Introduction

In the previous chapter, the types of steady viscous flows common to micro- and nanofluidics were presented. Of particular importance is the Poiseuille flow and flow past a sphere. In the present chapter, classical solutions for heat transport and mass transport of uncharged species that may occur in parallel with the Poiseuille flow are described. This chapter will lead into a discussion of electrostatics and electrochemistry, concepts that are so important in micro- and nanofluidics.

Both heat and mass transfer are discussed in this chapter. This is because of the similarity in the forms of the governing equations and boundary conditions and the similar nature of the transport properties: the thermal conductivity and the mass diffusivity or diffusion coefficient. Indeed, heat and mass transfer often occur simultaneously (Figure 5.1). Both heat and mass transfer can be grouped into two modes: conduction heat transfer, diffusion mass transfer, and convective heat and mass transfer. A third mode of heat transfer, radiation heat transfer, is not discussed.

Fortunately, most liquid flows in micro- and nanochannels do not encounter large temperature and concentration gradients so that in general, the fluid properties remain relatively constant. Thus the governing equations can usually be decoupled to some extent, even at Reynolds numbers not normally viewed as being small.

Several basic problems of heat transfer in channels are considered before presenting the formal definition of the fully developed temperature distribution. Unlike the formal definition of fully developed fluid flow, the solution for the fully developed temperature distribution depends on the boundary conditions on the temperature at the walls of a tube or channel.