• 대한기계학회논문집B
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• 제23권8호
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• pp.969-977
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• 1999

A similarity solution of a steady laminar flow of micropolar fluids past wedges has been studied. The similarity variables found by Falkner and Skan are employed to reduce the streamwise-dependence in the coupled nonlinear boundary layer equations. Numerical solutions of the equations are then obtained using the fourth-order Runge-Kutta method and the distribution of velocity, micro-rotation, shear and couple stress across the boundary layer are obtained. These results are compared with the corresponding flow problems for Newtonian fluid past wedges with various wedge angles. Numerical results show that, keeping ${\beta}$ constant, the skin friction coefficient is lower for a micropolar fluid, as compared to a Newtonian fluid. For the case of constant material parameter K, however, the velocity distribution for a micropolar fluid is higher than that of a Newtonian fluid.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2001년도 춘계학술대회논문집E
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• pp.196-201
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• 2001

In this paper, we have described the microchannel fluid behavior in a slot between rotating curvilinear surfaces of revolution using micropolar fluid theory. ]n order to solve this problem, we have used boundary layer equations and applied non-zero values of the microrotation vector on the wall. The results are compared with the corresponding flow problems for Newtonian fluid. Results show that both the velocity distribution and the microrotation component distribution for a micropolar fluid are lower than that of a Newtonian fluid.

• 유변학
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• 제11권2호
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• pp.122-127
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• 1999

일정한 표면 온도를 갖는 쐐기형 물체 주위를 지나는 미세 극성유체의 정상상태 층류유동에 대하여 고찰하였다. Falkner & Skan에 의하여 유도된 상사해법을 이용하여 유동방향의 비선형 경계층 방정식의 해를 구하였다. 4계 Runge-Kutta법을 사용하여 Pr 수가 1일 경우의 열전달 특성을 수치적으로 해석하였고, 물질 매개변수에 대한 영향을 고찰하였다. 경계층을 가로지르는 무차원 속도와 Nusselt 수의 분포는 쐐기형 물체 주위를 지나는 Newtonian 유체의 경우와 비교하였다. Pr 수가 1이고 일정한 쐐기각을 가질 경우 물질 매개변수 K값이 증가할수록 Newtonian 유체의 경우보다 미세 극성유체의 경우 경계층의 두께가 증가하는 결과를 보였다. 그러나 물질매개변수 K값이 일정할 경우, Newtonian 유체보다 미세 극성유체의 열전달율이 더 작은 경향을 나타내었다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제26권4호
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• pp.224-243
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• 2022

In this paper, we prove the global existence of classical solutions to the 2D incompressible Boussinesq equations for the micropolar fluid. Furthermore, applying the Fourier splitting methods, we obtain the lager time decay properties.

• Journal of Mechanical Science and Technology
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• 제18권3호
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• pp.491-498
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• 2004

An analysis of the plane Couette flow between two parallel plates of a viscous, incompressible, micropolar fluid is presented. Especially, the effects of non-zero values of the micro-gyration boundary condition coefficient and pressure gradient on the flow fields are studied. Numerical results show that the micro polar parameter was found to have much more of an impact on the flow behaviors. It is also observed that the micro-gyration boundary condition coefficient influenced on the coefficients of skin friction and couple stress due to its different effect on the surface stress.

• 충청수학회지
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• 제34권1호
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• pp.85-92
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• 2021

In present paper, inspired by the recently paper [1], we give the mixed pressure-velocity regular criteria in view of Lorentz spaces for weak solutions to 3D micropolar equations in a half space. Precisely, if (0.1) ${\frac{P}{(e^{-{\mid}x{\mid}^2}+{\mid}u{\mid})^{\theta}}{\in}L^p(0,T;L^{q,{\infty}}({\mathbb{R}}^3_+))$, p, q < ∞, and (0.2) ${\frac{2}{p}}+{\frac{3}{q}}=2-{\theta}$, 0 ≤ θ ≤ 1, then (u, w) is regular on (0, T].

• Journal of applied mathematics & informatics
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• 제8권2호
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• pp.539-550
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• 2001

In the present investigation, we study the influence of a transverse magnetic field through a porous medium. Laplace transform techniques are used to derive the solution in the Laplace transform domain. The inversion process is carried out using a numerical method based on Fourier series expansions. Numerical computations for the temperature, the microrotation and the velocity distributions as well as for the induced magnetic and electric fields and carried out and represented graphically.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제8권2호
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• pp.51-73
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• 2004

A boundary layer analysis is used to study the effects of Hall and ion-slip currents on the steady magneto-micropolar of a viscous incompressible and electrically conducting fluid over a horizontal plate. By means of similarity solutions, deviation of fundamental equations on the assumption of small magnetic Reynolds number are solved numerically by using the shooting method. The effects of various parameters of the problem, e.g. the magnetic parameter, Hall parameter, ion-slip parameter, buoyancy parameter and material parameter are discussed and shown graphically.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제9권2호
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• pp.45-53
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• 2005

This paper investigates the influence of thermal conductivity and variable viscosity on the problem of micropolar fluid in the presence of suction or injection. The fluid viscosity is assumed to vary as an exponential function of temperature and the thermal conductivity is assumed to vary as a linear function of temperature. The governing fundamental equations are approximated by a system of nonlinear ordinary differential equations and are solved numerically by using shooting method. Numerical results are presented for the distribution of velocity, microrotation and temperature profiles within the boundary layer. Results for the details of the velocity, angular velocity and temperature fields as well as the friction coefficient, couple stress and heat transfer rate have been presented.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2001년도 추계학술대회논문집B
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• pp.591-596
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• 2001

Micron-size mechanical devices are becoming more prevalent, both in commercial applications and in scientific inquiry. Within the last decade, a dramatic increase in research activities has taken place, mostly due to the rapidly expanding growth of applications in areas of MEMS(Micro-Electro-Mechanical Systems), bioengineering, chemical systems, and advanced energy systems. In this study, we have described the effects of vortex viscosity variation on the flowfields in a micro-slot between rotating surfaces of revolution using a micropolar fluid theory. In order to solve this problem, we have used boundary layer equations and applied non-zero values of the microrotation vector on the wall. The results are compared with the corresponding flow problems for Newtonian fluid. Results show that the coefficient $\delta$ controls the main part of velocity ${\upsilon}_x$ and the coefficient M controls the main part of microrotation component ${\Omega}_{\theta}$.