# Heat flow equation question (probbaly easier than i think)

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Hi everyone

Firstly, i'm at UNI doing this assignment, and stuck on this one part. Its only first year Engineering and it's a really easy engineering subject, probably don't need to go into this much detail but I suppose if i can then i may aswell do it

We're doing a climate control system for a house in india, i've got an equation that somewhat models the outside maximum and outside minimum temperatures for the city the house is being built in...

Tmax = 30 + 5sin(tπ/11)

Tmin = 20 + 5sin(tπ/11)

Where t = time in months (January = 0, December = 11)

T = temperature

Also, the rate of heat flow equation is ...

Q/t = [kA(Thot - Tcold) ] / d

Where,

Q/t = rate of heat flow ???

k = thermal conductivity of the barrier (0.653 W/m.K in this case)

A = Area of the wall , I'll assume its 3m x 5m

T = temperature (hot is outside, cold is inside i'd suppose)

d = thickness of barrier, and in this case the bricks are lets say 270mm thick

My question is... How on earth do i figure out what the inside temperature could be when i've got two unknowns, the rate of heat flow and the inside temperature...

If anyone can help me with these simple equations that'd be heaps appreciated...

I'm sure there's a way you can manipulate the equation or even there might be a whole different equation that you could use..

I know everything except inside temperature (thats what I want to find out) and the rate of heat flow...

THANKS EVERYONE! John.

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I think typical room temperatures are around 20°C. But what would keep you from keeping the inside-temp as a variable and obtaining the necessary specification of your climate control system as a function of the demanded inside temperature?

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I was trying to get a function of the inside temperature against time... say a sin wave of the yearly temperature changes against time for the inside of the house, and then I can compare the inside temp against the outside temp and hopefully say THEREFORE IT KEEPS IT COOL IN THE SUMMER TIME AND WARM IN THE WINTER TIME (thats what the clay bricks are meant to do ... thats what i'm using in this assingment)

Hope you all sort of understand what i'm tryin to do, i cant really explain it that well....

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I can´t answer how to (analytically) get the inside temperature as a function of time, atm. But, no offense meant, I am not entirely sure if that´s what you´really looking for. So allow me the question: What kind of engineer are you? Are you a civil engineer that looks for a material with suitable thermal properties to isolate the house (why is the material given, then?) or are you a mechanical engineer that wants to know the energy energy consumtion of a climate control system? In the latter case, the inside temperature would be dictated by the residents of the house and probably be constant => you just have to know the energy flux via heat and compensate for it.

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Ok thanks for your help athiest..

Heres what i'm trying to do.. I dont HAVE to do this but i thought i may aswell just to give more proof that the clay bricks are good option for a climate control system for this house.. i'm no engineer as of yet, and this enginering subject is just a crap subject for general engineering (no major chosen yet)..

I'm trying to find the inside temperature against time because then i can show that it will stay fairly constant and a suitable temperature.

I dont know how else to explain this. i guess I could just leave out the section because the tutors at Uni didn't know how to do it and they tried to speak some rubbish to me but its complete crap... he didn't know...

Anyway thanks..

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A straightforward solution would be plugging the equation into a computer and play around with different starting conditions; the system will probably go into a state that´s independent of the intial conditions after some time, anyways. You'll most certainly need a guesstimate of the interior's total heat capacity, though. You can get that from the heat capacity of air (shouldn´t be too hard to find on the net) and the volume of the interior. There´s a few other small issues that might need to be cleared up before you can simulate it on a computer, such as the question what the minimum and maximum temperature actually mean (is it mid-day vs. midnight? how does the temperature behave inbetween? what time-scale do you simulate on? ect.). Could be fun to simulate if you like programming, but if you´re not used to numerical simulations you should not underestimate it as a "done in an afternoon" issue.

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