ABSTRACT
Because of the nonzero viscosity of real fluids, all flows feature the no-slip condition at a solid boundary, resulting in a boundary layer flow with high transverse velocity gradients and wall shear stress. The effect of viscosity is predominantly confined to the boundary layers. Outside the boundary layer, the effect of viscosity may be considered negligible and the flow modeled as a potential flow, discussed in Chapter 6. Anderson (2005) captures the groundbreaking role of Ludwig Prandtl in first presenting the concept of the boundary layer in 1904 to the Mathematical Congress in Heidelberg, Germany, in an article titled, “On the Fluid Motion with Very Little Viscosity.” In his 10-minute presentation on the subject, Prandtl revolutionized the understanding and analysis of fluid flows of great engineering interest. The idea of a thin boundary layer at the surface of a body in fluid flow explains the mechanism of separation under an adverse pressure gradient in the flow direction. If we had today’s computing power to numerically solve the complete set of Navier-Stokes equations, we would have perhaps missed the development of the boundary layer theory and the simplifications it brings in solving many engineering problems involving fluid flow, including heat and mass transfer.
