The Boussinesq approximation is applied to problems where the fluid varies in temperature (or composition) from one place to another, driving a flow of fluid and heat transfer (or mass transfer). The fluid satisfies conservation of mass, conservation of momentum and conservation of energy. In the Boussinesq approximation, variations in fluid properties other than density  are ignored, and density only appears when it is multiplied by , the gravitational acceleration. If  is the local velocity of a parcel of fluid, the continuity equation for conservation of mass is
If density variations are ignored, this reduces to
The general expression for conservation of momentum of an incompressible, Newtonian fluid (the Navier–Stokes equations) is
where  (nu) is the kinematic viscosity and  is the sum of any body forces such as gravity. In this equation, density variations are assumed to have a fixed part and another part that has a linear dependence on temperature:
where  is the coefficient of thermal expansion. The Boussinesq approximation states that the density variation is only important in the buoyancy term.
If  is the gravitational body force, the resulting conservation equation is
In the equation for heat flow in a temperature gradient, the heat capacity per unit volume, , is assumed constant and the dissipation term is ignored. The resulting equation is
where  is the rate per unit volume of internal heat production and  is the thermal conductivity.
The three numbered equations are the basic convection equations in the Boussinesq approximation.