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Is there an equation to figure out what the temperature of an the area will be a certain distance from the heat source?

For example, if I know there is a heat source at $0~\mathrm{m}$, and the temperature is $100~\mathrm{^\circ C}$, is there a way to find out what the temperature will be at $50~\mathrm{m}$ away from the heat source? Is there some sort of equation for this? All of this is happening in oxygen.

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This is a heat transfer related problem. You can certainly do that. For solid medium heat transfer you need to use Fourier heat transfer equation
\[q=-k\cdot\nabla T\]
Here, k= material's conductivity and $\nabla T$ = 1st derivative of the Temp. along the driving force or heat
For Liquid and gas phase you should use law for thermal convection. And for vacuum medium you should use radiation law. There are lots of ways to do this but from your problem statement i think it's a numerical grid type problem. For your better understanding, i would suggest 'Engineering heat transfer' by william s janna (I may be biased here because i like this book) but you can certainly use any other standard heat transfer book or internet.

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  • $\begingroup$ Where in the equation does distance from heat source go? And what units do I use? $\endgroup$
    – Jayden Miller
    Commented May 2, 2015 at 5:40
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    $\begingroup$ @Jayden Miller this is a partial differential equation. You will probably have to solve it numerically, which means breaking up the volume you are interested in into small boxes and then solving the heat transfer equation across the boundary of each one, most likely using a computer program. You can use any units you want as long as they are consistent. SI units is probably easiest. If you give more specific details in your problem statement, there may be a way to simplify the problem to one dimension, which would make it a lot easier. $\endgroup$
    – thomij
    Commented May 2, 2015 at 14:58

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