GATE ME 2019 Set 2 — Question 34
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Heat Transfer → Convection → Forced & Free Convection
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Question
A thin vertical flat plate of height , 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 , where 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 keeping all other factors constant.
If the average heat transfer coefficient for the first plate is and that for the second plate is , the value of the ratio is ______.
Correct answer
2 to 2
Solution
The Nusselt number is given by . The Rayleigh number is , which implies . Substituting this into the Nusselt relation: . Thus, the heat transfer coefficient scales as . The ratio of the heat transfer coefficients for two plates of heights and is: .
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