GATE Mechanical Engineering (ME) 2014 Shift 1 Solved Paper

The non-dimensional fluid temperature profile near the surface of a convectively cooled flat plate is given by $\frac{{\mathit{T}}_{\mathit{w}}-\mathit{T}}{{\mathit{T}}_{\mathit{w}}-{\mathit{T}}_{\mathit{\infty }}}=\mathit{a}+\mathit{b}\frac{\mathit{y}}{\mathit{L}}+\mathit{c}{\left(\frac{\mathit{y}}{\mathit{L}}\right)}^2$, where y is measured perpendicular to the plate, L is the plate length, and a, b and c are arbitrary constants. T_w and T_∞ are wall and ambient temperatures, respectively. If the thermal conductivity of the fluid is k and the wall heat flux is q”, the Nusselt number $\mathit{N}\mathit{u}=\frac{{\mathit{q}}^{\mathit{″}}}{{\mathit{T}}_{\mathit{w}}-{\mathit{T}}_{\mathit{\infty }}}\frac{\mathit{L}}{\mathit{k}}$ is equal to