Thermal Modeling
Material Conductivities
| material | conductivity |
|---|---|
| wood effective r-value including air | 0.045 W/m/K |
| wood | 0.12 W/m/K |
| glass | 0.8 W/m/K |
| foam | 0.02 W/m/K |
Activity-01 Forward Model of UA for Laser-Cut Box
Find the UA value of a wood box. (This is the laser cut box we’ve been using.) We have laser cut a 10 cm cube of 5mm thick wood. What is the expected UA value assuming a conductivity of wood of 0.12 W/m/K? We include air films for this example.
Activity-02 Forward Model Laser-Cut Box plus insulation
Find the UA model of our laser cut box with the addition of rigid foam.
The box is still a 10 cm cube and now has 15 mm of rigid foam insulation.
Include the insulation from air films in you calculation.
| wood thermal conductivity | 0.12 W/m/K |
| glass thermal conductivity | 0.8 W/m/K |
| foam thermal conductivity | 0.044 W/m/K |
| interior air film R-value | 0.12 m^2/K/W |
| exterior air film R-value | 0.03 m^2/K/W |
Activity-03 Forward Model Laser-Cut Box with Foam and Windows
Compute the UA product of our laser-cut box with insulation using a forward model.
We have laser cut a 10 cm cube of 5 mm thick wood. Assume a thermal conductivity of wood is 0.12 W/m/K.
The physical box has three windows that are 25 mm by 75 mm and are 1 mm thick. Let’s make the approximation that the front wall is 10 cm by 10cm and all glass. Assume a thermal conductivity of glass of 0.8 W/m/K.
Activity-04 Backward Model Laser-Cut Box
The data below is for our 10 cm laser cut wood box. In this data run, we apply four watts of heat. The curves on the left are for the four temperature sensors.
- inside air temperature
- inside wall temperature
- outside wall temperature
- outside air temperature
- State in words your approach to the problem.
- Find the R-value in metric units for each of the three layers and identify the three layers.
Activity-05 Backward Model Laser-Cut Box plus insulation
The data below is for our 10 cm laser cut wood box with added foam insulation. In this data run, we apply 2 watts of heating. The curves on the left are for the four temperature sensors.
- inside air temperature
- inside wall temperature
- outside wall temperature
- outside air temperature
- State in words your approach to the problem.
- Find the R-value in metric units for each of the three layers and identify the three layers.
Activity-06 Backward Model Laser-Cut Box with Windows and Insulation
The figure below shows the data for our box with windows with 1W applied to the heater and 2W applied to the heater.
What is the observed UA of our laser-cut box with windows?
Activity-07 Estimate Solar Gain
The data below shows the box under solar gain
Estimate the intensity of transmitted solar radiation in W/m^2 using the UA of the box and the observed steady-state temperature difference.
MOD-01 Forward Model of 20 cm Cube
We have laser cut a 20 cm cube of 3mm thick wood with a thermal conductivity of 0.05 W/m/K. What is the estimated UA value using a forward model?
MOD-02 Backward Model of Box
We place a 20 watt heater in a box with an unknown UA value. After a long time, the inside temperature in the box settles to 30C while the outside temperature remains at 20C. Use a backwards model to estimate the UA value of the box.
MOD-03 Backwards Model of Laser-Cut Box
We have the following temperature data for our heated box. What is your estimate of the r-values for
- inside air film
- wood wall
- outside air film
We place a 20-watt heater in a cubic box that is 20 centimeters on a side with a wall thickness of 3 mm. After a long time, the inside temperature in the box settles to 30C while the outside temperature remains at 20C. Use a backwards model to estimate the conductivity of the wall material.
MOD-04 Euler Prediction of Temperature
The rate of change of the temperature with time is given by the following formula.
\frac{dT}{dt} = \frac{P_h - UA(T - T_{out})}{mc}
If the power of the heater P_h = 1W, the heat capacity mc = 50 J/K, and the UA value is UA = 2 W/K, the outside temperature and inside temperature T = T_out = 20C.
Use the Euler method with one minute steps to estimate the temperature 10 seconds and 20 seconds after the start.
MOD-05 R and U value of wood
We are using 5mm wood with a conductivity of 0.045 W/m/K.
What is the U-value and R-value in metric and US units?
Forward Model of 20 cm Cube with insulation
We have laser cut a 20 cm cube of 3mm thick wood with a thermal conductivity of 0.05 W/m/K. We add another 3mm layer of insulation with a thermal conductivity of 0.02 W/m/K. What is the estimated UA value using a forward model?
Steady State Temperature
Use a forward model to estimate the steady state temperature of a box.