2 Consider airflow over a plate surface maintained at a temperature of 220°C. The temperature profile of the airflow is given as The airflow at 1 atm has a free stream velocity and temperature of 0.08 m/s and 20°C, respectively. Determine the heat flux on the plate surface and the convection heat transfer coefficient of the airflow

Heat flux on the plate surface is 1.45 x 10⁴ W/m², Heat transfer coefficient is 72.6 W/m². K

Explanation:

The temperature profile of the airflow is given as

T (y) = T∞ - (T∞ - Ts) exp[ (-V/α fluid) y]

Calculate the mean film temperature of air

T (f) = T (s) + T∞/2, where T (s) is the surface temperature of the plate and T∞ is the temperature of free stream

Substitute Ts = 220 C and T∞ = 20 C

T (f) = 220 + 20/2 = 120 C

Obtain the properties of air from Table A - 15 (Properties of air at 1 atm pressure) in the text book of from the internet at T (f) = 120 C, which would give us the quantities of thermal diffusivity (α fluid) and the thermal conductivity (k) of air

α fluid = 3.565 x 10⁻⁵ m²/s

k = 0.03235 W/m. k

Calculate the temperature gradient for the given profile

T (y) = T∞ - (T∞ - Ts) exp ({-V/α fluid}y)

Where, T∞ is the ambient temperate, V is the free stream velocity of air and y is the temperature displacement thickness

Differentiate the expression with respect to y

dT/dY = - (T∞ - Ts) {-V/α fluid}e[ (-V/α fluid) x 0]

dT/dy = - (T∞ - Ts) {-V/α fluid}

Substitute T∞ = 20 C, Ts = 220 C, V = 0.08 m/s and α = 3.565 x 10⁻⁵ m²/s

dT/dy = - (20 - 220) (-0.08/3.565 x 10⁻⁵)

dT/dy = - 448807.8541

Calculate the heat flux on the plate surface

Q = - kdT/dy

K = 0.03235 W/m. k, dT/dy = - 448807.8541

Q = - (0.03235) (-448807.8541)

Q = 1.45 x 10⁴ W/m²

Therefore, the heat flux on the plate surface is 1.45 x 10⁴ W/m²

Calculate the heat transfer coefficient

Q = h (Ts - T∞), where h is the transfer coefficient

1.45 x 10⁴ = h (220 - 20)

H = 72.6 W/m2. k

Therefore, the heat transfer coefficient is 72.6 W/m². K