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

Answer:

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

$T_f = \frac{T_s + T_{\infty}}{2} \\\\=\frac{400+300}{2} \\\\=350K$

dynamic viscosity =

$\mu =20.9096\times 10^{-6} m^2/sec$

density = 0.9946kg/m³

Pr = 0.708564

K= 229.7984 * 10⁻³w/mk

Reynolds number,

$Re = \frac{SUD}{\mu} =\frac{\ SUl}{\mu}$

$=\frac{0.9946 \times 12.5\times 2.7}{20.9096\times 10^-^6} \\\\Re=1605375.043$

we have,

$Nu=\frac{hL}{k} =0.037Re^{4/5}Pr^{1/3}\\\\\frac{h\times2.7}{29.79\times 10^-63} =0.037(1605375.043)^{4/5}(0.7085)^{1/3}\\\\h=33.53w/m^2k$

we have,

heat transfer rate from top plate

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