$A$ beaker contains a fluid of density $\rho \, kg/m^3$,specific heat $S \, J/kg \, ^\circ C$,and viscosity $\eta$. The beaker is filled up to height $h$. To estimate the rate of heat transfer per unit area $(Q/A)$ by convection when the beaker is placed on a hot plate,a student proposes that it should depend on $\eta$,$\left( \frac{S\Delta \theta}{h} \right)$,and $\left( \frac{1}{\rho g} \right)$,where $\Delta \theta$ (in $^\circ C$) is the temperature difference between the bottom and top of the fluid. In that situation,the correct option for $(Q/A)$ is:

• A
  $\eta \cdot \left( \frac{S\Delta \theta}{h} \right) \left( \frac{1}{\rho g} \right)$
• B
  $\left( \frac{S\Delta \theta}{\eta h} \right) \left( \frac{1}{\rho g} \right)$
• C
  $\frac{S\Delta \theta}{\eta h}$
• D
  $\eta \frac{S\Delta \theta}{h}$