Question

An object of irregular shape has a characteristic length of L = 0.5 m and is maintained at a uniform surface temperature of Ts = 400 K. When placed in atmospheric air at a temperature of T[infinity] = 300 K and moving with a velocity of V = 25 m/s, the average heat flux from the surface to the air is 10,000 W/m2 . If a second object of the same shape, but with a characteristic length of L = 2.5 m, is maintained at a surface temperature of Ts = 400 K and is placed in atmospheric air at T[infinity] = 300 K, what will the value of the average convection coefficient be if the air velocity is V = 5 m/s?.

Answer 1

Answer:

The value of the average convection coefficient is 20 W/Km².

Explanation:

Given that,

For first object,

Characteristic length = 0.5 m

Surface temperature = 400 K

Atmospheric temperature = 300 K

Velocity = 25 m/s

Air velocity = 5 m/s

Characteristic length of second object = 2.5 m

We have same shape and density of both objects so the reynold number will be same,

We need to calculate the value of the average convection coefficient

Using formula of  reynold number for both objects

$R_{1}=R_{2}$

$\dfrac{u_{1}L_{1}}{\eta_{1}}=\dfrac{u_{2}L_{2}}{\eta_{2}}$

$\dfrac{h_{1}L_{1}}{k_{1}}=\dfrac{h_{2}L_{2}}{k_{2}}$

Here, $k_{1}=k_{2}$

$h_{2}=h_{1}\times\dfrac{L_{1}}{L_{2}}$

$h_{2}=\dfrac{q}{T_{2}-T_{1}}\times\dfrac{L_{1}}{L_{2}}$

Put the value into the formula

$h_{2}=\dfrac{10000}{400-300}\times\dfrac{0.5}{2.5}$

$h_{2}=20\ W/Km^2$

Hence, The value of the average convection coefficient is 20 W/Km².