Heat Transfer Enhancement in Micro-Scale Geometries

Abstract

Micro-geometries or “microfluidics” are commonly utilised in a widespread variety of applications such as, bioengineering devices, microelectronic devices, electronics cooling, chemical micro-reactors and mini or micro-heat exchangers. In the microscale systems (with “small” dimensions typically less than 1 millimeter), however, fluid mixing has been understood as one of the most fundamental and difficult-toachieve issues because the flow of Newtonian fluids becomes increasingly controlled by viscous forces rather than inertia (as molecular diffusion is dominant at these small scales). As a consequence, the enhancement of convective heat transfer is problematic under these conditions (steady and laminar flow regime). In this thesis, two different regimes of instabilities, namely “purely-inertial” and “purely-elastic”, have been adopted to enhance the convective heat transfer in the micro-scale geometries. Purely-inertial instability refers here to the secondary flow that arise in curved channels, also known as Dean flows, due to the centrifugal forces and also in crossed channels (cross-slot), symmetry-breaking bifurcations, which results in an axially-oriented spiral vortex along the outlet channels. While, purely-elastic instability is created in the flow of non-Newtonian viscoelastic fluids through curved channels due to the non-linear interaction between elastic stresses generated within the flowing viscoelastic solutions and the streamline curvature or through cross-slot device as a consequence of the planar extensional flow field (strong elongational flow) at the stagnation point. Fluid flow and convective heat transfer characteristics have been investigated experimentally and supporting numerical calculations for Newtonian flow within two different micro-geometries: a square cross-section serpentine microchannel and a square cross-section crossslot micro-device. A group of Newtonian fluids, aqueous glycerine solutions and aqueous sucrose solutions, was utilised to carry out the experiments for purelyinertial flows whilst high-viscosity polymeric viscoelastic fluids, shear-thinning and approximately constant-viscosity Boger solutions, were used for the experiments to investigate purely-elastic instabilities. xxi For Newtonian fluids, the experimental results of the averaged Nusselt number show good agreement with the present numerical data where the deviations of the mean Nusselt number between the experimental results and numerical data are 10.7% and 8.6% with P r = 1038 and 137, respectively. As a result of the existence of secondary flows in the flow fields of the serpentine microchannel geometry, the heat transfer performance of the serpentine microchannel is higher than that of the equivalent straight microchannel with the same cross-section over the entire range of Reynolds number (Dean number). Simultaneously, the relative pressure-drop losses in the serpentine microchannel rise with increasing Dean number. However, this increase is much smaller over the whole range of Dean number than the heat transfer enhancement. The maximum percentage increase of relative pressure-drop losses for both Prandtl numbers, 1038 and 137, is up to 2% and 39%, respectively, whereas the enhancement of heat transfer for P r = 1038 and 137 increases by 56% and 158%, respectively. For the viscoelastic solutions, the values of the product of friction factor-Reynolds number (fRe(N−Newt.)) normalised by friction factor-Reynolds number product for laminar fully-developed Newtonian fluid flow (fRe(Newt.)) in a straight square duct versus Weissenberg number indicated that, for W i < 5, the normalised nondimensional pressure drop is similar to that for a Newtonian fluid and with further increasing Weissenberg number (5 < W i < 25) the purely-elastic instability develops and leads to an increase in the normalised pressure-drop. The increase in the normalised non-dimensional pressure-drop values for all viscoelastic solutions beyond W i ≈ 25 are much greater than the Newtonian limit, suggesting that the complexity of the elastic instabilities increase with increasing W i. Elastic turbulence generated in the flow of viscoelastic solutions is shown to enhance the convective heat transfer in the serpentine microchannel by approximately 200% for 50 ppm PAA in glycerine-based solution and 80 ppm PAA in sucrose-based solution and reaches up to 380% for 200 ppm PAA in glycerine-based solution and 500 ppm PAA in sucrose-based solution under creeping-flow conditions in comparison to that achieved by the equivalent Newtonian fluid flow at identical Graetz number. For Newtonian fluids, a symmetry-breaking bifurcation occurs at the stagnation point in the cross-slot geometry when the Reynolds number increases beyond a certain critical value (≈ 40) [107, 150] and an axially-oriented spiral vortex is created along the outflow channels. Therefore, this spiral vortex promotes the mixing process in the cross-slot. This three-dimensional behaviour of the bifurcated flow enhances the heat transfer between the hot and cold fluids by convection along