1. ME-442 Final Project
December 9th, 2014
Heat Transfer and Finite Element Analysis on a Circular
Electric Hot Plate
KristopherSaladin, 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

2. 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 Plate
Results 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
𝑁
𝑚2
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 2
3 3
4 4
Figure (2) – VonMisesStress (
𝑵
𝒎 𝟐
) inCast Iron Cylindrical Plate

3. 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
1.68𝑥10−13
𝑚 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 (3) – Total Displacement (m) for a Cast Iron Cyl. Plate
Figure (4) – Temp. Distribution (K) for a Cast Iron Cylindrical Plate

4. Case 2 – Glass Cylindrical Plate
As 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
𝑁
𝑚2 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 3.35𝑥10−13
𝑚. This was almost
double what the displacement for
cast iron was (again illustrated by
the properties of glass).
Figure (5) – VonMisesStress (
𝑵
𝒎 𝟐
) in a GlassCylindrical Plate
Figure (6) – Total Displacement (m) for a Glass Cylindrical Plate

5. 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 Plate
The 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
𝑁
𝑚2 , 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 GlassCylindrical Plate
Figure (8) – VonMisesStress (
𝑵
𝒎 𝟐
) in a Cast Iron Improved Plate

6. 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 1.21𝑥10−13
𝑚 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 (9) – Total Displacement(m) Cast Iron Improved Plate
Figure (10) – Temp. Distribution (K) for a Cast Iron Improved Plate

7. 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
1. Engineering Toolbox, specific heats &
emissivity of metals.
http://www.engineeringtoolbox.com/
2. Google unit conversions.
http://www.google.com
3. Wikipedia, information on Hot Plates.
http://en.wikipedia.org/wiki/Hot_Plate
4. Amazon information on current hot plate
designs/dimensions as well as max.
temperature ranges.
http://www.amazon.com/Scilogex-
86143101-MS-H280-Pro-Circular-Top-
Magnetic/dp/B00AYGIFCA/ref=lp_31800
2011_1_1?s=industrial&ie=UTF8&qid=14
17566734&sr=1-1