$14.$ Air flows in a pipe under fully developed conditions with an average velocity of $1\mathrm{.}25\backslash (\backslash$mathrm$\{$m$\}/\backslash$mathrm$\{$s$\}\backslash )$ and a temperature of $\backslash (20^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ The pipe's inner diameter is $4$ cm $,$ and its length is $4$ m $.$ The first half of the pipe is kept at a constant wall temperature of $\backslash (100^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ The second half of the pipe is subjected to a constant heat flux of $200$ W $.$ Determine $\backslash (($a$)\backslash )$ the air temperature at the $2$ m length, $($b$)$ the air temperature at the exit, $($c$)$ the total heat transfer to the air, and $\backslash (($d$)\backslash )$ the wall temperature at the exit of the tube. Evaluate the properties of air at $\backslash (80^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$