Hydrodynamic and Thermal Characteristics of Combined Electroosmotic and Pressure Driven Flow in a Microannulus

Abstract

The present study considers both the hydrodynamic and thermal characteristics of combined electroosmotic and pressure driven flow in a microannulus. Analytical solutions are presented using the Debye–Hückel linearization along with the uniform Joule heating and negligible viscous dissipation assumptions, whereas exact results are achieved numerically. Here, the range of validity for the Debye–Hückel linearization is found to be about two times of that for a parallel plate microchannel. Accordingly, this linearization may successfully be used to evaluate the potential and velocity distributions up to the zeta potentials of 100 mV, provided that the dimensionless Debye–Hückel parameter is above 10; nevertheless, the calculated wall shear stresses may be significantly different from the exact ones, even for lower zeta potentials. The viscous heating effects are found to be limited to low values of the dimensionless Debye–Hückel parameter. These effects are pronounced in the presence of a favorable pressure gradient, whereas the opposite is true for an opposed pressure gradient. Furthermore, the influence of increasing the annular geometry parameter, that is the inner to outer radii ratio, generally is to decrease both the inner and outer Nusselt numbers. It is also revealed that the pressure effects vanish at higher values of this parameter.

Unsteady Pressure-Driven Electrokinetic Slip Flow and Heat Transfer of Power-Law Fluid through a Microannulus

“…In Figure 2 a, in the limiting case of a Newtonian fluid, the numerical velocity computed based on Equation (30) is compared with the analytical velocity obtained from Equation (28) and the existing data presented in the study [ 28 ] by Yavari et al and [ 13 ] by Tsao. In Figure 2 b, for power-law fluids, the numerical velocities computed from Equation (30) are compared with the existing data from [ 30 ] by Shamshiri et al In Figure 2 c, the average temperature T m is numerically computed for different flow behavior indices n and grid numbers in terms of space J .…”

“… ( a ) The comparison among the analytical velocity, numerical velocity, and existing data from the studies [ 13 , 28 ] without consideration of slip velocity at the channel walls, ( b ) the comparison between numerical velocity and existing data in [ 30 ] different n , and ( c ) the grid independence study of the mean temperature for shear thinning fluid and shear thickening fluid when Br = 0.005, S = 2, and ζ 1 = ζ 2 = −1. …”

“…Therefore, another important category of the research on the electroosmosis problem is thermal characteristics [ 24 , 25 , 26 , 27 ]. Due to the large heat transfer area and high heat transfer coefficient, annular geometry is frequently encountered in micro heat exchangers and microelectronic cooling [ 28 , 29 ]. Nevertheless, only some literature reported the exploration of the thermal behaviors of electroosmosis in an annulus.…”

“…The thermal effects in a mixed electroosmotic pressure-driven flow of power-law fluids were numerically investigated in [ 30 ]. Yavari et al numerically analyzed both the hydrodynamic and thermal characteristics of an electrokinetic flow in the absence of viscous dissipation [ 28 ]. The numerical results show that the annular geometry parameter exerts an impressive influence on the heat transfer performance.…”

Transforming Navier‐stokes equation to a fourth order nonlinear differential equation for the study of electrolyte flow in a circular microchannel

“…The most recent research on electrokinetic-driven flow in microchannels was done in Refs. [28][29][30][31][32][33][34][35][36][37][38]. Petsev and Lopez [28] applied the method of matched asymptotic expansions to solve nonlinear Poisson-Boltzmann equation for the prediction of electrostatic potential in a capillary filled with an electrolyte solution.…”