A shell$-$and$-$tube flooded evaporator has a refrigeration load of $350$ kW and is employed to chill water from $\backslash (13^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ to $\backslash (6^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ The evaporating temperature is $\backslash (3^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and the refrigerant used is R $134$ a $.$ Calculate the heat transfer coefficients, heat transfer area, dimensions, and the chilled water pressure drop. Continue calculations until reasonable convergence is reached. Show and justify $($when needed$)$ all assumptions.