In a common situation, the diffusion coefficient is constant, there are no sources or sinks, and the velocity field describes an incompressible flow (i.e., it has zero divergence). Then the formula simplifies to:
In this form, the convection–diffusion equation combines both parabolic and hyperbolic partial differential equations.
In this case the equation can be put in the simple convective form:
Where, the derivative of the left hand side is the material derivative of the variable c.
In non-interacting material,  (for example, when temperature is close to absolute zero, dilute gas has almost zero mass diffusivity), hence the transport equation is simply the continuity equation:
Using Fourier transform in both temporal and spatial domain (that is, with integral kernel ), its characteristic equation can be obtained:
which gives the general solution:
where  is any differentiable scalar function. This is the basis of temperature measurement for near Bose–Einstein condensate via time of flight method.