Question

Air at 27oC and 1 atm flows over a flat plate 40 cm in length and 1 cm in width at a speed of 2 m/s. The plate is heated over its entire length to a temperature of 600C. Calculate the heat transferred from the plate.

Answer 1

Heat transferred = 22.9 watt

Step-by-step explanation:

Given that:

`T_1` = 27°C = (273 + 27) K = 300 K

`T_2`= 600°C = (600 +273) K = 873 K

speed v = 2 m/s

length x = 40 cm = 0.4 cm

width = 1 cm = 0.001 m

The heat transferred from the plate can be calculate by using the formula:

Heat transferred = h×A ×ΔT

From the tables of properties of air, the following values where obtained.

`k = 0.02476 \ W/m.k \\ \\ \rho = 1.225 \ kg/m^3 \\ \\ \mu = 18.6 * 10^(-6) \ Pa.s \\ \\ c_p = 1.005 \ kJ/kg`

To start with the reynolds number; the formula for calculating the reynolds number can be expressed as:

reynolds number =
`(\rho * v * x )/(\mu)`

reynolds number =
`(1.225 * 2 * 0.4)/(18.6 * 10^(-6))`

reynolds number =
`(0.98)/(18.6 * 10^(-6))`

reynolds number = 52688.11204

Prandtl number =
`(c_p \mu)/(k)`

Prandtl number =
`(1.005 * 18.6 * 10^(-6) * 10^3)/(0.02476)`

Prandtl number =
`(0.018693)/(0.02476)`

Prandtl number = 0.754963

The nusselt number for this turbulent flow over the flat plate can be computed as follows:

Nusselt no =
`(hx)/(k) = 0.0296 (Re) ^(0.8) * (Pr)^(1/3)`

`(h * 0.4)/(0.02476) = 0.0296 (52688.11204) ^(0.8) * (0.754968)^(1/3)`

`(h * 0.4)/(0.02476) =161.4252008}`

`h =(161.4252008 * 0.02476)/( 0.4)`

h = 9.992 W/m.k

Recall that:

The heat transferred from the plate can be calculate by using the formula:

Heat transferred = h×A ×ΔT

Heat transferred =
`h* A * (T_2-T_1)`

Heat transferred = 9.992 × (0.4 × 0.01) ×(873-300)

Heat transferred = 22.9 watt