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Heat Transfer
Convection & Radiation
GATE 2007
Medium

The temperature distribution within the thermal boundary layer over a heated isothermal flat plate is given by (T−Tw)/(T∞−Tw) = (3/2)(y/δt) − (1/2)(y/δt)³, where Tw and T∞ are the temperatures of plate and free stream respectively, and y is the normal distance measured from the plate. The local Nusselt number based on the thermal boundary layer thickness δt is given by

  • A1.33
  • 1.50
  • C2.0
  • D4.64

Explanation

Differentiating the profile at y=0: d/dy[(T−Tw)/(T∞−Tw)]|₀=3/(2δt). Then q"=−k(dT/dy)|₀=h(Tw−T∞) gives h=3k/(2δt), so Nu=hδt/k=3/2=1.50.

Source: GATE ME 2007 (2007)

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