GATE Mechanical Engineering (ME) 2019 Shift 2 Solved Paper

Question : 28 of 65

Marks: +1, -0

A 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

16 {L}

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

h_1{/}h_2

is____________.

Your Answer:

Validate

Solution:

N_{u}=K(R_{a})^{\;{1}/{4}}

We know that

R_{a}=G_{r} P_{r}

N_{u}=K(G_{r} P_{r})^{\;{1}/{4}}

\;{h L}/{K} ∝(G_{r})^{\;{1}/{4}} ∝(\;{g β ∆ T L^{3}}/{V^{2}})^{\;{1}/{4}}

h L ∝ L^{\;{3}/{4}}

h ∝ L^{-\;{1}/{4}}

\;{h_{2}}/{h_{1}} ∝(\;{L_{1}}/{L_{2}})^{\;{1}/{4}}=>\;{h_{1}}/{h_{2}} ∝(\;{L_{2}}/{L_{1}})^{\;{1}/{4}}=(16)^{\;{1}/{4}}=2

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