Theoretical study of MHD electro-osmotically flow of third-grade fluid in micro channel

The electro-osmatic flow of non-newtonian fluid in a micro-channel is investigated in this article. The governing equations are derived with the help of a stress tensor then later transformed into dimensionless form with non-dimensional quantities. The perturbation method is used to obtain the approximate analytical solution of the given problem. The viscosity of the fluid is taken as a variable in terms of temperature. The validity of the perturbation solution is provided. The Pseudo-spectral collocation method is used to calculate the error in the perturbation solution of velocity and temperature. The magnitude of error in velocity and temperature is 10⁻⁴ and 10⁻², respectively. The impact of emerging parameters on velocity and heat profiles is also presented. The computational results reveal that the velocity profile diminishing via non-Newtonian parameter Γ₁, electro-kinetic parameter Γ₂, magnetic field parameter M and viscosity parameter D while an opposite behavior is noted in the velocity versus pressure gradient parameter Γ₃, viscosity parameter E and wall's temperature θ_w, respectively. Further, the temperature profile increases against the enhancement of Brinkman number, Joule heating parameter, pressure gradient parameter, wall's temperature, viscosity parameter D while reverse behavior is observed via electro-kinetic and magnetic field parameters. This study will help to understand the basic idea of MHD electro osmotic flow of non-Newtonian fluid bounded within a microchannel under the influence of variable viscosity. Further, this research can be useful to design the different types of biomedical lab-on-a-chip and thermal microfluidic devices. The developed devices can be helpful in DNA analysis and biomedical diagnosis etc.