A long copper bar of rectangular cross section, whose width w is much greater than its thickness L, is maintained in con

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A long copper bar of rectangular cross section, whose width w is
much greater
than its thickness L, is maintained in contact with a heat sink at
its lower surface,
and the temperature throughout the bar is approximately equal to
that of the sink,
To. Suddenly, an electric current is passed through the bar and an
airstream of
temperature T(infinite) is passed over the top
surface, while the bottom surface continues
to be maintained at To. Obtain the differential equation and the
boundary and initial
conditions that could be solved to determine numerical the
temperature as a function of
position and time in the bar in three condutions (Dirichlet
condition,Neumann condition, and Convection surface
condition)