Internal Device Heat Analysis Report

Internal Device Heat Analysis Report

Nick Dominesey

Assisted by: Team P13022

January 20th, 2013

Model of 1-D Analysis:

Abstract:

We assumed that the body was at steady state and that the device was only an additional heat source. Thus, the analysis doesn’t include the metabolic heat generation of the body nor does it include the perfusion rate or circulation of heat due to the blood. In theory, this analysis seems quite simple but there is certainly a lot going on inside the body that is truly difficult to model. The result of this analysis has many flaws and is likely to have a large amount of error.

From the data, particularly the ANSYS model as it is likely to be more accurate since it requires fewer assumptions, we can conclude that the device is not likely to pose a threat to the body when generating up to 2 Watts of heat energy. The factor of safety between the results and our limitations is about 4 which leaves an allowance of more heat generation within the internal device.

Objective:

The purpose of this analysis is to first prove whether the heat generated from the device would be harmful to the body or not.Studies have shown that the body will adapt to some temperature range and that the heat flux into the body is a more important statistic. Therefore, for the studies we believe that the temperature should be allowed to rise several degrees but the heat flux should not exceed 80mW/cm2 before damage is done to the tissue. In order to ensure a factor of safety of 2, we will design our device for a limit of 40 mW/cm2. From the data we should be able to see the resulting temperature at the contact point between the internal organs and the titanium shieldbased on heat generation within the device. From the results, we hope to be able to come to one of two possible conclusions.

One conclusion would be that the heat generated within the device is so small (negligible) that it will not be harmful to the body. The other conclusion would be that the heat generation is too large within the device and that it will be harmful to the body.

A simple 1 dimensional energy balance analysis was conducted using a total temperature resistance relationship to find the temperature on the surface of the device for a range of heat generation. In order to verify this analysis, an equation for the temperature distribution found. The results were similar but not matching up enough to be considered completely credible. A third analysis was then conducted in ANSYS for multiple values of heat generation.

Data:

Reference Temperatures[C]:

Body Temp1= 37 C

Ambient Air Temp2= 25 C

Device dimensions [m]:

Length=0.1312 (design)

Width=0.0490 (design)

Thickness=0.0586 (design)

Area=0.0064 m2

Volume=0.000377m3

Surface Area=0.0340 m2

Body/Device Thickness Dimensions [m]:

Internal Organs3=0.030

Abdomen3=0.010 (estimate)

Fat=0.010 (estimate)

Titanium=0.003 (design)

Skin3=0.003

Clothing=0.003 (estimate)

Conduction Coefficients [W/m*K]:

Device5=1.000 (estimate)

Internal Organs4=0.500

Abdomen4=0.500

Fat4=0.300

Titanium5=19.000

Skin3=0.300

Clothing5=0.029

Convection Coefficients [W/m*K]:

Air5=10.000

Heat Resistance [m2*K/W]:

Device=0.059

Internal Muscles/Organs=0.060

Abdomen=0.020

Fat=0.033

Titanium=0.000

Skin=0.010

Clothing=0.109

Air=0.100

Assumptions:

1-D in the x-direction
Steady-State
Constant properties
Negligible contact resistance
Adiabatic on left side of device (x<0)
Uniform heat generation within the device
Uniform heat conductivity
Neglect radiation at the surface
Neglect heat generation and perfusion of the body

Analysis:

ENERGY BALANCE:

The energy equation was applied to the device to determine the amount of heat dissipated in the direction of the skin and the interior of the body.

Where q is the energy generation, A is the area perpendicular to the direction of the heat flow, is the heat flux, T1 is the temperature at the surface of the device, T2 is an external temperature, and is the heat flux resistance. Heat flux resistance through conduction and convection are defined by the following equations, respectively:

Where L is the length of the material, k is the thermal conductivity, and h is the convection coefficient.

The following thermal circuits were used to determine the total thermal resistance from the device to the skin and from the device to the interior of the body, respectively:

The heat flux resistance from the device to the skin can be described by;

The total heat flux resistance from the device to the interior of the body can be described by;

The results of the analysis for various amounts of heat generation can be seen in Figure 1.

