Question

A spherical steel ball of $12mm$ diameter is initially at $1000K.$ It is slowly cooled in a surrounding of $300K.$ The heat transfer coefficient between the steel ball and the surroundings is $5W/m^{2}K.$ The thermal conductivity of steel $20W/mK.$ The temperature difference between the centre and the surface of the steel ball is

• A.
  
  
  Large because conduction resistance is far higher than the convective resistance
• B.
  
  
  Large because conduction resistance is far less than the convective resistance
• C.
  
  
  small because conductive resistance is far higher than the convective resistance
• D.
  
  small because conduction resistance is far less than the convective resistance

Answer 1

The correct option is D


small because conduction resistance is far less than the convective resistance
Biot number,

$Bi=\frac{\text{Conduction resistance}:\frac{l}{kA}}{\text{Convection resistance}:\frac{1}{hA}}=\frac{hl}{k}$

where $l=\frac{V}{A}=\frac{\pi }{6}\frac{d^3}{\pi d^2}=\frac{d}{6}$

$\therefore$ $Bi=\frac{h}{k}\frac{d}{6}=\frac{5\times 0.012}{20\times 6}=0.0005$

It means that the conduction resistance is far less than convective resistance