# Heat Transfer Through a Two Material System due to a Light Source

• ryanferg
In summary, the conversation discusses the task of modeling heat transfer from a light source into a system consisting of two connected materials. The goal is to find the temperature change in the bottom surface of the system, with the two materials initially in thermal equilibrium with the surroundings. The approach of using the lumped capacitance method is discussed, but it is deemed too simplistic and the suggestion is made to use the transient 1D heat conduction equation for each layer, taking into account the continuity of heat flux at the junction between the layers. The potential need to include convective and radiative heat loss is also mentioned, and it is noted that the calculations may need to be done numerically. The conversation also touches on the use of Matlab for simulations
ryanferg
TL;DR Summary
Heat Transfer Through Two Material System due to Light Source with Known Power
I have been given the task of modeling the heat transfer from a light source of known power into a system consisting of two connected materials. I must find the temperature change in the bottom surface. The two materials are initially in thermal equilibrium with the surroundings.

My first thought was to uses the lumped capacitance approach, thinking the resistance to convection will be much higher than that of conduction. I also assumed that heat lost throughout to the surroundings due to radiation or convection was negligible.

The percentage of light absorbed by the top material will be determined experimentally, so the heat flux into the top surface would be the power of the light (watt/cm^2) * % of light absorbed. Multiplying this flux by the area it is applied on and the time the light is on gives the total heat applied in joules, and setting that equal to rho*V*c(Tf-Ti) to get Tf, the new temperature of the top layer.

I was then thinking to use the new temperature difference between the top layer and bottom layer to get the heat flow due to conduction into the bottom layer, and then essentially repeating the same process to get the new final temp of the bottom layer (when integrating the conduction heat flow, I am unsure if I would use the same time as before, the amount of time the light was on).

However, this feels too simple to me and like I must be overlooking something. Is there a more accurate way to go about this? Are my assumptions valid?

Last edited by a moderator:
Welcome to PF.

Is this for schoolwork? If for regular work, what is the application?

Thanks. I am a college student; this is for summer internship. I am modeling part of a pyroelectric sensor. It consists of a top layer material that is high in absorptivity to absorb as much light as possible from a given power source and convert it to heat. This heat will then be transferred through conduction to the second layer underneath, a pyroelectric material, which is a material that induces voltage/current when exposed to a temperature change. I will be writing a script where material properties, geometries, power of light source, etc. can be input, and the output will be the temperature change of the pyroelectric and as a result induced current or voltage.

berkeman
Congrats on the internship! We normally would move schoolwork-type questions to the schoolwork forums, but since this is for an internship it's probably okay here for now.

Is this purely a hand-calculation modeling, or will you also be running simulations in some software package? If you will be doing simulations, what software package/suite will you be using? Will you also be building an experimental setup to validate your calculations and modeling?

Thanks! I am first planning to write out the math by hand and make sure my theory is right, then transfer it into a MatLab script to easily change materials, powers, or geometries and see the effect on the temperature change. I will also generate plots on matlab.
Eventually, the sensor will be manufactured and experiments will be run to test the actual results. However, the purpose of my program is to determine which top material and geometry optimizes the sensor before it is built and resources are wasted.

Last edited:
berkeman
In my judgment, your approach is overly simplified. Is all the laser heat released at the top surface?

You should be using the transient 1D heat conduction equation for each layer, with continuity of the heat flux at the junction between the layers. You may also need to include convective heat loss to the surroundings at the top and bottom surfaces (and, if the temperature increase is high, radiative heat loss as well).

This may have to be done numerically.

berkeman and ryanferg
I agree, it definitely was too simple. Can you explain more about the 1-d transient conduction? I have the equation written out, but I am unsure how to apply it in this situation to eventually get a delta t of the bottom layer pyroelectric. The temperature change will be small, so I am assuming radiation will be ignored. For convection heat loss, the biot number is extremely low, meaning conduction is dominant, so I was also thinking that this could be negligible. Thanks.

At first, I thought the two materials were solids but you mentioned convection. If they are gases, what prevents mixing?

Sorry for the confusion, they are both solids.

ryanferg said:
I agree, it definitely was too simple. Can you explain more about the 1-d transient conduction? I have the equation written out, but I am unsure how to apply it in this situation to eventually get a delta t of the bottom layer pyroelectric. The temperature change will be small, so I am assuming radiation will be ignored. For convection heat loss, the biot number is extremely low, meaning conduction is dominant, so I was also thinking that this could be negligible. Thanks.
Are you saying that you do not know how to solve the transient heat conduction equation for a 2 layer laminate with constant heat flux at the upper surface?

ryanferg said:
I agree, it definitely was too simple. Can you explain more about the 1-d transient conduction? I have the equation written out, but I am unsure how to apply it in this situation to eventually get a delta t of the bottom layer pyroelectric. The temperature change will be small, so I am assuming radiation will be ignored. For convection heat loss, the biot number is extremely low, meaning conduction is dominant, so I was also thinking that this could be negligible. Thanks.
What is it that you are actually trying to determine for your sensor?
The pyroelectric material acts according to change in its temperature.
Thus a small thermal mass would be appropriate.
Adding a covering material adds to the thermal mass of the unit with a resulting decrease in frequency response ( pulse period of the laser input ). Adding a covering unit with low conductivity ( or ie not thermally thin ) would result in a lagged response time due to the temperature gradient within the covering material.

Once the sensor reaches steady state temperature, either in active move with the laser input, or in relaxation mode with the laser off, the signal decays.

Somehow the thermal mass has to be incorporated into the modelling, as well as the exchange of the heat with the environment so that the unit can cool off after each laser pulse.

## 1. What is heat transfer through a two material system due to a light source?

Heat transfer through a two material system due to a light source is the process by which heat energy is transferred from one material to another when exposed to a light source. This can occur through three mechanisms: conduction, convection, and radiation.

## 2. How does conduction contribute to heat transfer in a two material system?

Conduction is the transfer of heat energy through direct contact between two materials. In a two material system, heat energy is transferred from the material with a higher temperature to the material with a lower temperature, until both materials reach thermal equilibrium.

## 3. What is the role of convection in heat transfer through a two material system?

Convection is the transfer of heat energy through the movement of fluids or gases. In a two material system, convection can occur when the heated material expands and rises, while the cooler material contracts and sinks. This creates a continuous cycle of heat transfer.

## 4. How does radiation affect heat transfer in a two material system?

Radiation is the transfer of heat energy through electromagnetic waves. In a two material system, radiation can occur when one material absorbs the light energy from a light source and re-emits it as heat energy, which is then transferred to the other material.

## 5. What factors can influence the rate of heat transfer in a two material system due to a light source?

The rate of heat transfer in a two material system due to a light source can be influenced by several factors, including the intensity and wavelength of the light source, the thermal conductivity of the materials, and the temperature difference between the two materials. Other factors such as surface area, distance between the materials, and the presence of insulating materials can also affect the rate of heat transfer.

Replies
1
Views
2K
Replies
34
Views
3K
Replies
1
Views
2K
Replies
15
Views
2K
Replies
2
Views
2K
Replies
4
Views
2K
Replies
10
Views
2K
Replies
27
Views
5K
Replies
9
Views
2K
Replies
2
Views
2K