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Air at 200 degC and at velocity of 2 m/s over a plate maintained at 1000degC. The length and width of the plate are 800 mm and 400mm resp. using exact solution; calculate the heat transfer rate from.

First of the plate
ii) Full plate
iii) Next half of the plate.

Nu=0.322 $Re^(0.5)$ $Pr^(0.333)$ Prosperities of air at 600℃ are ρ=1.06 kg⁄$m^3$ ,μ=(7.211kg)⁄mh,v=18.97×$10^(-6)$ $m^2$⁄s,Pr=0.696

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For the first of the plate(characteristic length would be 400mm)

Re=$\frac{VL}{v}$=$\frac{(2×.4)}{(18.97×10^-6) }$=42.171×$10^3$

which is less than critical reynolds number Therefore

Nu=0.322×$Re^.5$ $Pr^.333$

Nu=$0.322×(42.171×10^3)^.5×0.696^.333$

Nu=58.60= $\frac{h_x x}{k}$

k=53.8 from heat transfer table for 600℃ for air

58.60= $\frac{h×.4}{53.8}$

h=7881.7w/$m^2$ k

Q=$hA(T_s-T_a )$

Q=7881.7×.4×.4(1000-200)

Q=1.00885×1$0^6$ Watt

For entire plate we would consider the entire length:

Re=$\frac{(2×.8)}{(18.97×10^(-6)}$=84.34×$10^3$

in this case also reynolds number is less than critical reynolds number Therefore

Nu=0.322×$Re^.5$ Pr^$.333

Nu=$0.322×(84.34×10^3 )^.5×0.696^.333$

Nu=$\frac{hL}{k}$=82.88

h=$\frac{82.88×53.8}{(.8)}$=5.5738×$10^3$

Q=$hA(T_s-T_a )$=1.4268928×$10^6$ watts

For second half of the plate:

$Q_3$=$Q_2$-$Q_1$=1.4268928×$10^6$-1.000885×$10^6$

=418.3928×$10^3$ watts

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