Analytical solutions of dissipative heat transfer on the peristaltic flow of non-newtonian fluids in asymmetric channels

Abstract

Peristalsis is a natural mechanism responsible for the propulsion and the segmentation of biofluids in living structures, and this mechanism is important due to its efficient pumping characteristics. An essential feature of peristalsis is dissipation, thus dissipative heat transfer must be considered in the propulsion of biofluids. Most biofluids exist with different non-Newtonian fluid characteristics and experimental investigations reveal that the physiological structures are non-uniform with asymmetric peristaltic waves. This research focuses on the development of mathematical models which take into account the dissipative heat transfer on the peristaltic flow of non-Newtonian fluids. The non-Newtonian fluids include Walter’s B, fourth grade and Sisko fluids and the flow have been considered in the horizontal and inclined asymmetric channels. Governing equations are first modeled in the laboratory frame and then transformed into the wave frame. Resulting equations are non-dimensionalized and the nonlinearity has been reduced by adopting the long wavelength and small Reynolds number approximations. Explicit forms of the analytical solutions have been obtained using the regular perturbation method. Influences of various parameters such as velocity slip parameter, Sisko fluid parameter, Brinkman, Eckert, Deborah, Soret and Schmidt numbers on the flow quantities namely velocity, shear stress, pumping, trapping, temperature, concentration and heat transfer coefficients have been investigated. Results show that pumping, trapping and temperature are reduced for increasing velocity slip parameter. Temperature and heat transfer coefficients are increased with the increase of Brinkman, Eckert and Deborah numbers. Concentration decreases with the increase of Brinkman, Soret and Schmidt numbers. Comparative study amongst viscous, shear thinning and shear thickening fluids has also been presented.