Derivation of Second Order Partial Differential Equation Indicating Wave and Heat Equation through the Use of the Navier Stokes Equation for Unsteady and Incompressible Flow: Scientific Explanation

Abstract

In this paper, we have tried to approach the concepts of two dimensional wave equation and one dimensional heat equation through the means of the Navier Stoke’s equation for unsteady and incompressible flow. Our pursuit to do so has been supported with ample justifications and analytic discussions. The strong relation shared by the fluid dynamics, wave mechanics and heat flow has been brought to light through our attempts. Garnering sufficient insights on such relations can expand the knowledge levels and bring forth significant implications of the Navier Stokes equation.