Heat Transfer Characteristics of an Electroosmotic Flow of Viscoelastic Fluid in Slit Microchannel

In this work, we derive an analytical solution for heat transfer characteristics of a thermally developing flow of viscoelastic fluids under the application of an electroosmotic force. The walls are subjected to either in isothermal condition or a constant wall heat flux is employed. First, we derive a Helmholtz-Smoluchowski (HS) type slip velocity for the viscoelastic fluids, which is further used to simplify the energy equation. The Laplace transform method is employed with respect to the longitudinal variable to get a reduced form of the energy equation. The resulting expressions are inverted using residue calculus and as well as a Fourier series based numerical method to obtain the temperature distribution within the microchannel. Based on the analytical solution, we also derive an expression for the local heat transfer coefficient and Nusselt number. Two types of viscoelastic fluids, linear and exponential PTT fluid, are considered here. From this study it is found that, with increasing viscoelastic parameter, the advective heat transport is more in case of exponential-PTT fluid compared to linear-PTT fluid and hence requires less channel entrance length to reach at the fully developed state. The results obtained here, may have important implication towards the thermal management of bio-microfluidic devices. Nomenclature De Deborah number  Permittivity of the medium (F/m) e Elementary charge (C)  EDL potential (V) x E Applied electric field (V/m)  Zeta potential (V) J Non-dimensional Joule heat 1   EDL thickness (m) B k Boltzmann constant (J/K)  Non-dimensional channel length f k Thermal conductivity (W/mK)  Non-dimensional channel height n Cationic/anionic number densities (m) τ Viscoelastic stress tensor 0 n Bulk ionic number density(m )  Fluid viscosity (kg/ms) Nu Local Nusselt number  Relaxation time of the fluid T Pe Thermal Peclet' number  Extensibility parameter of the fluid W q Wall heat flux (W/m ) b  Bulk ionic conductivity (S/m) W Q Non-dimensional wall heat flux f  Fluid density (kg/m ) T Absolute temperature (K) P c Specific heat capacity (J/kg K) 0 T Inlet temperature (K)  Non-dimensional temperature W T Wall temperature (K) m  Non-dimensional mean temperature HS U Helmholtz-Smoluchowski velocity (m/s) trτ Trace of stress tensor τ z Valence Erfi Imaginary error function