Soil Temperature and the Semi-Infinite Solid Approach

1. Soil Temperature and the
Semi-Infinite Solid
Approach
Alexa Schiazza

2. To determine the temperature of
soil at a specific depth and
unknown time, using both
experimental and theoretical
methods.
Project Objective:

3. Experimental

4. Project Set-up
● Place two thermometers near each other
in dark soil
○ Thermometer 1 at a depth of 0.04 m
○ Thermometer 2 at a depth of 0.06 m
● Beginning at 11:00 am record
temperature readings every 10 minutes
until 2:00 pm

5. Experimental Data

6. Determining Experimental Values
@ 12:30 pm
● 12:30 pm is the midpoint of the
temperature readings, so look at it for
this example
● Using 12:30 pm as your x value find the
corresponding y value (temperature)
● Find values at times that were not
recorded by using the equation of the
graph to estimate temperature values
x = 0.04 m
T = 289.82 K
x = 0.06 m
T = 293.71 K
Temperature
Reading

7. Theoretical 𝝴
𝞂
t
x
Ti
Using the semi-infinite
solid approach

8. Equations for Semi-Infinite
Solid Method:
q’’= 𝝰sG+𝝴𝞂(Tsky
4-Ts
4)
T(x,t)= ((2q’’(𝝰t/𝝅)½)/k) *exp(-x2/(4𝝰t)) -((q’’x)/k)*(1-erf (x/ (2sqrt(𝝰t))))+Ti
Boundary Conditions:
1. Constant surface heat flux
2. Temperature deep within material
unaffected by surface condition

9. 𝝰s 0.75
G 900 W/m2
𝝴 0.93
𝞂 5.67 * 10-8 W/m2K
Tsky 285 K
Ts 300 K & 304 K
q’’ 595.77 W/m2K & 572.53
W/m2K
𝝰 k/𝝆Cp = 6.16 * 10-7
t 5400 sec ( 12:30 pm )
k 0.837 W/mK
x 0.04 m & 0.06 m
Ti 289.82 K & 293.71 K
q’’
T(x,t)

10. Determining Theoretical Values
@ 12:30 pm
q’’
x = 0.04 m → 595.77 W/m2K
x = 0.06 m → 572.53 W/m2K
T(x,t)
x = 0.04 m → 324.30 K
x = 0.06 m → 333.09 K

11. Discussion

12. Comparison of Experimental and
Theoretical Values
Depth Percent Error
x = 0.04 m 11.90 %
x = 0.06 m 13.41 %
x = 0.04 m
T = 289.82 K
x = 0.06 m
T = 293.71 K
x = 0.06 m
T = 324.30 K
x = 0.06 m
T = 333.09 K
Theoretical: Experimental:

13. Sources of Error
● Did not have an exact temperature of the ground (Ts)
○ Estimated by adding 10 K to the temperature of the ground
● The thermometers were metal
○ Heated and throw temperatures off
○ Covered with a sock to try and avoid
● All values were estimated
○ Based on reputable online sources or class notes

14. COMSOL

15. Citations
● Drapcho, C. 2020. BE 4120 Unpublished course notes, Clemson University
● https://www.e-education.psu.edu/meteo300/node/687
● https://www.engineeringtoolbox.com/solar-radiation-absorbed-materials-d_1568.html
● https://www.engineeringtoolbox.com/thermal-conductivity-d_429.html
● https://thermtest.com/materials-database
● https://giphy.com/gifs/homework-dNgK7Ws7y176U/fullscreen