Answer: The outer surface temperature is
.
Explanation:
Given: Heat = 3 kW (1 kW = 1000 W) = 3000 W
Area = 10 ![m^{2}](https://tex.z-dn.net/?f=m%5E%7B2%7D)
Length = 2.5 cm (1 cm = 0.01 m) = 0.025 m
Thermal conductivity = 0.2 W/m K
Temperature (inner) = ![415^{o}C](https://tex.z-dn.net/?f=415%5E%7Bo%7DC)
Formula used is as follows.
![q = KA \frac{(t_{in} - t_{out})}{L}](https://tex.z-dn.net/?f=q%20%3D%20KA%20%5Cfrac%7B%28t_%7Bin%7D%20-%20t_%7Bout%7D%29%7D%7BL%7D)
where,
K = thermal conductivity
A = area
L = length
= inner surface temperature
= outer surface temperature
Substitute the values into above formula as follows.
![q = KA \frac{(t_{in} - t_{out})}{L}\\3000 W = 0.2 \times 10 \times \frac{415 - t_{out}}{0.025 m}\\t_{out} = 377.5^{o}C](https://tex.z-dn.net/?f=q%20%3D%20KA%20%5Cfrac%7B%28t_%7Bin%7D%20-%20t_%7Bout%7D%29%7D%7BL%7D%5C%5C3000%20W%20%3D%200.2%20%5Ctimes%2010%20%5Ctimes%20%5Cfrac%7B415%20-%20t_%7Bout%7D%7D%7B0.025%20m%7D%5C%5Ct_%7Bout%7D%20%3D%20377.5%5E%7Bo%7DC)
Thus, we can conclude that the outer surface temperature is
.
Answer:
3.99 mm
Explanation:
To treat a diffusive process in function of time and distance we need to solve 2nd Ficks Law. This a partial differential equation, with certain condition the solution looks like this:
![\frac{C_{s}-C_{x}}{C_{s}-C{o}} =erf(x/2\sqrt{D*t})](https://tex.z-dn.net/?f=%5Cfrac%7BC_%7Bs%7D-C_%7Bx%7D%7D%7BC_%7Bs%7D-C%7Bo%7D%7D%20%3Derf%28x%2F2%5Csqrt%7BD%2At%7D%29)
Where Cs is the concentration in the surface of the solid
Cx is the concentration at certain deep X
Co is the initial concentration of solute in the solid
and erf is the error function
First we need to solve the Cs-Cx/Cs-Co on the left to search the corresponding value later on a table.
![\frac{0.15}{0.35} =0.4285](https://tex.z-dn.net/?f=%5Cfrac%7B0.15%7D%7B0.35%7D%20%3D0.4285)
We look on a table and we see for erf(z)=0.4284 z=0.40
Then we solve for x
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True..
Don’t mind this
OSHA requires that fall protection be provided at elevations of four feet in general industry workplaces, five feet in shipyards, six feet in the construction industry and eight feet in longshoring operations.
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