A finned tube compact heat exchanger $($type CF$-7\mathrm{.}0-5/8$J$)$ is used in a heat pump. The core $($tubes and fins$)$ is fabricated from copper, and the tubes have an inside diameter of $15$ mm $.$ The liquid flowing within the tubes provides an an inside convection coefficient of $\backslash (\backslash$mathrm$\{$hi$\}=800\backslash$mathrm$\{$~W$\}/\backslash$mathrm$\{$m$\}^\{2\}\backslash$mathrm$\{$~K$\}\backslash ).$ Cross flow air passes over the tubes at $1$ bar and $300$ K $.$ The air mass flow rate is $\backslash (0\mathrm{.}7\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$s$\}\backslash ),$ the frontal area of the heat exchanger is $\backslash (0\mathrm{.}2\backslash$mathrm$\{$~m$\}^\{2\}\backslash )$ and the length of the core is $0\mathrm{.}4$ m $.$

a$)$

What is the gas side overall heat transfer coefficient $($in $\backslash (\backslash$mathrm$\{$W$\}/\backslash$mathrm$\{$m$\}^\{2\}\backslash$mathrm$\{$~K$\}\backslash ))?$

Expected answer: