The convective heat transfer and pressure drop in flow past two types of tube array are solved numerically by the Finite Analytic Method in this investigation. The tube arrays considered are an in-line tube array and a staggered tube array with longitudinal and transverse pitch of two. The flow field solution is obtained and analyzed in Part I of the study. In the present Part II, the temperature field, heat transfer characteristics, and pressure drop are investigated. The fluid and tubes are considered to be at the same temperature, except for the array tube, which is heated or cooled. The solution domain covers three pitches of tube arrays in order to simulate accurately the non-periodic behavior of the temperature field downstream of the heated tube. In general, the heat transfer in a staggered array of tubes is found to be higher than that in an in-lined array of tubes. However, the pressure drop in a staggered array arrangement is also higher. Local heat transfer varies between in-line and staggered tube arrays and depends on Reynolds number and Prandtl number. At high Reynolds number, the local heat transfer tends to peak at the upstream surface of the heated tube but away from the stagnation point and becomes minimum at the separation point. Heat transfer in recirculation zones are, in general, small.
The convective motion in two types of tube array is solved numerically by the Finite Analytic Method. The Finite Analytic Method utilizes the local analytic solution of governing differential equations in obtaining its discretized algebraic representation. Both in-line tube arrays and staggered tube arrays with longitudinal and transverse pitches of 2 are studied. The geometries are expressed in boundary-fitted coordinates on which the Navier–Stokes equations and energy equation are solved. Solutions for Reynolds numbers of 40, 120, 400, and 800 are obtained. Differences in stream function, vorticity function, and location of separation and reattachment for flow past in-line tube arrays and staggered tube array are predicted and compared. The zone of separation for both arrays tends to increase with increasing Reynolds number. The predicted results on flow field and heat transfer are shown to agree with available experimental measurements.
Biochemical applications of microchips often require a rapid mixing of different fluid samples. At the microscale level, fluid flow is usually a highly ordered laminar flow and diffusion is the primary mechanism for mixing owing to the lack of disturbances, yielding inefficiency for practical biochemical analysis. In this work, we design a prototype active micromixer by employing the electrothermal effect. We apply to the flow microchannel a non-uniform AC electric field, which can generate an electrothermal force on the fluid flow and induce vortex pairs for enhancing mixing efficiency. The performance of this active micromixer is studied and compared, under the same mixing quality, with that of a conventional passive micromixer of the same size with obstacles in the flow channel by three-dimensional finite element simulations. The numerical results show that the pressure drop between the inlet and the outlet for the active micromixer is much less than (only 3000th) that for the passive micro-mixer with the same mixing quality. To obtain an optimal mixing quality, we have systematically studied the mixing quality by varying the geometrical arrangements of the electrodes. An almost complete mixing can be obtained using a specific design. Moreover, the temperature increases around the electrodes are lower than 3 K, which does not adversely affect the biochemical analysis. It is suggested that the prototype active micromixer designed is promising and effective and useful for biochemical analysis.
We investigate a immunoassay biosensor that employs a Quartz Crystal Microbalance (QCM) to detect the specific binding reaction of the (Human IgG1)-(Anti-Human IgG1) protein pair under physiological conditions. In addition to experiments, a three dimensional time domain finite element method (FEM) was used to perform simulations for the biomolecular binding reaction in microfluidic channels. In particular, we discuss the unsteady convective diffusion in the transportation tube, which conveys the buffer solution containing the analyte molecules into the micro-channel where the QCM sensor lies. It is found that the distribution of the analyte concentration in the tube is strongly affected by the flow field, yielding large discrepancies between the simulations and experimental results. Our analysis shows that the conventional assumption of the analyte concentration in the inlet of the micro-channel being uniform and constant in time is inadequate. In addition, we also show that the commonly used procedure in kinetic analysis for estimating binding rate constants from the experimental data would underestimate these rate constants due to neglected diffusion processes from the inlet to the reaction surface. A calibration procedure is proposed to supplement the basic kinetic analysis, thus yielding better consistency with experiments.
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