• Bulletin of the Korean Mathematical Society
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• v.37 no.4
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• pp.697-710
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• 2000

We investigate the existence of solutions of the nonlinear heat equation under Dirichlet boundary conditions on $\Omega$ and periodic condition on the variable t, $Lu-D_tu$+g(u)=f(x, t). We also investigate a relation between multiplicity of solutions and the source terms of the equation.

• Journal of the Korean Mathematical Society
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• v.26 no.2
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• pp.189-194
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• 1989

• Water Engineering Research
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• v.2 no.3
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• pp.187-196
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• 2001

An approximate analytical solution of a nonlinear hydro-thermo coupled diffusion equation is derived using the dimensionless form of the equation and transformation method. To derive an analytical solution, it is drastically assumed that the product of first order derivatives in the non-dimensionalized governing equation has little influence on the solution of heat and moisture behavior problem. The validity of this drastic assumption is demonstrated. Some numerical simulation is performed to investigate the applicability of a derived approximate analytical solution. The results show a good agreement between analytical and numerical solutions. The proposed solution may provide a useful tool in the verification process of the numerical models. Also, the solution can be used for the analysis of one-dimensional coupled heat and moisture movements in unsaturated porous media.

• Journal of Advanced Marine Engineering and Technology
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• v.28 no.7
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• pp.1063-1071
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• 2004

Accurate heat release analysis of cylinder pressure data is important for evaluating performance in the development of diesel engine However, traditional single zone first law heat release model(SZM) has significant limitations due to the simplified assumption of uniform charge and neglecting local temperature inside cylinder during combustion process. In this study. heat release rate based on single zone heat release model has been evaluated by comparison with computational analysis results using Fire code which is based on multi-dimensional model(MDM). To overcome limitations due to simplicity of single zone assumption. especially the influence of specific heat ratio on gross heat release has been esteemed and newly suggested were the equation $\gamma$= $\gamma$(${T/T}_{max}$) which describes the variations of gases thermodynamic properties with mean temperature and maximum mean temperature inside cylinder Single zone heat release model applied with this equation is shown to give very good results over whole range of operating conditions when compared with computational analysis results based on multi-dimensional model.

• Journal of Environmental Science International
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• v.3 no.2
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• pp.89-100
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• 1994

It is very important to assess accurately the terms which are included in the heat budget equation of soil surface because they are used in the UM and miso-scale circulation modeling as well as in the micrometeorological studies. Each terms in the heat budget equation change according to the soil moisture content. So, it is necessary to specify clearly the relations between soil moisture content and these terms. Special experiment with micrometeorological measurements was executed to study these relations at Environmental Research Center of Tsukuba University, Japan. The results are as follow: 1. The soil moisture contents of 1 cm and 4 cm depth are oscillated with one day Period in drying process and the amplitude of variation of 1 cm depth is greater than that of 4 cm. 2. Increase in soil moisture contents due to precipitation result in decrease of albedo with step function. 3. Sensible heat is in reverse proportion to the soil moisture content and latent heat is in direct proportion to it. Latent heat is more sensitive than sensible heat according to the soil moisture variation. Net long wave radiation have high correlation with soil moisture. 4. Comparing with the radiative term with the flux term in wetting process due to precipitation, the energy transfer of the aero and thermodynamic flux is greater than that of the radiative heat flux.

• International Journal of Automotive Technology
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• v.4 no.3
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• pp.125-133
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• 2003

Several models for the evaluation of Gross Heat Release from the internel combustion engine (ICE) are often used in literature. One of these is the First Law - Single Zone Model (FL-SZM), derived from the First Law of Thermodynamic. This model present a twice advantage: first it describes with accuracy the physic of the phenomenon (charge heat release during the combustion stroke and heat exchange between gas and cylinder wall); second it hat a great simplicity in the mathematical formulation. The evaluation of Heat Release with the FL-SZM is based on pressure experimental measurements inside the cylinder, and ell the assumption of several parameters as the specific heat ratio, wall temperature, polytropic exponent for the motored cycle evaluation, and many others. In this paper the influence of gases thermodynamic properties on Cross Heat Release has been esteemed. In particular the influence of an appropriate equation for k=k(T) (specific heat ratio vs. temperature) which describes the variations of gases thermodynamic properties with the mean temperature inside the cylinder has been evaluated. This equation has been calculated by new V order Logarithmic Polynomials (VoLP), fitting experimental gases properties through the least square methods.

• Transactions of the Korean Society of Mechanical Engineers
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• v.14 no.2
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• pp.276-287
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• 1990

In this paper research result of transient thermal stress analysis of power plant turbine rotors for life prediction under severs operating conditions is presented. Galerkin's recurrence scheme is used for numerical solution of discretized FEM equation of transient heat conduction equation. Boundary conditions for the equation and operating conditions are intensively investigated for accurate life prediction of turbine rotors in operation. A computer program for on-site application is developed and tested. Distribution of thermal stress in turbine rotors during various operating condition is analyzed with the program and it is found that the peak thermal stress appears during cold stage conditions at the first stage of high pressure rotors.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.24 no.1
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• pp.93-102
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• 2020

The concept of temperature distribution in inhomogeneous semi-infinite solids is examined by making use of direct integration method. The analysis is done on the solution of the in-plane steady state heat conduction problem under certain boundary conditions. The method of direct integration has been employed, which is then reduced to Volterra integral equation of second kind, produces the explicit form analytical solution. Using resolvent- kernel algorithm, the governing equation is solved to get present solution. The temperature distribution obtained and calculated numerically and the relation with distribution of heat flux generated by internal heat source is shown graphically.

• Proceedings of the KSME Conference
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• 2003.11a
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• pp.103-108
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• 2003

In this paper, the current lead for superconducting device is studied by numerical method. The current lead is cooled by surrounded $N_{2}$ gas by natural convection. The heat conduction equation for current lead and boundary layer equation for $N_{2}$ gas must be solved simultaneously. The boundary layer equation for $N_{2}$ gas is highly nonlinear for varied temperature of current lead. So the linearization method is adopted for simplicity. Numerical results using natural convection cooling are compared with the conventional cooling methods such as conduction cooling and vapor cooling methods. The main difference of natural convection cooing is the non-zero temperature gradient at the top of current lead for the minimum heat dissipation into superconducting devices. For the optimized conduction-cooling and vapor-cooling current leads, the temperature gradient at the top of current lead is zero. Also, the heat flow at the cold end is much smaller than conduction cooling case.

• Bulletin of the Society of Naval Architects of Korea
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• v.19 no.4
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• pp.19-29
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• 1982

Galerkin's finite element method is applied to a two-dimensional heat convection-diffusion problem arising in the hydrodynamic lubrication of thrust bearings used in naval vessels. A parabolized thermal energy equation for the lubricant, and thermal diffusion equations for both bearing pad and the collar are treated together, with proper juncture conditions on the interface boundaries. it has been known that a numerical instability arises when the classical Galerkin's method, which is equivalent to a centered difference approximation, is applied to a parabolic-type partial differential equation. Probably the simplest remedy for this instability is to use a one-sided finite difference formula for the first derivative term in the finite difference method. However, in the present coupled heat convection-diffusion problem in which the governing equation is parabolized in a subdomain(Lubricant), uniformly stable numerical solutions for a wide range of the Peclet number are obtained in the numerical test based on Galerkin's classical finite element method. In the present numerical convergence errors in several error norms are presented in the first model problem. Additional numerical results for a more realistic bearing lubrication problem are presented for a second numerical model.