A beaker contains a fluid of density ρ kg / m^3, specific heat S J/ kg^° C and viscosity η. The beaker is filled up to height h. To estimate the rate…

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