Question

An object of irregular shape has a characteristic length of 1 m and is maintained at a uniform surface temperature of 450 K. When placed in atmospheric air at a temperature of T? 300 K and moving with a velocity of 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 5 m, is maintained at a surface temperature of 450 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 20 m/s?

Answer 1

Air properties:

density - , viscosity - , specific heat capacity - C , conductivity - k

velocity - V, characteristic length - Lc

Reynold number - Re ,   Prendtl number - Pr ,   Nusselt number - Nu

number 1 and 2 denotes first and second condition respectively.

Re1 = (*V1*Lc1) / = ( * 100*1) / = * 100 / .....................................................(1)

Re2 = (*V2*Lc2) / = ( * 20*5) / = * 100 / ........................................................(2)

In both condition air temperature is same (300^oC) . therefore air properties , , C, and k will be constant in both the conditions.

Therefore from equation (1) and (2) Re1 = Re2

similarly Pr1 = Pr2 = ( * C) / k

Nusselt number is a function of Re and Pr ; Nu (Re, Pr)

Nu1 (Re1, Pr1) = Nu2 (Re2, Pr2) ...................(As Re is same in both condition and Pr is same in both condition)

Also Nu = h*Lc / k   , h is average convection coefficient

thus    h1 * Lc1 / k = h2 * Lc2 / k

           h1* Lc1 = h2 * Lc2

           h2 = h1* Lc1 / Lc2 ....................................................................................(3)

But given that,

heat flux = h1 ( 450 - 300)

20000 = h1*150

h1 = 133.33 W/m²-k

Putting the value of h1 in equation (3)

h2 = 133 *1 / 5 = 26.66 W/m²-k