Heat Transfer Questions & Answers  
Question by Student 201800128
Dear Professor
I have a question about problems that involve mixed heat transfer of radiation and either convection or conduction. In Assignment 1 the expressions of variables come in $T_{1}$ and $T_{1}^4$. I am not able to find an analytic solution to the problem and therefore turn to numerical methods. I am wondering if it is common to use numerical methods in these problems, such as Newton's Method, or if there is some kind of trick I am not aware of.
Cheers
03.21.18
When you can't find the root to an equation analytically, use a Picard iteration. Thus, let's say we have one equation for one unknown $\phi$ as follows: $$ \phi^4 +\phi^3 +2 \phi=3000 $$ Replace one of the $\phi$ with $\phi_{n+1}$ and the other $\phi$s with $\phi_n$: $$ (\phi_{n})^4 +(\phi_n)^3 +2 \phi_{n+1}=3000 $$ Then isolate $\phi_{n+1}$ as a function of $\phi_n$. At the first iteration (n=1), set $\phi_1$ to a good guess for the root. Then obtain $\phi_2$ this way. Once $\phi_2$ is known, you can obtain $\phi_3$, and so on, until you reach the root. 2 points bonus.
03.22.18
Question by Student 201327106
Dear professor, today, you did not write the assumptions of Temperature Profile Sketch. Can I know the assumptions?
03.26.18
1D H-T along $x$, S-S.
Question by Student 201427125
Dear professor professor said that assignment #2, #3, use iterative(?) process, but I didn't complete NUMERICAl ANAlYSIS. So what is iterative process?
03.27.18
You can read about it here:
​ https://bernardparent.ca/viewtopic.php? ... 6645#p6645
Question by Student 201227125
Professor, at fin problem, Wall and fin was contacted. but why does not consider contact resistance in solve heat rate $q_x$? If wall and fin only one parts(not contact), we should define assumption that?
03.29.18
Yes, this would be an additional assumption if the fin and the base are separate pieces. But often they are welded together and there is no resistance. 1 point bonus.
Question by Student 201327106
Professor, in Fin Efficiency with non-insulated tip, you wrote $$ A_m=tL, L_c=L+t/2 $$ I don't know why $$L_c=L+t/2$$
If you work out the problem but impose a convective heat transfer BC at the tip, then you can show that $L_c=L+t/2$. Maybe I'll ask you this question in the midterm..
03.30.18
Question by Student 201327106
Professor, in shape factor example with heat generating hollow cylinder between two plates, you wrote $$q=SL\pi r_i^2$$ But, I think $$q=SA=2SL\pi r_i^2$$ with radius $$r_i$$ Thank you.
I don't understand your question. The heat generation is $$ q=SV=SAL=S\pi r_i^2 L $$ because $A$ is the area within a circle of radius $r_i$.
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