A mathematical model is developed to investigate the combined viscous electro-osmotic flow and heat transfer in a finite length micro-channel with peristaltic wavy walls. The influence of Joule heating is included. The unsteady two-dimensional conservation equations for mass, momentum and energy conservation with viscous dissipation, heat absorption and electro-kinetic body force, are formulated in an ( ) co-ordinate system. The Joule heating term appears as a quadratic function of axial electrical field in the energy conservation equation. The momentum and energy equations are coupled via the thermal buoyancy term. The peristaltic waves propagating along the micro-channel walls are simulated via a time-dependent co-sinusoidal wave function for the transverse vibration of the walls. Both single and train wave propagation are considered. Constant thermo-physical properties are prescribed and a Newtonian (Navier-Stokes) viscous model employed for the fluid. The transport equations are transformed from the wave frame to the laboratory frame and the electrical field terms rendered into electrical potential terms via the Poisson-Boltzmann equation, Debye length approximation and ionic Nernst Planck equation. The dimensionless emerging linearized electro-thermal boundary value problem is solved using integral methods. A parametric study is conducted to evaluate the impact of isothermal Joule heating term on axial velocity, temperature distribution, pressure difference, volumetric flow rate, skin friction (wall shear stress function) and Nusselt number (wall heat transfer rate). The modification in streamline distributions with Joule heating and electro-osmotic velocity is also addressed to elucidate trapping bolus dynamics.
**TOPICS:**
Dynamics (Mechanics), Pressure, Momentum, Flow (Dynamics), Buoyancy, Heat, Heat transfer, Electric fields, Electric potential, Wave propagation, Fluids, Absorption, Joules, Waves, Electrokinetics, Energy dissipation, Skin friction (Fluid dynamics), Wave functions, Electroosmosis, Energy conservation, Vibration, Approximation, Boundary-value problems, Peristaltic flow, Temperature distribution, Trains, Heating, Microchannels, Shear stress