Afr. Mat. https://doi.org/10.1007/s13370-018-0553-9 Propagation of waves in micropolar thermodiffusion elastic half-space Rajneesh Kumar 1 · Sachin Kaushal 2 · M. Marin 3 Received: 2 January 2016 / Accepted: 24 January 2018 © African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2018 Abstract The present paper is devoted to the study of propagation of plane waves in micropolar thermodiffusion elastic half-space in the context of generalized theories of ther- moelasticity. The variations of amplitude ratios for plane waves (longitudinal wave, thermal wave and mass diffusive wave) are computed analytically and depicted graphically for lon- gitudinal wave against the angle of incidence. The impact of relaxation times, micropolarity and diffusion have been studied. Some particular cases of interest are also deduced from the present investigation. Keywords Micropolar · Thermodiffusion · Amplitude ratios · Plane waves Mathematics Subject Classification 74F05 · 74J05 · 76R50 1 Introduction In problems of waves and vibrations, the classical theory of elasticity fails to provide complete information and the results, so obtained do not confirm with experimental ones particularly in media with granular structure. Classical continuum theories are useful to explain the mechan- ical behaviour of simple mateials like coal, concrete etc, but they are unable to explain the behaviour of complex materials such as bones, blood, cellular solids, polymer, the analysis of such materials requires incorporating the theory of oriented media and hence classical elasticity is inadequate to represent the behavior of such materials, for this reason Eringen [1, 2] developed theories for elastic solids, fluid and further for a subclass of micromorphic B Sachin Kaushal sachin_kuk@yahoo.co.in 1 Department of Mathematics, Kurukshetra University, Kurukshetra 136118, India 2 Department of Mathematics, School of Chemical Engineering and Physical Sciences, Lovely Professional University, Phagwara, Punjab, India 3 Department of Mathematics, University of Brasov, Brasov, Romania 123