Sloshing waves in a heated viscoelastic fluid layer in an excited rectangular tank

• A heated viscoelastic fluid layer in a rectangular tank.
• The tank is subjected to a horizontal periodic oscillation.
• The system of equations is solved by means of Laplace transform.
• The inversion of the Laplace transform is carried out using a numerical approach.
• Numerical results are provided to illustrate the effects of the parameters.

In this paper, we have investigated the motion of a heated viscoelastic fluid layer in a rectangular tank that is subjected to a horizontal periodic oscillation. The mathematical model of the current problem is communicated with the linearized Navier–Stokes equation of the viscoelastic fluid and heat equation together with the boundary conditions that are solved by means of Laplace transform. Time domain solutions are consequently computed by using Durbin's numerical inverse Laplace transform scheme. Various numerical results are provided and thereby illustrated graphically to show the effects of the physical parameters on the free-surface elevation time histories and heat distribution. The numerical applications revealed that increasing the Reynolds number as well as the relaxation time parameter leads to a wider range of variation of the free-surface elevation, especially for the short time history.