A thin flat plate measuring $280$ mm $600$ mm at a temperature of $80$C is cooled on one face by air at $10$C flowing at $28$ m$/$s parallel to the $600-$mm edges of the plate. Its emissivity is $0\mathrm{.}74$ and it is placed in a large chamber with walls at $15$C$.$ The other face is insulated. $($a$)$ Calculate the rate of convective heat transfer from the plate. $[10]($b$)$ Where, if anywhere, does the boundary layer on the plate become turbulent? $[2]($c$)$ Sketch and label a graph showing the variation of heat flux along the length of the plate. Sketch and label a diagram of the structure of the boundary layer. $[4]($d$)$ Calculate the convective heat flux $200$ mm downstream of the leading edge of the plate. $[4]($e$)$ Calculate the radiant heat transfer from the plate to the chamber walls. the answer to a$)$ is $667$ W b$)0\mathrm{.}31$ from leading edge c$)1546$ Wm$2,3\mathrm{.}35$ W d$)60\mathrm{.}95$W