# How buoyancy and convection are related?

If I'm not wrong buoyancy formula is $$F_{B}=\rho gv_{sub}$$

In convection it is said that fluids with less density come up and parts with lower density ,which are cooler , go down and this cycle will continue till heat source stop supplying .

By considering buoyancy , when part of a fluid becomes less dense it should technically go down as a result of $\rho$ decreasing in $F_{B}=\rho gv_{sub}$ .

So how buoyancy is helping less dense parts rise ?

Appreciate any help!

Because $\rho$ here is the density of the surrounding fluid not of the hot part.
Let's say a small amount of fluid gets hot and has the density $\rho_{\text{hot}}$. It is now less dense than the surrounding fluid of density $\rho_{\text{cold}}$ which is cold. Hence its weigth which is proportionnal to $\rho_{\text{hot}}$ is less than its buoyancy force; which is proportional to $\rho_{\text{cold}}$ and it rises.