$(10$ pts$)$ Cold water at $T_i{|}_c||=10C$ and a flow rate of $(m^{}){|}_c||=2k\frac{g}{s}$ is heated by hot water at $T_i{|}_h||=90C$ and a flow rate of $(m^{}){|}_h||=4k\frac{g}{s}$ using a heat exchanger having one shell pass and four tube passes $($Fig$.1).$ If the product of the area and overall convection coefficient is $U_m{A}_t=10,000\frac{W}{K},$ calculate the hot water outlet temperature $T_o{|}_h||$ with the aid of the $-$NTU method. As a first approximation, assume a specific heat of $c_p=4,200\frac{J}{kgK}$ for both sides. $($Specific heat is not a terribly strong function of temperature for water in the ranges of temperature characteristic of this problem.$)$

Fig. $1$: $4-$tube$-$pass heat exchanger.