• 대한수학회보
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• 제60권6호
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• pp.1673-1685
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• 2023

Inspired by Hongjie Dong and Qi S. Zhang's article [3], we find that the analyticity in time for a smooth solution of the heat equation with exponential quadratic growth in the space variable can be extended to any complete noncompact Riemannian manifolds with Bakry-Émery Ricci curvature bounded below and the potential function being of at most quadratic growth. Therefore, our result holds on all gradient Ricci solitons. As a corollary, we give a necessary and sufficient condition on the solvability of the backward heat equation in a class of functions with the similar growth condition. In addition, we also consider the solution in certain L^p spaces with p ∈ [2, +∞) and prove its analyticity with respect to time.

• 항공우주시스템공학회지
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• 제6권4호
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• pp.24-28
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• 2012

In this paper, 2-D experiment and steady-state computational fluid analysis were conducted for measuring the hear transfer coefficient of pintle type controllable thruster in high pressure and temperature. In case of 2-D experiment, transient liquid crystal technique was used for measuring heat transfer coefficient for the 2-D pintle model. The experimental result was used to validate the CFD result. The CFD results well predicted the heat transfer coefficient on the pintle surface except the nozzle downstream region, where the results by CFD was higher than experimental results. The CFD results were also compared with the result by Bartz equation and the it was shown that the Bartz equation overestimated the heat transfer coefficient on the nozzle throat as much as 80%.

• 설비공학논문집
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• 제6권1호
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• pp.1-10
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• 1994

The flow and heat transfer characteristics behind a backward facing step located in a vertical channel has been studied. In this study, the numerical prediction has been performed by solving the Navier-Stokes equation and energy equation simultaneously with the SIMPLE algorithm embedied in TEACH code. Local heat flux was measured by using Schlieren Interferometer. The flow visualization was performed using the cylindrical lens and the laser beam that is scattered by the supplied glycerine particles. The velocity and temperature distributions, recirculation region, reattachment length, and local heat flux are obtained under the various parameters to investigate the buoyancy effect on the flow and heat transfer characteristics behind the step.

• 대한기계학회논문집B
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• 제23권1호
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• pp.1-11
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• 1999

The three-dimensional laminar mixed convection flow between the conductive printed circuit boards. on which the heat generating rectangular blocks are uniformly distributed, has been examined in the present study. The flow and heat-transfer characteristics are assumed to be pseudo periodic in the streamwise direction and symmetric in the cross-stream direction. Using an algorithm of SIMPLER, the continuity equation. the Navier-Stokes equations and the energy equation are solved numerically in the three-dimensional domain Inside the channel. The convective derivative terms are discretized by the QUICK scheme to accurately capture the flow field. The flow and the heat transfer characteristics are thoroughly examined for various Re and Gr.

• Journal of applied mathematics & informatics
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• 제15권1_2호
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• pp.127-146
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• 2004

In this paper we consider a heat flow in an inhomogeneous. body without internal source. There exists special initial and boundary conditions in this system and we intend to find a convenient coefficient of heat conduction for this body so that body cool off as much as possible after definite time. We consider this problem in a general form as an optimal control problem which coefficient of heat conduction is optimal function. Then we replace this problem by another in which we seek to minimize a linear form over a subset of the product of two measures space defined by linear equalities. Then we construct an approximately optimal control.

• Journal of Mechanical Science and Technology
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• 제17권12호
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• pp.2042-2052
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• 2003

An experimental study was performed to investigate heat transfer characteristics of turbulent swirling flow in an axisymmetric annuli. The static pressure, the local flow temperature, and the wall temperature with decaying swirl were measured by using tangential inlet conditions and the friction factor and the local Nusselt number were calculated for Re=30000∼70000. The local Nusselt number was compared with that obtained from the Dittus-Boelter equation with swirl and without swirl. The results showed that the swirl enhances the heat transfer at the inlet and the outlet of the test tube.

• 설비공학논문집
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• 제2권3호
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• pp.226-233
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• 1990

Fixed bed is known to be an effective heat transfer augmentation device which could be applied to heat exchangers. In this study, pressure drop in vertical cylindrical and annular fixed beds with air flowing through was experimentally investigated. Based on the experimental data and some analytical considerations, the demensionless correlation of pressure drop has been determined and shown in empirical forms. In particular, the experimental equation for the pressure drop was derived using the particle diameter and the bed diameter as variables, which would be more practical and useful in the design of heat transfer devices, instead of void fraction which had been used previously as the major variables by others. The present empirical equation obtained for the cylindrical fixed bed were found to be applicable also to an annular fixed bed when the concept of effective diameter was introduced.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2004년도 춘계학술대회
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• pp.1376-1381
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• 2004

Understanding the thermal conductivity and heat transfer processes in superlattice structures is critical for the development of thermoelectric materials and optoelectronic devices based on quantum structures. $Chen^{(1)}$ developed ballistic diffusive equation(BDE) for alternatives of the Boltzmann equation that can be applied to the complex geometrical situation. In this study, a simulation code based on BDE is developed and applied to the 1-dimensional transient heat conduction across a thin film and transient 2-dimensional heat conduction across the film with heater. The obtained results are compared to the results of the $Chen^{(1)}$ and Yang and $Chen^{(1)}$. Finally, steady 2-dimensional heat conduction in the quantum dot superlattice are solved to obtain the equivalent thermal conductivity of the lattice and also compared with the experimental data from $Borca-Tasciuc^{(2)}$.

• Structural Engineering and Mechanics
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• 제82권5호
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• pp.679-690
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• 2022

This research effort examines the flow behavior and heat transfer assessment of water carrying iron (iii) oxide magnetic fluid due to a rotating and moving plane lamina under the influence of magnetic dipole. The effect of rotational viscosity and magnetic body force is taken into consideration in the present study. The involvement of the moving disk makes a significant contribution to the velocity distribution and heat transfer in rotational flow. Vertical movement of the disk keeps the flow unsteady and the similarity transformation converts the governing equation of unsteady flow into nonlinear coupled differential equations. The non-dimensional equation in the present system is solved through the finite element procedure. Optimizing the use of physical parameters described in this flow, such results can be useful in the rotating machinery industries for heat transfer enhancement.

• 대한기계학회논문집
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• 제18권6호
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• pp.1551-1558
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• 1994

An experiment was conducted to investigate whether an equation of heat transfer coefficient derived form energy equation of two-phase plug flow can be actually applied to the industrial field. The heat is constantly transfered to the sand beds from the wall of heat exchanger while the sand moves down through cylindrical heat exchanger by gravity from feed hooper. To increase heat transfer, turbulators such as glass ball and steel pipe packings were used. In addition, the experiment in the case of fluidizing the sand beds was also carried out. The temperatures of the sand beds and the wall were measured along the heat exchanger axis. The density and porosity of the sand beds were also measured. The deviations of the mean velocity of sands from the velocity on the wall surface because of the slip conditions on the wall were negligible (within 3%). The heat transfer coefficients when the turbulators were used and when the sand beds were fluidized were found to be much greater than those of the plain plug flow.