The local Nusselt number correlation for a flat plate with a constant surface he

Question

The local Nusselt number correlation for a flat plate with a constant surface heat flux is given as
Nux = 0.175Rex^0.35Pr^1/3 (Laminar) Nux = 0.27Rex^0.5Pr^1/3 (Turbulent)

and the fluid properties are evaluated at the free stream temperature. Assume transition at Rex = 500,000.

Air flows over a plate with a free stream temperature of 27°C and a velocity of 25 m/s. The plate is 200 cm long and the surface heat flux is 275 W/m2.

For T=300k: ? (kg/m3)=1.1614, µ ×10^-7 (N-s/m2)=184.6, ? ×10^-6 (m2/s)=15.89,
k ×10^-3 (W/m-K)=26.3, a ×10^6 (m2/s)= 22.5 , Pr=.707

A) Find the Surface temperature 27cm from the leading edge

B) Find the surface temperature 55cm from the leading edge

If you can only answer one part that will be extremely beneficial. Thank you!

Explanation / Answer

(a) At 27 cm from leading edge, Reynolds number, Re27 = VL/ = 25*0.27/(15.89*10-6) = 424,795

Since Re27 < 500,000, the flow is laminar.

Hence, Nux = 0.175Rex^0.35Pr^1/3

= 0.175*4247950.350.7071/3 = 14.54

Nux = hx/k

So, h = 14.54*(26.3*10-3)/0.27 = 1.417 W/m2K

But, h = qw/(Tw-T)

So, 1.417 = 275/(Tw-300)

This gives, Twall = 494 K

(b)

At 55 cm from leading edge, Reynolds number, Re55 = VL/ = 25*0.55/(15.89*10-6) = 865,323

Since Re55 > 500,000, the flow is turbulent.

Hence, Nux = 0.27Rex^0.5Pr^1/3

= 0.27*8653230.50.7071/3 = 223.75

Nux = hx/k

So, h = 223.75*(26.3*10-3)/0.27 = 21.8 W/m2K

But, h = qw/(Tw-T)

So, 21.8 = 275/(Tw-300)

This gives, Twall = 312.6 K

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