Question

An object of irregular shape has a characteristic length of L 1 m and is maintained at a uniform surface temperature of Ts 400 K. When placed in atmospheric air at a temperature of T 300 K and moving with a velocity of V 100 m/s, the average heat flux from the surface to the air is 20,000 W/m2 . If a second object of the same shape, but with a characteristic length of L 5 m, is maintained at a surface temperature of Ts 400 K and is placed in atmospheric air at T 300 K, what will the value of the average convection coefficient be if the air velocity is V 20 m/s

Answer 1

average convection coefficient is 0.090597 W/m²K

Step-by-step explanation:

Given data

velocity V = 100 m/s

temperature Ts = 400 K

temperature T = 300 K

average heat flux = 20,000 W/m2

length of L = 5 m

solution

we know that heat flux that is h × ( Ts -T)

so h = 20000 / (400 - 300)

h = 200 W/m²K

and

we know Nusselt number is proportional to reynold number power to 4/5

so

Nu ∝
`Re^(4/5)`

so Nu = h×L/k

so we can say

h1L1 / h2L2 =
`(V1L2/V2L2)^(4/5)`

here L1 = 1m , L2 = 5m, V1 = 100 m/s and V2 = 20 m/s and h1 = 200 W/m²K

put all these value here

200(1) / h2 (5) =
`(100(5)/20(5))^(4/5)`

h2 = 0.090597 W/m²K

so average convection coefficient is 0.090597 W/m²K