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

1. A \(\,\eta \cdot \left( {\frac{{S\Delta \theta }}{h}} \right)\left( {\frac{1}{{\rho g}}} \right)\)
2. B \(\,\left( {\frac{{S\Delta \theta }}{{\eta h}}} \right)\left( {\frac{1}{{\rho g}}} \right)\)
3. C \(\,\frac{{S\Delta \theta }}{{\eta h}}\)
4. D \(\eta \,\frac{{S\Delta \theta }}{h}\)