A double$-$pipe heat exchanger is used to cool a hot fluid before it flows into a

system of pipes. The inner surface of the pipes is primarily coated with

polypropylene lining. The double$-$pipe heat exchanger has a thin$-$walled inner

tube, with convection heat transfer coefficients inside and outside of the inner

tube estimated to be $1400$ W$/$m$2$

K and $1100$ W$/$m$2$

K$,$ respectively. The heat

exchanger has a heat transfer surface area of $2\mathrm{.}5$ m$2,$ and the estimated fouling

factor caused by the accumulation of deposit on the surface is $0\mathrm{.}0002$ m$2$

K$/$W$.$

The hot fluid $($cp $=3800$ J$/$kgK$)$ enters the heat exchanger at $200$C with a flow

rate of $0\mathrm{.}4$ kg$/$s$.$ In the cold side, cooling fluid $($cp $=4200$ J$/$kgK$)$ enters the heat

exchanger at $10$C with a mass flow rate of $0\mathrm{.}5$ kg$/$s$.$

Determine:

$5-$a the effectiveness for the parallel$-$flow configuration,

$5-$b the outlet temperature of the hot fluid for parallel$-$flow configuration,

$5-$c the effectiveness for the counter$-$flow configuration,

$5-$d The outlet temperature of the hot fluid for counter$-$flow configuration.