Figure 1

TEMPERATURE DISTRIBUTION:

The temperature distribution analysis was performed by integrating the heat equation:

To obtain the general solution:

Using the boundary conditions for the device:

We find the characteristic solution to be:

Note that this varies from the solution in the book (Fundamentals of Heat and Mass Transfer) in that the second term is negated. The temperatures T1 and T2 were solved for by applying energy balances to both sides of the device.

Figure 2

(for 0<q<0.5)

Table 1

Heat Generation (W)Flux (mW/cm2)

0.00 0.0000

0.40 5.2384

0.80 10.4769

1.20 15.7153

1.60 20.9537

2.00 26.1922

ANSYS ANALYSIS:

Figure 3: Heat Flux in W/m2 for 2 W of Heat Generation

Figure 4: Temperature Distribution for 2 W of Heat Generation

Conclusion:

Initially, the energy equation was applied to the surfaces of the device. Figure 1 shows the Heat Rate for each surface. One data plot shows the dissipation to the body and the other shows the heat dissipation to air. Adding these values reveals the total heat dissipation from the device for various inputs of heat generation. The lines represent the total curve while the dots reveal the region that is within the temperature range of the device that will not cause harm to the body. The maximum heat generation allowed from this analysis appears to be about 0.6W.

To follow the worst case scenario, one would look at the plot of heat generation with respect to the temperature of the air. This shows how much heat will be dissipated when we assume that there is no heat dissipation into the body (adiabatic). The maximum heat generation allowed from this analysis appears to be about 0.35W.

The heat equation was solved to determine the temperature distribution from the device to the clothing surface for multiple heat generation values. Figure 2 shows the relationship between temperature and heat generation (W)for a range of 0 to 0.5 Watts of heat generation. We can see from the figures that the temperature of the device facing the inside of the body remains near 40 degrees Celsius when the heat generation is below around 0.4 Watts. Table 1 shows the heat flux values for up to 2 Watts of heat generation. This data shows that the device would safely be able to generate amount of heat energy while remaining below our constraint of 40mW/cm2.

In general the temperature distribution solution seems to fit a model that we would expect better than the previous solutions. The problem still remains that on the right side of the device, the initial temperature and heat generation of the human body is not accounted for. Also, this is not entirely the worst case scenario because if the left side of the device were to be adiabatic, then the temperature would be unknown and thus, a solution could not be obtained. Also, this model neglects the heat generation in the body but assumes that the body’s energy was used to bring the device temperature up to body temperature initially where it then reaches steady state and can then be neglected in the solution.

Both of the solutions results in relatively high temperature values for low heat flux values. As we are not satisfied with the results, a solution will be pursued in ANSYS. Figure 3 is a contour plot of the heat flux. If the values are reduced to mW/cm2 then the result would be a tenth of the values that are displayed. This means that for 2 Watts of heat generation, the maximum heat flux from the device would be 16.6mW/cm2. Looking more carefully at the plot we see that this occurs only at the corners of the device. In the body the maximum heat flux is actually only about 11.2mW/cm2. The 2D analysis results show that a much smaller heat flux can be obtained than from the 1D analysis for the same amounts of heat generation.

In Figure 4, the temperature appears to rise relatively high. This is not likely to pose too much of an issue when we look at some of the assumptions that we’ve made. We assumed that the body was at steady state and that the device was only an additional heat source. Thus, the analysis doesn’t include the metabolic heat generation of the body nor does it include the perfusion rate or circulation of heat due to the blood. In theory, this analysis seems quite simple but there is certainly a lot going on inside the body that is truly difficult to model. The result of this analysis has many flaws and is likely to have a large amount of error. However, it is a good model to be used in order to get a grasp of what is happening.

Appendix:

1.)

2.)

3.)Heat and Mass Transfer Textbook. pg26Example 1.6

4.)Heat and Mass Transfer Textbook. pg 163. Example 3.12

5.)

6.)Thermal Consideration for the Design of an Implanted Cortical Brain-Machine Interface.