Forced convection material balance equations

Temperature and concentration gradients are absent inside an ideal stirred reactor. Mixing can be achieved by forced or free-convective movement of a material. For such a reactor the energy balance equation can be written as ... 

The third chapter covers convective heat and mass transfer. The derivation of the mass, momentum and energy balance equations for pure fluids and multi-component mixtures are treated first, before the material laws are introduced and the partial differential equations for the velocity, temperature and concentration fields are derived. As typical applications we consider heat and mass transfer in flow over bodies and through channels, in packed and fluidised beds as well as free convection and the superposition of free and forced convection. Finally an introduction to heat transfer in compressible fluids is presented. 

The basic equation of Newtonian fluid motion, the Navier-Stokes equations, can be developed by substitution of the constitutive relationship for a Newtonian fluid, P-1, into the Cauchy principle of momentum balance for a continuous material [ 7]. In writing the second law for a continuously distributed fluid, care must be taken to correctly express the acceleration of the fluid particle to which the forces are being apphed through the material derivative Du/Dt, where Du/Dt = du/dt -H (u V)u. That is, the velocity of a fluid particle may change for either of two reasons, because the particle accelerates or decelerates with time temporal acceleration) or because the particle moves to a new position, at which the velocity has different magnitude and direction convective acceleration). 

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