• Proceedings of the KIEE Conference
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• 1999.07g
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• pp.3282-3285
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• 1999

Fluid characteristics at microscale were tried to be solved in this paper by showing how they deviate with conventional flow governing equations. (e.g. Navier-Stokes Equation) In earlier studies, this deviation phenomena was caused because of omitting no slip flow condition, micropolar effect and EDL(Electric Double Layer)effect of fluid which are usually negligible at macroscaled phenomena. The characteristics of fluid flow were tried to be studied by measuring pressure difference of specified length of the channels using the almost squared micromachined channels. By acquiring pressure difference, we could drive different values (viscosity, flow velocity. etc) from it and these data will be compared with macroscaled flow characteristics. As making microchannel is not easy work and that our knowledge is at mere stage, we had to fail to make it in this time. The hardest thing in this work is to make a hole which is directly connected with channel. The more efficient and easy way of making microchannel is proposed in this paper.

• Bulletin of the Korean Mathematical Society
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• v.29 no.1
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• pp.125-135
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• 1992

In various viscus flow problems it has been the custom to replace the convective derivative by the ordinary partial derivative in problems for which the data are small. In this paper we consider the Benard Convection problem with small data and compare the solution of this problem (assumed to exist) with that of the linearized system resulting from dropping the nonlinear terms in the expression for the convective derivative. The objective of the present work is to derive an estimate for the error introduced in neglecting the convective inertia terms. In fact, we derive an explicit bound for the L$_{2}$ error. Indeed, if the initial data are O(.epsilon.) where .epsilon. << 1, and the Rayleigh number is sufficiently small, we show that this error is bounded by the product of a term of O(.epsilon.$^{2}$) times a decaying exponential in time. The results of the present paper then give a justification for linearizing the Benard Convection problem. We remark that although our results are derived for classical solutions, extensions to appropriately defined weak solutions are obvious. Throughout this paper we will make use of a comma to denote partial differentiation and adopt the summation convention of summing over repeated indices (in a term of an expression) from one to three. As reference to work of continuous dependence on modelling and initial data, we mention the papers of Payne and Sather [8], Ames [2] Adelson [1], Bennett [3], Payne et al. [9], and Song [11,12,13,14]. Also, a similar analysis of a micropolar fluid problem backward in time (an ill-posed problem) was given by Payne and Straughan [10] and Payne [7].