Theoretical conjugate heat transfer analysis in a parallel flat plate microchannel under electro-osmotic and pressure forces with a Phan-Thien-Tanner fluid

In this paper we solve, numerically and asymptotically, the steady-state analysis of a conjugate heat transfer process in an electro-osmotic and fully developed laminar flow including Joule heating effects. In addition, the viscoelastic fluid obeys the simplified Phan-Thien-Tanner (SPTT) constitutive equation. Taking into account the finite thermal conductivity of the micro-channel wall, the dimensionless temperature profiles in the fluid and solid wall have been obtained as functions of the dimensionless parameters involved in the analysis: a conjugate parameter, α, which represents the competition between the longitudinal conductive heat in the micro-channel wall to the convective heat transfer in the fluid; εDeκ2, a parameter that describes the viscoelastic behavior of the fluid; the well-known Peclet number, Pe; a normalized power generation term, Λ, being the ratio of heat flux from the external wall to the Joule heating (and smaller or equal to unity); the ratio of pressure to the electro-osmotic forces, Γ; and the aspect ratios of the micro-channel and the solid wall, β and ε, respectively. The results for the temperature fields, in the fluid and micro-channel wall show a strong dependence of the above dimensionless parameters, therefore, this set of parameters controls directly the thermal performance of this micro-channel model.