The transport equation, also known as the advection equation, is a partial differential equation (PDE) that describes the evolution of a quantity, such as concentration or temperature, as it is transported by a flow field.
The transport equation is derived by applying the principles of conservation of mass and the advection-diffusion equation, which takes into account the effects of both advection (transport by the flow field) and diffusion (random movement of particles) on the evolution of the quantity being transported.
The advection term represents the transport of the quantity by the flow field, while the diffusion term accounts for the spreading of the quantity due to random motion. The source term takes into account any external sources or sinks of the quantity, such as chemical reactions or boundary conditions.
The transport equation assumes that the flow field is steady and incompressible, and that the quantity being transported is conserved and has a continuous distribution. It also neglects any other forces or effects that may influence the transport of the quantity.
The transport equation has numerous applications in various fields, such as fluid dynamics, heat transfer, and chemical engineering. It is commonly used to model the transport of pollutants in the atmosphere, the spread of contaminants in groundwater, and the diffusion of drugs in the human body.
