The Equation for the Stokesian Stream Function and

Authors: Günter Brenn

Publish Date: 2017

Volume: , Issue: , Pages: 25-49

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Abstract

This chapter presents and discusses the equation for the Stokesian stream function The equation emerges as the one nonzero component of the curl of the twodimensional momentum equation with the velocity components given as spatial derivatives of the stream function The stream function is defined such that its derivatives yield a solenoidal velocity field The analyses of the flows discussed in Part I of this book are based on this function In view of our search for analytical solutions we are restricted to laminar twodimensional flow in simple geometries The equations of change therefore need no turbulence modelling the concept of the Stokesian stream function can be applied for representing the flow velocity and the boundary conditions are easy to formulate and implement analytically in the general solutions The fluids are treated as incompressible and Newtonian or linear viscoelastic The linear viscoelastic liquids exhibit a viscosity depending on frequency but not on shear rate Furthermore we restrict this analysis to flows without heat and mass transfer ie we solve the continuity and momentum equations and disregard the influence of viscous dissipation on the energy budget of the flow We are therefore restricted to flow without viscous heating Problems of heat and mass transfer are the subjects of Part II of this book

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