If you have a limited amount of metal (let's say m) to be casted for making...

 

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If you have a limited amount of metal (let's say m) to be casted for making a rectangular fin, what would be the optimum fin geometry (Length to the height ratio)? Ignore the amount of metal to be used for making the surface structure; the metal is used only for making the "fin". Assume that the base temperature is Tw,andtheendofthetipisinsulated. The air temperature is T. If you have a limited amount of metal (let's say m) to be casted for making a rectangular fin, what would be the optimum fin geometry (Length to the height ratio)? Ignore the amount of metal to be used for making the surface structure; the metal is used only for making the "fin". Assume that the base temperature is Tw,andtheendofthetipisinsulated. The air temperature is T.