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Question:

In which direction does heat flow between two objects of different temperatures?

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Answer:

I found it interesting that you used the term heat flow, not heat transfer. In the simplest terms, direction of heat flow is determined by convention, an arbitrary declaration by the scientific community. Therefore, the answer could be either. However, since you asked heat flow, and heat is generally classified as the hotter element, then heat flow would be from hot to cold. Then there is the theory that there are no lights - only darkness absorbers. But I digress...
There is an old saying, that heat rises, and for the most part that's true. Now, when it comes to heat transfer, heat will always travel or migrate to a cooler surface. Example, a furnace, the flame regardless of fuel source builds the heat, which in turn travels to the bonnet or duct work to be distributed, hence the name heat exchanger. The older the heat exchanger gets, the less heat it will transfer because the molecules die and the ,metal becomes dead and lifeless. Another example is when they figure the size of furnace to install in a home, they use what is called heat loss calculations which again means the heat is lost, by travelling from the warmer inside, to the cooler outside, and in the summer it's reversed and called heat gain for air conditioning calculations.

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