Özet:

The problem of convection-diffusion heat conduction from the external environment to the curvilinear channel with a system of inserts filled with a homogeneous viscous fluid in the approximation of small Reynolds numbers is considered. A major stimulus for the research was the need for a controlled and managed heat transfer process that occurs on crystals of microprocessors and other microelectronic devices while a permanent complication of these devices and aspiration for miniaturization. The main idea of the local increase of heat flows in microchannels is associated with the possibility of forming quasi-stationary localized vortex structures in the areas adjacent to the inserts and the corners of the channel due to external pressure applied. Mathematical formulation of the problem is described by the system of the second-order differential equations with partial derivatives in a conservative form and appropriate initial and boundary conditions. The problem is solved numerically on a uniform grid using a simple explicit upwind differencing method for solving parabolic equations (Navier-Stokes equations, heat conduction convection-diffusion equations) and the method of successive over-relaxation for solving elliptic equations (Poisson equations for the stream function and Poisson equations for pressure). The numerical model was tested on a two-dimensional problem of homogeneous viscous fluid flow in the rectilinear channel and on a one-dimensional problem of heat conduction in a solid medium. The data of numerical experiments are in good agreement with the analytical solutions and the data published in the scientific literature. Studies have shown that increased coolant velocity leads to higher heat flow across borders due to the formation of localized vortex structures in the corner areas of the channel. It was found that heat flows increase when introducing a system of inserts of different heights for the fluid flows with Reynolds numbers Re> 30 ... 40. The level of heat transfer in the curvilinear channel with inserts for a given fluid velocity can be increased to 60% compared with the channel without inserts by increasing the pressure difference applied to the channel input and output. The obtained dependences and estimates of levels of heat flows can provide some support to designers and engineers in the microelectronics industry, other interested experts in the field of fluid mechanics and heating engineering. Author Biographies Александр Андреевич Гуржий, National Technical University of Ukraine “Kiev Polytechnic Institute” 37 pr. Pobedy, Kiev, Ukraine, 03056 Doctor of Science in Physics and Mathematics, professor Department of Automation design of energy processes and systemsFaculty of heat power engineering

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