Question

Which of the following curves shows correct relation between convective resistance $\left(R\right)$ and radius of hot sphere $\left(r\right)$ being placed in a stream of cold air ?

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

We know that, convective resistance, $R=\frac{1}{h_{c}A}$, where $h_c$ is convection
coefficient and $A$ is surface area.
$\Rightarrow R\propto \frac{1}{A}$
$\Rightarrow R\propto \frac{1}{r^2}$ ........(1) $[A=4\pi r^2]$
Relation (1) is identical to the relation of hyperbola, $y\propto \frac{1}{x^2}$. Thus, curve between convective resistance and radius of sphere is a hyperbola.
Option $C$ is correct.