Temperature jump in second Stokes' problem by nonlinear analysis

TL;DR

This paper investigates the temperature jump phenomenon in the second Stokes' problem involving oscillating surfaces in viscous fluids, using nonlinear analysis and the method of small parameters.

Contribution

It introduces a nonlinear analytical approach to determine the temperature jump in the second Stokes' problem, expanding understanding beyond linear models.

Findings

Temperature difference exists between the surface and the far environment.

The nonlinear analysis provides a new expression for the temperature jump.

The method of small parameters effectively captures the temperature behavior.

Abstract

The second Stokes problem about behavior of the viscous fluid (matter) filling half-space is considered. A flat surface limiting half-space makes harmonious oscillations in the eigen plane. The equations of mechanics of the continuous environment are used. It is shown, that in considered process there is the temperature difference between temperature of a surface and temperature environments far from a surface. Usually similar difference is called as temperature jump. The method of small parameter is applied. Temperature jump in the second approach is found out.