Helium at a free stream temperature of \(T_{\infty}=25^{\circ} \mathrm{C}\) is in parallel flow over a flat plate of length \(L=3 \mathrm{~m}\) and temperature \(T_{s}=85^{\circ} \mathrm{C}\). However, obstacles placed in the flow intensify mixing with increasing distance \(x\) from the leading edge, and the spatial variation of temperatures measured in the boundary layer is correlated by an expression of the form \(T\left({ }^{\circ} \mathrm{C}\right)=25+60 \exp (-600 x y)\), where \(x\) and \(y\) are in meters. Determine and plot the manner in which the local convection coefficient \(h\) varies with \(x\). Evaluate the average convection coefficient \(\bar{h}\) for the plate.