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You are looking for a combination of features that demand balance. You can't have all three in combination. If the material heats up quickly it will not absorb much heat and it will also lose heat rapidly. If it cools slowly it will be able to absorb a lot of heat, but will take a while to heat up. And so forth.

Posted
what material heats the fastest, cools the slowest and absorbs the most heat. i wish to plae it in my fireplace. or even build a fireplace enclosure.
Given the use you want, I'd say you won't be much concerned with how fast it heats up (which, as said, goes hand in hand with how fast it cools), and you would mostly want it to have a high specific heat. Water is almost the highest. Given the high temperature, if you are able to store a large quantity of water vapour it would add the latent heat as well. Of course, you want it to release heat at an appropriate rate for the intended use.

 

For a fireplace, I would suggest designing things ao as to absorb as much as possible of the heat that is about to leave the chimeney, without damping out the draft that keeps the fire going. In this way you gain efficiency as well as duration. Yes, a well designed fireplace can improve things compared to most traditional ones.

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