Abstract
In this paper, the unsteady flow of a fluid of finite depth with an oscillating bottom is examined. The flow is assumed in the absence of viscous dissipation. The governing equations of the flow are decoupled in the velocity and temperature fields. The velocity and temperature fields have been obtained analytically. The effects of various material parameters on these fields have been discussed with the help of graphical illustrations. It is noticed that the upward thrust (ρfy) vanishes when Reiner Rivlin coefficient of viscosity (μc) is zero and the transverse force (ρfz) perpendicular to the flow direction vanishes for thermo-viscosity coefficient (α8) is zero. The external forces generated perpendicular to the flow direction is a special feature of thermo-viscous fluid when compared to the other type of fluids.
Highlights
Considerable interest has been evinced in the recent years on the study of viscous flows because of its natural occurrence and its importance in industrial geophysical and medical applications
It is noticed that the upward thrust
The investigation of the flow of thermo-viscous flows has become an important topic due to the recovery of crude oil from the pores of reservoir rocks, the extraction and filtration of oil from wells, the oil reservoir treated by the reservoir engineer, the extraction of energy from geo-thermal regions are some of the areas in which thermo-viscous flows have been noticed
Summary
Considerable interest has been evinced in the recent years on the study of viscous flows because of its natural occurrence and its importance in industrial geophysical and medical applications. The concept of thermo-viscous fluids which reflect the interaction between thermal and mechanical responses in fluids in motion due to external influences was introduced by Koh and Eringin in 1963 For such a class of fluids, the stress-tensor ‘ t ’ and heat flux bivector ‘ h ’ are postulated as polynomial functions of the kinematic tensor, viz., the rate of deformation tensor ‘ d ’: dij = (ui, j + u j,i ) / 2 and thermal gradient bivector ‘ b ’. Animasaun[4] studied dynamics of unsteady MHD convective flow with thermo phoresis of particles and variable thermo-physical properties past a vertical surface moving through binary mixture Keeping this in mind the relevance and growing importance of thermo-viscous fluids in geophysical fluid dynamics, chemical technology and industry; the present paper attempts to study the variations of velocity and temperature fields on the unsteady flow of thermo-viscous fluid over a flat plate with an oscillating bottom for the various material parameters
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