Resolve two heat flow formulas to isolate a single variable

A

AntonyWhite

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Jan 19, 2022
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Hi All,

I'm sorry if this is either in the wrong place or if I'm asking for something impossible, it's been so long since I really had to use algebra that I genuinely cannot recall. That said, my request is this:

I have a problem regarding heat flow, I have two formulas for calculating the heat flow, each based on the conditions on one or the other side of a surface. Knowing that heat flow is equivalent on both I can rewrite them, but I cannot manipulate it myself because I do not know how to handle the power function?

q = (T1 - T2) / R
q = 8.92 (T2 - T3)^1.1

Where:
T1 > T2 > T3

I need to remove q, so I have rewritten as;
(T1 - T2) / R = 8.92 (T2 - T3)^1.1

I would love to be able to rewrite it as;
T2 = ?

Is that possible, if it is, I'd love to see the workings so that I can relearn what I have forgotten over the last few decades.

Thanks in advance
 
AntonyWhite said:
Hi All,

I'm sorry if this is either in the wrong place or if I'm asking for something impossible, it's been so long since I really had to use algebra that I genuinely cannot recall. That said, my request is this:

I have a problem regarding heat flow, I have two formulas for calculating the heat flow, each based on the conditions on one or the other side of a surface. Knowing that heat flow is equivalent on both I can rewrite them, but I cannot manipulate it myself because I do not know how to handle the power function?

q = (T1 - T2) / R
q = 8.92 (T2 - T3)^1.1

Where:
T1 > T2 > T3

I need to remove q, so I have rewritten as;
(T1 - T2) / R = 8.92 (T2 - T3)^1.1

I would love to be able to rewrite it as;
T2 = ?

Is that possible, if it is, I'd love to see the workings so that I can relearn what I have forgotten over the last few decades.

Thanks in advance
Click to expand...
If you know T1 & T3 & R, you can approximate the value of T2 through numerical iteration.
 
Subhotosh Khan said:
If you know T1 & T3 & R, you can approximate the value of T2 through numerical iteration.
Click to expand...
That has been my historical approach but it becomes quite power hungry on large data sets and as a result I've tended to remove the power and merge it into the 8.92 as a constant which for many cases where the difference between T2 and T3 is is within certain limits it works well enough but it soon diverges outside of the norm.

All the same, thank you for your time, at least if I know its not possible I can stop dwelling on it.
 
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