• Transactions of the Korean Society of Mechanical Engineers
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• v.14 no.6
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• pp.1621-1628
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• 1990

Numerical solutions are presented for the heat transfer from radiating and convecting fins. Consideration is given to thin, annular fins attached to a tube surface for which the temperature is constant. Fin to fin, fin to base, and fin to environment radiative interactions are considered. It is assumed that the radiating surface is diffuse-gray, the environment is black, and the surrounding fluid is transparent. The radiation terms are formulated by using Poljak's net-radiation methoad. The mathematical description of the simultaneously heat transport by conduction, convection, and radiation leads to a nonlinear integro-differential equation. This has been solved for a wide range of the pertinent physical parameters by using finite difference method and iteration method based on the Newton-Raphson technique. The temperature distributions, heat transfer rates, fin efficiencies, and fin effectivenesses are presented in dimensionless form. The results definitely indicate that the use of fins leads to a significant increase in heat transfer compared with the unfinned tube.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.7
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• pp.1675-1683
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• 1995

A numerical study of the fluid flow and heat transfer characteristics of the two-dimensional impingement jet with a confinement plate has been carried out. The fluid flow was calculated by solving the full Navier-Stokes equation. In doing that, the well known SIMPLER algorithm was used and the trouble making convection term was discretized according to QUICKER scheme. The energy equation was simply solved by using the SOR method. For the Reynolds number of 10000, two channel heights, say 1.5 and 3.0 times the jet exit width, and two thermal boundary conditions constant wall temperature and constant wall heat flux were considered. Discrete heat sources were flush mounted along the impingement plate at a distance of 0, 2, 3, 4, 5, 6, 10, 12, times the jet exit width from the stagnation point. The length of each heat source is 4 times the jet exit width long. The Nusselt number averaged over each heat source was compared with experiment. Comparison shows that both calculations and experiment have the secondary peak of Nusselt number at downstream of stagnation point, even though there is a little quantitative difference in between. The difference is believed due to abscure thermal boundary condition in experiment and also accuracy of turbulence model used. The secondary peak is shown to be caused by rigorous turbulent flow motion generated as the wall jet flow is retarded and developes into the channel flow without flow reversal.

• Fire Science and Engineering
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• v.28 no.1
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• pp.52-57
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• 2014

In this paper, the unsteady incompressible Navier-Stokes equations coupled with energy equation were solved to find out the optimal location of electrical heat trace for anti-freeze of water inside the pipe for fire protection. Since the conduction equation of pipe was coupled with the natural convection of water, the analysis of conjugate heat transfer was conducted. A commercial code (ANSYS-FLUENT) based on SIMPLE-type algorithm was used for investigating the unsteady flows and temperature distributions in water region. From the numerical experiments, the isotherms and the vector fields in water region were obtained. Furthermore, it was found that the lowest part of the pipe cross-section was an optimal position of electrical heat trace assuming the constant thermal expansion coefficient of water since the minimum temperature of the water with the position is higher than those with the other positions.

• Journal of the Korean Institute of Telematics and Electronics
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• v.21 no.5
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• pp.90-99
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• 1984

A onetimensional distribution of the temperature and the heat source in the SOI (silicon-on-insulator) multi-layer structure illuminated by tungsten lamps from both sides was obtained by solving the heat equation in steady state on a finite difference grid using successive over-relaxation method. The heat source distribution was obtained by considering such features as spectral components of the light source, multiple reflection at the internal interfaces, temperature and frequency dependence of the light absorption coefficient, etc. The front and back surface temperatures, which are boundary conditions for the heat equation, were derived from a requirement that they satisfy the radiation conditions. The radiation flux as well as the conduction flux was considered in modelling the thermal behaviour at the internal interfaces. Since the temperature and the heat source profiles are strongly dependent upon each other, the calculation of each profile was iterated using the updated profile of the other until they are consistent with each other. The experimental temperature at the front surface of the wafer as measured by Pyrometer was about 1200$^{\circ}$K, while the simulated temperature was 1120$^{\circ}$K.

• Bulletin of the Korean Mathematical Society
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• v.49 no.5
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• pp.939-947
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• 2012

In this paper, we give a generalization of the embeddings of Riemannian manifolds via their heat kernel and via a finite number of eigenfunctions. More precisely, we embed a family of Riemannian manifolds endowed with a time-dependent metric analytic in time into a Hilbert space via a finite number of eigenfunctions of the corresponding Laplacian. If furthermore the volume form on the manifold is constant with time, then we can construct an embedding with a complete eigenfunctions basis.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.651-661
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• 2010

We consider the inverse problem of the identification of a piecewise-constant conductivity in a bar given the extra information of the heat flux through one end of the bar. Our theoretical results show that such an identification is unique. This approach utilizes a "layer peeling" argument. A computational algorithm based on this method is proposed and implemented. The advantage of this algorithm is that it requires only 3D minimizations irrespective of the number of the unknown discontinuities. Its numerical effectiveness is investigated for several conductivities.

• The Pure and Applied Mathematics
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• v.13 no.1 s.31
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• pp.1-10
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• 2006

The unsteady Hartmann flow of an electrically conducting, viscous, incompressible fluid bounded by two parallel non-conducting porous plates is studied with heat transfer. An external uniform magnetic field and a uniform suction and injection are applied perpendicular to the plates while the fluid motion is subjected to a constant pressure gradient. The two plates are kept at different but constant temperatures while the Joule and viscous dissipations are included in the energy equation. The effect of the magnetic field and the uniform suction and injection on both the velocity and temperature distributions is examined.

• Journal of computational fluids engineering
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• v.16 no.2
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• pp.11-16
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• 2011

Numerical analyses have been carried out to analyze the three-dimensional turbulent heat transfer by impingement jet on a concave surface with variation of geometric configurations. Three-dimensional Reynolds averaged Navier-stokes equations have been calculated using the shear stress transport turbulent model. The numerical results for heat transfer rate were validated in comparison with the experimental data. The distance between jet nozzles and angle of inclined jet nozzle were selected as the geometric variables. Area-averaged Nusselt numbers on concave surface are evaluated to find the characteristics of heat transfer with the two geometric variables. The heat transfer increases as the distance between jet nozzles increases, and the inclined impinging jets show much better heat transfer performance than the vertical impinging jet.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.12 no.9
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• pp.835-842
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• 2000

Film boiling heat transfer of the subcooled turbulent liquid film flow on a horizontal plate was investigated by theoretical and experimental studies. In the theoretical analysis, by solving the integral energy and momentum equations analytically, some generalized expressions for Nusselt number was deduced. Next, by comparing the deduced equations with the experimental data on the turbulent film boiling heat transfer of the subcooled thin liquid film flow, the semi-empirical relation between the Nusselt number based on the modified heat transfer coefficient and the Reynolds number was obtained. The correlating equation was very similar to that of the turbulent heat transfer in a single phase flow, and it was found that the heat transfer was dissipated to increase the liquid temperature.

• Progress in Superconductivity and Cryogenics
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• v.22 no.3
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• pp.25-30
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• 2020

The diminishing of heat leak into cryogenic vessels can prolong the storage time of cryogenic liquid. With the storage of cryogenic liquid reducing, the heat leak decreases, while the actual storage time increases. Regarding to the theoretical analysis, the obtained results seems to be constructive for the cryogenic insulation system applications. This study presents a predictive assessment of heat leak occurring in non-vacuum tanks with a single layer of insulation. A Radial steady-state heat transfer, based on heat conduction equation, is taken into consideration. Graphical results show the thermal performance of the insulation used, they also allow us to choose the appropriate insulation thickness according to the shape and diameter of the storage tank.