In cryogenic equipment, cold gas flows in parallel over the surface of a $1-$m$-$long plate.The gas velocity is $4$ m$/$s at a temperature of $-70\backslash$deg C$.$ The gas has a thermal conductivity of $0\mathrm{.}01979$ w$/$m$.$K$,$ a kinematic viscosity of $9\mathrm{.}319$x $10-6$m$^2/$s$,$ and a Prandtl number of$0\mathrm{.}7440.$ A stainless steel $($ASTM A$437$ B$4$B$)$ bolt is embedded in the plate at mid$-$length.The minimum temperature suitable for the ASTM A$437$ B$4$B stainless steel bolt is$-30$C$($ASME Code for Process Piping,ASME B$31\mathrm{.}3-2014,$Table A$-2$M$).$To keep the bolt from getting below its minimum suitable temperature, the plate is subjected to a uniform heat flux of $250$ W$/$m$2.$ Determine