Question

Air, at a free-stream temperature of 27.0°C and a pressure of 1.00 atm, flows over the top surface of a flat plate in parallel flow with a velocity of 12.5 m/sec. The plate has a length of 2.70 m (in the direction of the fluid flow), a width of 0.65 m, and is maintained at a constant temperature of 127.0°C. Determine the heat transfer rate from the top of the plate due to forced convection.

Answer 1

Step-by-step explanation:

Given that:

V = 12.5m/s

L= 2.70m

b= 0.65m

`T_( \infty) = 27^0C= 273+27 = 300K`

`T_s= 127^0C = (127+273)= 400K`

P = 1atm

Film temperature

`T_f = (T_s + T_(\infty))/(2) \\\\=(400+300)/(2) \\\\=350K`

dynamic viscosity =

`\mu =20.9096* 10^(-6) m^2/sec`

density = 0.9946kg/m³

Pr = 0.708564

K= 229.7984 * 10⁻³w/mk

Reynolds number,

`Re = (SUD)/(\mu) =(\ SUl)/(\mu)`

`=(0.9946 * 12.5* 2.7)/(20.9096* 10^-^6) \\\\Re=1605375.043`

we have,

`Nu=(hL)/(k) =0.037Re^(4/5)Pr^(1/3)\\\\(h*2.7)/(29.79* 10^-63) =0.037(1605375.043)^(4/5)(0.7085)^(1/3)\\\\h=33.53w/m^2k`

we have,

heat transfer rate from top plate

`\theta _1 =hA(T_s-T_(\infty))\\\\A=Lb\\\\=2.7*0.655\\\\ \theta_1=33.53*2.7*0.65(127/27)\\\\ \theta_1=5884.51w`