IJPAM: Volume 70, No. 6 (2011)

REFLECTION AND REFRACTION AT AN INTERFACE
BETWEEN TWO DISSIMILAR THERMALLY
CONDUCTING VISCOUS LIQUID HALF-SPACES

Sunita Deswal$^1$, Lakhbir Singh$^2$, Baljeet Singh$^3$
$^{1,2}$Department of Mathematics
G.J. University of Science and Technology
Hisar, 125001, Haryana, INDIA
$^3$Department of Mathematics
Post Graduate Government College
Sector-11, Chandigarh 160011, INDIA


Abstract. The present investigation is concerned with the problem of reflection and refraction of plane waves at an interface between two dissimilar thermally conducting viscous liquid half-spaces. The required boundary conditions at the interface are satisfied by particular solutions in both the half-spaces to obtain the relations between the amplitude ratios of different reflected and refracted waves for both Lord-Shulman (L-S) and Green-Lindsay (G-L) theories of generalized thermoelasticity. The complex absolute values of the amplitude ratios are computed numerically for a particular example of the model. In the presence as well as absence of thermal and viscous parameters, these values of amplitude ratios are plotted against the angle of incidence to observe the effects of viscosity and thermal fields.

Received: March 2, 2011

AMS Subject Classification: 74Jxx

Key Words and Phrases: thermally conducting, viscous liquid, plane waves, reflection, refraction, amplitude ratios, thermal relaxation times

Download paper from here.



Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 70
Issue: 6