Effects of radiative heat flux and joule heating on electro-osmotically flow of non-Newtonian fluid: Analytical approach

Background: The motion of fluids through the micro-tube, micro-channel, membranes, porous material and other fluid conduits because of the applied potential is known as electro-osmotic flow. The electro-osmosis process is a process in which electrodes generate the flow, and these electrodes are placed at each end of the micro-channel in the reservoirs. The electro-osmotic flow is induced through the surface charge in a small amount. The surface of most channels is made of glass and polymer which in an electrolyte solution have a negative charge. The reason for this is the abundance of positively charged anions in the double layer close to the channel walls. Because of the channel's electrical potential, the electrostatic forces attract the excess charges in the double layer and move towards the negative electrode. An electro-osmotic flow of non-Newtonian fluids is of significant importance in micro-fluidic systems and micro-devices. Due to the importance of electro-osmotic flow, under the influence of radiative heat flux, a theoretical analysis is conducted in this study to investigate the important characteristics of the electro-osmotic flow of third-grade fluid in the microplate. The viscosity of the fluid is either constant or temperature-dependent. The results are compared with experimental work done on a Newtonian fluid. This investigation for the third-grade fluid under the radiative heat flux and variable viscosity has not been reported previously to the best of our knowledge. Method of solution: Using the perturbation method, the approximate analytical solution to the problem of the nonlinear boundary value is obtained. The perturbation method is a relatively simple and high-precision method, that is used to find the approximate analytical solutions. In each case of the viscosity model, the analytical expressions of the velocity and temperature profiles are presented. Computational results and conclusions: The effects of fluidic parameters on velocity and temperature profiles of electro-osmotic flows are discussed graphically. The computational results show that the velocity and temperature decrease against the radiation parameter, non-Newtonian parameter and electro-kinetic parameter. Applications: In the first step, the results of this study provide a useful insight into the basic idea of the electro-osmotic flow of third-grade fluid within a micro-channel with the variable properties and thermal radiation in parallel geometry. Besides, the current study could be beneficial in the design of various biomedical lab-on-chip devices. These devices can be used for the transport of liquids in narrow containment (sample injection) and the production of chemical waste. These devices can also be useful for biomedical diagnosis and analysis (i.e. DNA analysis and clinical detection of viruses and bacteria etc.). Our analysis can also be used by designers of the thermal microfluidic devices. The efficiency of the heating techniques of the microfluidic system can be increased. It can also be used to enhance and control on-chip heat transfer, which increases the capacity of the polymeric microfluidic system.