Question: Show, using two different approaches ( viz conduction through the base versus convection from the entire exposed surface ) , that the total heat transfer

Show, using two different approaches (viz "conduction through the base" versus "convection from the entire exposed surface"), that the total heat transfer from a fin insulated at the tip is indeed what is given in our Equation Sheet. You will need to show every intermediate step in your derivations, as you use differentiation (at x =0) for the first method or integration (from x =0 to x =L) for the second method.

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