GATE 2019 ME (ME2) – Question 34
A thin vertical plate has height L and infinite width normal to the figure. It loses heat by natural convection. Plate and surrounding temperatures and fluid properties are constant. $Nu=KRa^{1/4}$, with constant K; both numbers use plate height. Height increases to 16L with all other factors unchanged. Find $h_1/h_2$.
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Correct answer: 2 to 2
Explanation
At fixed temperatures and properties, $Ra\propto L^3$ and $Nu\propto hL$. Thus $hL\propto L^{3/4}$, giving $h\propto L^{-1/4}$. Increasing height by 16 halves h, so **$h_1/h_2=2$**.