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A continuous cross$-$circulation dryer is fed with $10$ kg$.$hr$$ wet solid mass with a moisture content of $28\%($wet$-$basis$),$ which is to be dried to $13\%$ moisture content $($wet$-$basis$).$ The drying gas enters at a velocity of $2\mathrm{.}7$ m$.$s$$ at $80\backslash$deg C with $0\mathrm{.}02$ kgwater$/$kgdry$-$air absolute humidity and exits at $52\backslash$deg C$.$ The dryer width is $800$ mm and the duct height is $15$ mm$.$

Determine the length of the dryer required for this operation.