c$\_($p$)=4180($J$)/($k$)$g$*$K $15\backslash$deg C at

a rate of $0\mathrm{.}25$k$($g$)/($s$)$ and is heated to $42\backslash$deg C by hot water $($c$\_(\backslash$rho $)=4190($J$)/($k$)$g$*$K$)$ that enters at $103\backslash$deg C at a rate of $3$k$($g$)/($s$).$ The overall

heat transfer coefficient is $950($W$)/($m$^(2))*$K$.$

The NTU can be determined from the following table.

Heat exchanger type NTU relation

$1$ Double$-$pipe:

Parallel$-$flow

NTU $-($ln$[1-$s$(1+$c$)])/(1+$c$)$

Counter$-$flow

NTU $=(1)/($c$-1)$ln$((\backslash$epsi $-1)/(\backslash$epsi c$-1))($ for c$<mn>1</mn><mi>)</mi>$

NTU $=(\backslash$epsi $)/(1-\backslash$epsi $)($ for c$=1)$

$2$ Shell and tube:

One$-$shell pass

$2,4,...$tube passes

NTU$\_(1)=-(1)/(\backslash$sqrt$(1+$c$^(2)))$ln$(((2)/($E$\_(1))-1-$c$-\backslash$sqrt$(1+$c$^(2)))/((2)/($e$\_(1))-1-$c$+\backslash$sqrt$(1+$c$^(2))))$

n$-$shell passes

$2$n$,4$n$,...$tube passes NTU$\_($n$)=$n$($NTU$)\_(1)$

To find effectiveness of the heat exchanger with one$-$

shell pass use, $\backslash$epsi $\_(1)-($F$-1)/($F$-$c$)$

where F$=(($e$\_($n$)$c$-1)/($E$\_($n$)-1))^($Le$)$

$3$ Cross$-$fliow $($single$-$pass$)$:

C$\_($max $)$ mixed,

c$\_($min$)$ unmixed

c$\_($min $)$ mibed,

NTU$=-$ln$[1+($ln$(1-\backslash$epsi c$))/($c$)]$

c$\_($max $)$ unmixed

NTU $=($ln$[$cln$(1-\backslash$epsi $)+1])/($c$)$

$4$ All heat exchangers

NTU $=-$ln$(1-$e$)$

Determine the rate of heat transfer of the heat exchanger using the $\backslash$epsi $-$NTU method.

The rate of heat transfer of the heat exchanger is