# RC diagram design

I am doing an RC diagram for a physical model of the heat dynamics of a building. I hope I can get some help here, as the RC diagrams originates from electrical engineering.

The diagram is the one shown below. It basically consists of different temperatures nodes $$\(T_{*})\$$, resistances $$\(R_{*})\$$, capacities $$\(C_{*})\$$, heating inputs $$\(\Phi_{*})\$$ from the heating system and the sun, and the fluctuating outdoor temperature $$\(T_{\mathrm{e}})\$$.

I need two things:

(1) The RC diagram is representing a mathematical model where the solar radiation, $$\\Phi_{\mathrm{s}}\$$, is multiplied by a function, $$\{\mathrm{gA_1}(\gamma)}\$$ or $$\{\mathrm{gA_2}(\gamma)}\$$. Right now I have illustrated it with the squares with the function inside, but it is not really clear that it should be multiplied with $$\\Phi_{\mathrm{s}}\$$. What would be a correct way of drawing it?

(2) One part ($$\P\$$) of the solar radiation, $$\\Phi_{\mathrm{s}}\$$, is entering $$\{\mathrm{gA_1}(\gamma)}\$$, and the remaining part ($$\1-P\$$) is entering $$\{\mathrm{gA_2}(\gamma)}\$$. Is there a suitable symbol for that?

• Welcome to EE.SE. This maybe more of a physics question as you are referring to the heat dynamics of a building, as well as the suns heat output.
– user105652
Commented Oct 15, 2018 at 23:05
• What is this function... "$gA(\gamma)$"? Is this some gain function multiplied by a transconductance?
– user103380
Commented Oct 16, 2018 at 0:19
• @KingDuken, gA$(\gamma)$ is a function of the solar azimuth (the horizontal angle from North) which in my case basically is equivalent to the time of the day. The gA functions are the ratio between solar energy entering the building and the intensity of the outdoor solar irradiation as a function of $\gamma$. So, if I e.g. receive 500 W/m$^2$ solar irradiation on an outdoor surface at 10 AM, I have an energy gain of 100 W inside the building. And if I receive 500 W/m$^2$ solar irradiation on an outdoor surface at 3 PM, I have an energy gain of 225 W inside the building. Commented Oct 16, 2018 at 8:18

(1) If your functions gA1(gamma) do not have any time dependency, then you can consider them as gain blocks. This would be (voltage) amplification in electrical engineering and the block symbol is OK for that, but the general amp symbol would fit even better:

(2) You can simply model this with two seperate heat sources, one of them is Phi_S1=P and the other is Phi_S2=1-P.

• As I just commented on my post, the gA function is actually time dependent. Commented Oct 16, 2018 at 8:25
• Then you will have to model this time dependency with an RC circuit or you won‘t be able to solve the whole circuit. Commented Oct 16, 2018 at 9:39
• All right. I think that was the answer I was looking for. Commented Oct 16, 2018 at 22:45