A beaker contains a fluid of density $\rho \, kg / m^3$, specific heat $S\, J / kg\,^oC$ and viscosity $\eta $. The beaker is filled upto height $h$. To estimate the rate of heat transfer per unit area $(Q / A)$ by convection when beaker is put on a hot plate, a student proposes that it should depend on $\eta \,,\,\left( {\frac{{S\Delta \theta }}{h}} \right)$ and $\left( {\frac{1}{{\rho g}}} \right)$ when $\Delta \theta $ (in $^oC$) is the difference in the temperature 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

  $\eta \,\frac{{S\Delta \theta }}{h}$