Abstract
This study presents a thermal analysis of a temperature-driven microfluidic cell through a nonlinear self-adaptive micro valve that provides the mechanisms for the system to maintain a given critical temperature in an efficient way. For the description of the dynamics of the microfluidic cell, a system of two ordinary differential equations subjected to a nonlinear boundary condition, which describes the behavior of the valve, is proposed. The solution of the model, for determined conditions, shows the strong nonlinearity between the overall thermal resistance of the device and the heat flux dissipated due to the action of the thermostatic valve, obtaining a variable thermal resistance from 1.6 × 10−5 to 2.0 × 10−4 Km2/W. In addition, a stability analysis of the temperature-driven microfluidic cell is presented. The stability of the device is essential for its proper functioning and thus, to prevent its oscillating behavior. Therefore, this work focuses on assessing the range of design parameters of the self-adaptive micro valve to produce a stable behavior for the entire system. The stability analysis was performed by studying the linear perturbation around the stationary solution, with the model solved for various heat flows, flow rates, and critical temperatures. Finally, a map of the design parameters space, which specifies the region with asymptotic stability, was found. In this map, the critical temperature (temperature at which the valve initiates the buckling) plays and important role.
Highlights
Physicists agree with Moore’s law and its 18-month doubling transistor density trend, where a transistor has about a five-year life before encountering size shrinking limitations imposed by the laws of thermodynamics and quantum physics
This deriveslaw mainlyof Fo from the delay between the changes in both the coolant flow rate and the temperature of tosolid assess linear stability ofis the stationary solutions the part that the governs the thermostatic valve, and aggravated in a system based on a matrix of microfluidic cells with self-adaptive valves [8] due to its increased complexity
The partial differential equations model (PDEs) model used in the comparison was a model that coupled the transfer of heat into weakly compressible fluids, in contact with solids
Summary
Physicists agree with Moore’s law and its 18-month doubling transistor density trend, where a transistor has about a five-year life before encountering size shrinking limitations imposed by the laws of thermodynamics and quantum physics. Heat conduction theproblem second chaos, and arefor known as the “thermostat problem”with [13,14,15,16] This deriveslaw mainlyof Fo from the delay between the changes in both the coolant flow rate and the temperature of tosolid assess linear stability ofis the stationary solutions the part that the governs the thermostatic valve, and aggravated in a system based on a matrix of microfluidic cells with self-adaptive valves [8] due to its increased complexity. In this case, the stability of a simple cooling cell is essential to ensure its correct operation. Assessed and the evaluation of the extended model is done
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