Ionic fluids subjected to externally applied electric fields experience Joule heating, which increases with the increased electric field and ionic conductivity of the medium. Temperature gradients induced by Joule heating can create buoyancy-driven flows produced by local density changes, as well as electrothermal transport due to the temperature-dependent variations in fluid permittivity and conductivity. This manuscript considers Joule heating-induced transport in microchannels by a pair of electrodes under alternating current electric fields. Resulting buoyancy-driven and alternating current electrothermal (ACET) flows are investigated theoretically, numerically and experimentally. Proper normalizations of the governing equations led to the ratio of the electrothermal and buoyancy velocities, as a new non-dimensional parameter, which enabled the construction of a phase diagram that can predict the dominance of ACET and buoyancy-driven flows as a function of the channel size and electric field. Numerical results were used to verify the phase diagram in various height microchannels for different ionic conductivity fluids and electric fields, while the numerical results were validated using the micro-particle-image velocimetry technique. The results show that ACET flow prevails when the channel dimensions are small, and the electric potentials are high, whereas buoyancy-driven flow becomes dominant for larger channel heights. The present study brings insights into Joule heating-induced transport phenomena in microfluidic devices and provides a pathway for the design and utilization of ACET-based devices by properly considering the co-occurring buoyancy-driven flow.

This attempt addresses the peristaltic transport of Jeffrey fluid in a curved channel. Heat transfer is discussed employing convective condition at the channel walls. Effects of radial applied magnetic field and Joule heating are retained. Convective boundary conditions at both walls with different temperature are also accounted. The relevant equations are modeled in view of lubrication approach. Closed form expression for stream function is constructed. Numerical solution of stream function, velocity and temperature is obtained via shooting method in Mathematica with the help of NDSolve command. It is observed that curvature has opposite effects on the lower and upper walls of channel. However temperature is an increasing function of curvature parameter. Temperature also decreases in presence of heat transfer convective parameter naturally the Biot number.

The combined effects of Joule and Newtonian heating in magnetohydrodynamic (MHD) flow of Jeffrey fluid over a stretching cylinder with heat source/sink are addressed. Suitable transformations are considered to reduce the non-linear boundary layer partial differential equations into the ordinary differential equations. Convergent series solutions of the resulting dimensionless problems are obtained. Effects of emerging physical parameters on the velocity and temperature profiles are examined. Comparison between viscous and Jeffrey fluids for different cases of flat plate and cylinder is made. Numerical values of skin friction coefficient and local Nusselt number are tabulated and analyzed for different values of emerging parameters.

This study presents a thermally fully developed electroosmotic flow of the non-Newtonian power-law fluids through a circle microchannel. A rigorous mathematic model for describing the Joule heating in an electroosmotic flow including the Poisson Boltzmann equation, the modified Navier Stokes equation and the energy equation is developed. The semi-analytical solutions of normalized velocity and temperature are derived. The velocity profile is computed by numerical integrate, and the temperature distribution is obtained by finite difference method. Results show that the velocity profiles depend greatly on the fluid behavior index n and the nondimensional electrokinetic width K. For a specified value of K, the axial velocity increases with a decrease in n, and the same trend for the effect of K on the velocity can be found for a specified value of n. Moreover, the dimensionless temperature is governed by three parameters, namely, the flow behavior index n, the nondimensional electrokinetic width K, and the dimen-sionless Joule heating parameter G. The variations of radial fluid temperature distributions with different parameters are investigated.

We consider a fully practical finite element approximation of the following degenerate system $$ {\frac{\partial }{\partial t}} \rho(u)- \nabla . ( \,\alpha(u) \,\nabla u ) \ni \sigma(u)\,|\nabla\phi|^2 ,\quad \nabla . (\, \sigma(u) \,\nabla \phi ) = 0$$ subject to an initial condition on the temperature, u,and boundary conditions on both u and the electric potential, ϕ. In the above p(u) is the enthalpy incorporating the latent heat of melting, α(u) > 0 is the temperature dependent heat conductivity, and σ(u) > 0is the electricalconductivity. The latter is zero in the frozen zone, u ≤ 0,which gives rise to the degeneracy in this Stefan system.In addition to showing stability bounds, we prove (subsequence) convergence of our finite element approximation intwo and three space dimensions. The latter is non-trivial due to the degeneracy in σ(u)and the quadratic nature of the Joule heating term forcing the Stefan problem.Finally, some numerical experiments are presented in two space dimensions.