Question by Student 201327128
I'm sorry, I'm not good at writing with a formula on the computer. So I attached a image.
 03.14.18
You need to typeset your post using . Only attach images for figures/schematics. Also, other students have provided good explanations already — we need to move on now.
 Question by Student 201527110 Professor, I have question about the differences between heat flux and energy density. At one glance, they have exactly same unit ($W/m^2$) and similar form ($\sigma T^2$). So is there any differences between those or assumptions (conditons) of those?
 03.15.18
Here you mean that the energy density in a room is the same as the heat flux due to radiation coming out of a black body. They may have a similar form but this doesn't mean they are subject to the same assumptions.. You can determine the assumptions from my explanations in class.
 Question by Student 201327139 Professor, I have a question about Assignment #1, Problem 3. I used heat eqs, $\frac{\partial}{\partial t} \left( \int_{V}^{} \rho cT dV \right) =-\int_{S}^{} q^{\prime\prime} \centerdot \vec{n}dS +\int_{V}^{}SdV$, $q^{\prime\prime}_{conv.1} = -q^{\prime\prime}_{conv.2}$, and $h_1(T_{P_1}-T_{\infty_1}) = h_2(T_{\infty_2}-T_{P_2})$, therefore I found a expression that $T_{P_2}=\frac {20}{3} \left( 80'C - T_{P_1} \right) +20'C$. I want to know another eqs for solving $T_{P_1}, T_{P_2}$. But I can't find it. Where can I get it? Thank you.
 03.21.18
Good question. You can get a second equation by applying the heat equation in integral form to one of the plates. Then, you'll have 2 equations for 2 unknowns. 2 points bonus.
 03.22.18
 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
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.
 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.
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