Purpose In this paper aims to investigate the numerical simulation of the electroosmotic flow of the Carreau-Yasuda model in the rectangular microchannel. Electromagnetic current is generated by applying an effective electric field in the direction of the current. Design/methodology/approach The non-Newtonian model used is the five-constant Carreau-Yasuda model which the non-Newtonian properties of the fluid can be well modeled. Using the finite difference method, the potential values at all points in the domain are obtained. Then, the governing equations (momentum conservation) and the energy equation are segregated and solved using a finite difference method. Findings In this paper, the effect of various parameters such as Weisenberg number, electrokinetic diameter, exponential power number on the velocity field and Brinkman and Pecklet dimensionless numbers on temperature distribution are investigated. The results show that increasing the Weissenberg dimensionless number and exponential power and diameter parameters reduces the maximum velocity field in the microchannel. Originality/value To the best of the authors’ knowledge, this study is reported for the first time.

Purpose The purpose of this study is to investigate heat transfer and electrokinetic non-Newtonian flow in a rectangular microchannel in the developed and transient states. Design/methodology/approach The Carreau–Yasuda model was considered to capture the non-Newtonian behavior of the fluid. The dimensionless forms of governing equations, including the continuity equation for the Carreau–Yasuda fluid, are numerically solved by considering the volumetric force term of electric current (DC). Findings The impact of pertinent parameters such as electrokinetic diameter (R), Brinkman number and Peclet number is examined graphically. It is observed that for increasing R, the bulk velocity decreases. The velocity of the bulk fluid reaches from the minimum to the maximum state across the microchannel over time. At the electrokinetic diameter of 400, the maximum velocity was obtained. Temperature graphs are plotted with changes in the various Brinkman number (0.1 < Br < 0.7) at different times, and local Nusselt are compared against changes in the Peclet number (0.1 < ℘e < 0.5). The results of this study show that by increasing the Brinkman number from 0.25 to 0.7, the temperature along the microchannel doubles. It was observed that increasing the Peclet number from 0.3 to 0.5 leads to 200% increment of the Nusselt number along the microchannel in some areas along the microchannel. The maximum temperature occurs at Brinkman number of 0.7 and the maximum value of the local Nusselt number is related to Peclet number 0.5. Over time in the transient mode, the Nusselt number also decreases along the microchannel. By the increasing of time, the temperature increases at given value of Brinkman, which is insignificant at Brinkman number of 0.1. The simulation results have been verified by Newtonian and non-Newtonian flows with adequate accuracy. Originality/value This study contributes to discovering the effects of transient flow of electroosmotic flow for non-Newtonian Carreau–Yasuda fluid and transient heat transfer through rectangular microchannel. To the authors’ knowledge, the said investigation is yet not available in existing literature.

A novel model on 2D unsteady conductive heat transfer in an infinite hollow cylinder is proposed. The cylinder is made of functionally graded material (FGM) that has variable properties both in radial and angular directions. Volumetric heat capacity and thermal conductivity coefficient are changed according to the power function of the radius. In the presence of variable coefficients, the governing equations of unsteady heat transfer in FGMs have caused the complexity. The Laplace transform method is used to transfer the energy equation from time to frequency domain whereas the meromorphic function is used for the inverse Laplace transform to obtain the desired solutions. The closed form solutions have been well validated and the results have been presented for different values of functionally graded indices for thermal conductivity coefficients and volumetric heat capacity. Two different FGM cases with different complicated thermal boundary conditions have been investigated. The first case has a constant temperature in the inner radius and a variable heat flux along with the convection condition in the outer radius. In the second case, the inner radius has a specific harmonic temperature and the outer radius is exposed to the convective conditions. It was observed that in both cases, the temperature value in the cylinder decreases with the increase of the FG index for the conductivity coefficient. The presented analytical solution provides a good tool for validating unsteady numerical solutions presented in the field of heat transfer in FGMs.