Thermally Fully Developed Electroosmotic Flow of Power-Law Nanofluid in a Rectangular Microchannel

Abstract

The hydrodynamic and thermal behavior of the electroosmotic flow of power-law nanofluid is studied. A modified Cauchy momentum equation governing the hydrodynamic behavior of power-law nanofluid flow in a rectangular microchannel is firstly developed. To explore the thermal behavior of power-law nanofluid flow, the energy equation is developed, which is coupled to the velocity field. A numerical algorithm based on the Crank–Nicolson method and compact difference schemes is proposed, whereby the velocity, temperature, and Nusselt number are computed for different parameters. A larger nanoparticle volume fraction significantly reduces the velocity and enhances the temperature regardless of the base fluid rheology. The Nusselt number increases with the flow behavior index and with electrokinetic width when considering the surface heating effect, which decreases with the Joule heating parameter. The heat transfer rate of electroosmotic flow is enhanced for shear thickening nanofluids or at a greater nanoparticle volume fraction.

The Effect of Streaming Potential and Viscous Dissipation in the Heat Transfer Characteristics of Power-Law Nanofluid Flow in a Rectangular Microchannel

“…Based on the method of variable separation and method of constant variation [34,39], the temperature field in the absence of viscous dissipation for Newtonian nanofluid electrokinetic flow through a rectangular microchannel has been firstly obtained as…”

“…When considering power-law nanofluid flow (n 1 and φ 0) with streaming potential effect and viscous dissipation, according to the coupling of Equations (9)-(11), (15), and (16), the velocity distribution and induced electric field strength need to be solved to acquire temperature distribution and Nusselt number. Due to the high nonlinearity of modified Cauchy momentum Equations (9) and (10) and energy Equations (15) and (16), high order finite difference methods have been applied to solve the velocity and temperature [34]. The term ∂/∂t is introduced to iteratively solve hydrodynamic field and thermal field from…”

“…, and f = w when solving Equations (9) and (10). The nonlinear coefficients are numerically treated by the compact difference scheme that can be found in our last works [17,34]. When solving Equations (15) and (16),…”

“…The discretization procedure is found in details in [17,34]. A specified criterion Er is given to identify that if the velocity is fully developed, i.e., f l − f l+1 < Er because ∂w/∂t t→∞ = ∂T/∂t t→∞ = 0 .…”

Numerical Analysis and Entropy Generation of Electrokinetic Flow of Power-Law Fluid in a Microtriangular Prism

“…is concept explored in the pioneering work of Bejan [27] where the author considered the thermodynamic second law features of heat transfer by forced convection on four different flow configurations: pipe flow, flow in a rectangular duct, boundary layer over flat plate, and cross-flow; then, he analysed the irreversibility due to heat transfer through finite temperature gradient and irreversibility due to the viscous effect. In a series of research studies, Khan and his co-authors investigated the entropy generation for a different flow and heat transfer problem.…”