A process fluid, initially at $20$ C$,$ must be heated to $80$ C at $20$ kg$/$s in a shell$-$and$-$tube heat exchanger consisting of multiple tubs in one shell. Condensing steam at $99\mathrm{.}8$ C$,$ supplied through the shell side, will be used to heat the fluid.

Data:

Latent heat of steam: $2250$ kJ$/$kg

Overall heat transfer coefficient: $9800$ W$/$m$2-$K

Heat capacity of the fluid: $3\mathrm{.}8$ kJ$/$kg$-$K How many tubes must be installed in the shell if each tube has an inside diameter and length of $0\mathrm{.}038$ m and $1\mathrm{.}5$ m$,$ respectively?