Other Convection and Microfluidic Scenarios

Abstract

This chapter includes a brief exposition of some recent work on microfluidic flows and/or LTNE flows in a variety of situations. There will no doubt be many future novel applications of these theories and new problems solved in what is an exciting area. We describe the process of natural convection in a polymerase chain reaction where copies of a DNA sequence are produced commencing with only a few template molecules. We include expositions of local thermal non-equilibrium convection with heat flux boundary conditions, with a horizontal pressure gradient, and with uniform horizontal flow. Local thermal non-equilibrium convection is described when the saturating fluid in the porous medium is one of viscoelatic type. Local thermal non-equilibrium convection in a Brinkman porous medium is described when the gravity field is time-periodic. We also describe a very interesting problem of the evolutionary behaviour of the velocity and temperature fields in a porous medium with local thermal non-equilibrium effects when a hot fluid is injected into the porous medium.