It is a question vector calculus and Maxwell's laws. I put it this way. Let's say, we are working in a $3$-Dimensional space ( e.g $x\cdot y\cdot z = 4\cdot3\cdot2$, a certain room/class of that size ) .
Within this room, the heat obey a certain equation ( for e.g. $T = 25 + 5z$ ) .We know that heat flows from higher temperature regions to lower temperature regions. With this information in mind
How could I be able to determine the amplitude and the direction of travel of the thermal energy with the Del operator ( gradient ) ? .
I'm not looking for a definitive response, but an equation that could give me potentially the result for the amplitude and the direction. I also want to know if thermal energy follows a loop pattern within my room (and be able to explain it mathematically by using the del operator once again of course)?
You can find the lecture source here.
Thank you.