Project ForgeA thin vertical flat plate of height L, and infinite width perpendicular to the plane of the figure, is losing heat to the surroundings by natural convection. The temperatures of the plate and the surroundings, and the properties of the surrounding fluid, are constant. The relationship between the average Nusselt and Rayleigh numbers is given as Nu=K·Ra^(1/4), where K is a constant. The length scales for Nusselt and Rayleigh numbers are the height of the plate. The height of the plate is increased to 16L keeping all other factors constant. If the average heat transfer coefficient for the first plate is h1 and that for the second plate is h2, the value of the ratio h1/h2 is ___
Explanation
Ra_L ∝ L³ (fixed ΔT and fluid properties), so Nu=K·Ra^(1/4) ∝ L^(3/4). Since Nu=hL/k, h=Nu·k/L ∝ L^(3/4)/L=L^(−1/4). So h1/h2=(L2/L1)^(1/4)=(16L/L)^(1/4)=16^(1/4)=2.
Source: GATE ME 2019 Session 2 (Set 3) (2019)
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