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

[ryanferg]

TL;DR

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?

 

[berkeman]

Welcome to PF.

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

 

[ryanferg]

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?

 

[ryanferg]

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.

 

[Chestermiller]

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.

 

[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.

 

[anorlunda]

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

 

[ryanferg]

Sorry for the confusion, they are both solids.

 

[Chestermiller]

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?

 

[256bits]

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.