Answer:
t=5.2seconds
Explanation:
First, we state our assumptions:![1. Temperature \ of \ the \ junction \ is \ uniform \ at \ any \ instant\\2. Radiation \ is \ negligible\\3. Constant \ properties](https://tex.z-dn.net/?f=1.%20Temperature%20%5C%20of%20%5C%20the%20%5C%20junction%20%5C%20is%20%5C%20uniform%20%5C%20at%20%5C%20any%20%5C%20instant%5C%5C2.%20Radiation%20%5C%20is%20%5C%20negligible%5C%5C3.%20Constant%20%5C%20properties)
Given ![T_i=25\textdegree C, k=20W/m.K\ , C_p=400J/kg.K \ \rho=8500kg/m^3](https://tex.z-dn.net/?f=T_i%3D25%5Ctextdegree%20C%2C%20k%3D20W%2Fm.K%5C%20%2C%20C_p%3D400J%2Fkg.K%20%5C%20%5Crho%3D8500kg%2Fm%5E3)
and gas stream![T_-=25\textdegree C , h=400W/m.K](https://tex.z-dn.net/?f=T_-%3D25%5Ctextdegree%20C%20%2C%20h%3D400W%2Fm.K)
We use the time constant to find the diameter of the junction:
![\tau _t=\frac{1}{hA}\rhoVC_p=\frac{1}{h\pi D^2}\times \frac{\rho \pi \D^3}{6}C_p](https://tex.z-dn.net/?f=%5Ctau%20_t%3D%5Cfrac%7B1%7D%7BhA%7D%5CrhoVC_p%3D%5Cfrac%7B1%7D%7Bh%5Cpi%20D%5E2%7D%5Ctimes%20%5Cfrac%7B%5Crho%20%5Cpi%20%5CD%5E3%7D%7B6%7DC_p)
![=>D=0.706mm](https://tex.z-dn.net/?f=%3D%3ED%3D0.706mm)
Now, check the validity of the lumped system analysis. With ![L_c=r_o/3](https://tex.z-dn.net/?f=L_c%3Dr_o%2F3)
#Lumped Analysis is OK
Bi<<0.1, therefore the lumped approximation is excellent. The time required for the junction to reach
:
![\frac{T(t)-T_\infty}{T_i-T_\infty}=e^-^b^t\\b=\frac{hA}{\rho VC}\\\\t=\frac{1}{b}In \frac{T_i-T_\infty}{T(t)-T_\infty}\\t=5.2s](https://tex.z-dn.net/?f=%5Cfrac%7BT%28t%29-T_%5Cinfty%7D%7BT_i-T_%5Cinfty%7D%3De%5E-%5Eb%5Et%5C%5Cb%3D%5Cfrac%7BhA%7D%7B%5Crho%20VC%7D%5C%5C%5C%5Ct%3D%5Cfrac%7B1%7D%7Bb%7DIn%20%5Cfrac%7BT_i-T_%5Cinfty%7D%7BT%28t%29-T_%5Cinfty%7D%5C%5Ct%3D5.2s)
It takes 5.2seconds for the junction to reach 199 oC
Displacement is the straight-line distance and direction from start-point to end-point, regardless of the actual path taken.
In this example, that's 10.3 km (rounded) in the direction 14 degrees west of South.
The nerves in the wormes body recieve electrical impulses transmitted through their inner core which makes them shimy if you will