areas of interest. The edge had the most cooling, the highest stress, and the most amount of displacement. The obvious conclusion would then be to change the edge geometry to allow for less displacement and less stress. Dimensions of the improved plate were shown in figure 1b. And since the most reliable material tested was cast iron, this was used again.

Figure (8) shows the von mises stress values for the improved plate. Interestingly enough, the prototype was an improvement on the previous cylindrical design. Maximum stress value for

this case was 1.12 Nm2

, less than half that of the cast iron cylindrical design. Stress is

concentrated to the center-area of the plate, shown in red. Concentrating the stresses away from the edges of the plat is ideal. This is to prevent the risk of fracture/breaking in the plate under heavier loads.

Figure (7) – Temp. Distribution (K) for a Glass Cylindrical Plate

The total displacement for the improved plate is shown in Figure (9). Again, we see the prototype was better than the original cylindrical design. The

maximum displacement only reaches 1.21 x10−13m which is slightly less than

the previous design. However, the key point here is that the max displacement moved away from the edges and now in the center-circular area of the plate. This is desired, because failure due to warping (permanent geometry change) is less likely to occur. Referring back to figure 3, the displacement caused the edges to round off and stretch beyond their original position.

Figure (10) shows the temperature distribution for the improved plate design. Shown here, the minimum temperature is 599K, clearly not a significant change from the previous 598K. However, this minor change could be a benefit if applied on a larger scale. Keeping the entire plate at a consistent temperature would allow for more evenly distributed heating. This could also increase the accuracy of the hot plate in experiments (keeping the item being heated at a more consistent temperature).

Figure (8) – Von Mises Stress (Nm2

) in a Cast Iron Improved Plate

Figure (9) – Total Displacement (m) Cast Iron Improved Plate

Engineering Toolbox, specific heats & emissivity of metals.

Google unit conversions.

Wikipedia, information on Hot Plates.

Amazon information on current hot plate designs/dimensions as well as max. temperature ranges.

Conclusions

Using COMSOL’s axis-symmetric geometric function, a hot plate was modeled for three different cases to look difference in stress, deformation, and temperature distribution. Case 1 was a control test that modeled a standard industry hot plate made from cast iron under normal use conditions. This was done to get a baseline of the hot plates performance and to look for areas of potential improvement. Case 2 was modeling the same hot plate as case 1 only using a different, non-typical, material for the hot plate itself. The material used in case 2 was glass. After observing a higher stress in the glass and a less consistent temperature distribution, it was determined that material properties for glass prevent it from being used in hot plates. Case 2 failed at improving the hot plate based on the material used, therefore; case 3 looked to improve the hot plate based on the geometry of the plate itself. The improved geometry, which can be seen in Figure (1b), helped improve the deformation by redirecting the stress away from the edge of the plate and the temperature by having a more consistent temperature distribution.

References

Figure (10) – Temp. Distribution (K) for a Cast Iron Improved Plate