Question

Atmospheric air at 25 °C and 8 m/s flows over both surfaces of an isothermal (179C) flat plate that is 2.75m long. Determine the heat transfer rate per unit from the plate for 3 width different values of the critical Reynolds number: 100,000; 500,000; and 1,000,000

Answer 1

Answer:

Re=100,000⇒Q=275.25 $\frac{W}{m^2}$

Re=500,000⇒Q=1,757.77$\frac{W}{m^2}$

Re=1,000,000⇒Q=3060.36 $\frac{W}{m^2}$

Explanation:

Given:

For air      $T_∞$=25°C  ,V=8 m/s

  For surface $T_s$=179°C

     L=2.75 m    ,b=3 m

We know that for flat plate

$Re$⇒Laminar flow

$Re>30\times10^5$⇒Turbulent flow

Take Re=100,000:

 So this is case of laminar flow

  $Nu=0.664Re^{\frac{1}{2}}Pr^{\frac{1}{3}}$

From standard air property table at 25°C

  Pr= is 0.71  ,K=26.24$\times 10^{-3}$

So    $Nu=0.664\times 100,000^{\frac{1}{2}}\times 0.71^{\frac{1}{3}}$

Nu=187.32   ($\dfrac{hL}{K_{air}}$)

187.32=$\dfrac{h\times2.75}{26.24\times 10^{-3}}$

     ⇒h=1.78$\frac{W}{m^2-K}$

heat transfer rate =h$(T_∞-T_s)$

                           =275.25 $\frac{W}{m^2}$

Take Re=500,000:

So this is case of turbulent flow

  $Nu=0.037Re^{\frac{4}{5}}Pr^{\frac{1}{3}}$

$Nu=0.037\times 500,000^{\frac{4}{5}}\times 0.71^{\frac{1}{3}}$

Nu=1196.18  ⇒h=11.14 $\frac{W}{m^2-K}$

heat transfer rate =h$(T_∞-T_s)$

                             =11.14(179-25)

                           = 1,757.77$\frac{W}{m^2}$

Take Re=1,000,000:

So this is case of turbulent flow

  $Nu=0.037Re^{\frac{4}{5}}Pr^{\frac{1}{3}}$

$Nu=0.037\times 1,000,000^{\frac{4}{5}}\times 0.71^{\frac{1}{3}}$

Nu=2082.6  ⇒h=19.87 $\frac{W}{m^2-K}$

heat transfer rate =h$(T_∞-T_s)$

                             =19.87(179-25)

                           = 3060.36 $\frac{W}{m^2}$