Heating Power of a Substance

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Is there a way to determine the "heating power" of a substance with a known specific heat and mass, onto another object of another known specific heat and mass.

Say if I had a tank of water and dropped in a piece of metal for example, let the metal heat up, but not let the system come to equilibrium.
Now I want to figure out the temperature of the metal chunk after X amount of seconds in the water. So I would need to find the rate at which energy is being absorbed from the water into the metal.
How? I havent dont these types of problems in years, and even then, the question had, "and the system is let to reach equilibrium" line at the end.

Now lets take it a step further,
insead of a closed system with a set amount of "hot" and "cold" mass, say one or both of those were moving past eachother, like hot steam traveling through a condenser, or hot water moving through a pipe in a bucket of cold water.


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You are dealing with a forced convection problem, for which you need to know the heat transfer coefficient of the metal object in that particular medium. Knowing this number, the problem just becomes one of writing out Newton's Law of Cooling (in this case, "heating") and plugging in numbers.

The problem with the heat transfer coefficient is that it is highly specific to the material, its geometry, the medium surrounding it, and the flow characteristics.

In general, the temperature of the object will exponentially approach the temperature of the surroundings, the time constant depending on the extent of "thermal contact" between object and surroundings.


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So it would seem the problem is considerably more dificult than I oringally had figured.
While looking more into heat transfer coefficients, it seems like there are so many variables that could influence the final value, you almost have to determine it yourself for a particular object, which almost defeats the point of having it.

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