Design a double pipe heat exchanger for heating water using hot oil. The hot oil is

available at a temperature of $120$C and needs to heat the water from $25$C to $70$C$.$ The

water and the oil flow in opposite directions $($countercurrent flow$),$ and the flow rate of

water is $2$ kg$/$s$.$ Assume that the heat capacity of water is $4\mathrm{.}18$ kJ$/$kg $$

$$ C and that the

oil has a heat capacity of $2\mathrm{.}1$ kJ$/$kg $$

$$ C$.$ The heat exchanger will have a temperature

difference of at least $10$C between the fluids at the outlet.

For a typical mineral oil, the following properties are assumed:

$$ Density, oil $=850$ kg$/$m$3$

$($at $30$C$).$

$$ Dynamic Viscosity, $$oil $=0\mathrm{.}15$ Pa $$ s $($at $30$C$).$

$$ Thermal Conductivity, koil $=0\mathrm{.}145$W$/$m $$

$$ C$.$

$$ Specific Heat, Chot $=2\mathrm{.}1$ kJ$/$kg $$

$$ C $($at $30$C$).$

$$ Prandtl Number, P roil $=150.$