Question

he upper surface of a metal plate is being cooled with parallel air flow while its lower surface is subjected to a uniform heat flux of 810 W/m2. The air has a free stream velocity and temperature of 2.5 m/s and 15°C, respectively. Determine the surface temperature of the plate at x = 1.5 m from the leading edge. Start the iteration process with an initial guess of 45°C for the surface temperature.

Answer 1

`T_(surface)=343.86\°c`

Step-by-step explanation:

We define the constant, so

`k=0.0258W/m^2K\\\upsilon_(air)=1.608*10^5m^2/s\\Pr=0.7282`

So, begin calculating the Reynolds number, so

`(Re)_(x=1.5) = (V_(\infty)x)/(\upsilon_(air))\\(Re)_(x=1.5) = (2.5*1.5)/(1.608*10^(-5))}\\(Re)_(x=1.5) = 2.33*10^(5)`

How reynolds number is greater than critical reynolds number, the flow

of the air is near about the turbulent flow,

we now calculate the local nusselt number

`(Nu)_x = 0.332 (Re)^(1/2)_x(Pr)^(1/3)\\(Nu)_x= 0.322(2.33*10^5)^(1/2)*(0.782)^(1/3)\\(Nu)_x = 143.1977`

calculate the local convection heat transfer coefficient

`h_X = ((Nu)_xk)/(x)\\h_x= (143.1977*0.0258)/(1.5)\\h_x=2.46300 W/m^2K`

Apply the energy balance equation

`q=h_x(T_(surface)-T_(\infty))\\810=2.463*(T_(surface)-15)`

`T_(surface)=343.86\°c`