Project ForgeThe non-dimensional fluid temperature profile near the surface of a convectively cooled flat plate is given by (Tw−T)/(Tw−T∞)=a+b(y/L)+c(y/L)², where y is measured perpendicular to the plate, L is the plate length, and a, b and c are arbitrary constants. Tw 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 Nu=(q″/(Tw−T∞))(L/k) is equal to
- Aa
- b
- C2c
- D(b+2c)
Explanation
At the wall (y=0), T=Tw forces a=0. Differentiating: dT/dy=−(Tw−T∞)(b/L+2cy/L²), so at y=0, dT/dy|wall=−(Tw−T∞)b/L. By Fourier's law, the wall heat flux into the fluid is q″=−k(dT/dy)|wall=k(Tw−T∞)b/L. Substituting into the given Nu expression: Nu=[k(Tw−T∞)b/L]·L/[(Tw−T∞)k]=b.
Source: GATE ME 2014 (Session 1 / Set-1) (2014)
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