• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.22 no.12
• /
• pp.1715-1725
• /
• 1998

A two-dimensional transient inverse heat conduction problem involving the estimation of the unknown location, ($X^*$, $Y^*$), and timewise varying unknown strength, $G({\tau})$, of a line heat source embedded inside a rectangular bar with insulated boundaries has been solved simultaneously. The regular conjugate gradient method, RCGM and the modified conjugate gradient method, MCGM with adjoint equation, are used alternately to estimate the unknown strength $G({\tau})$ of the source term, while the parameter estimation approach is used to estimate the unknown location ($X^*$, $Y^*$) of the line heat source. The alternate use of the regular and the modified conjugate gradient methods alleviates the convergence difficulties encountered at the initial and final times (i.e ${\tau}=0$ and ${\tau}={\tau}_f$), hence stabilizes the computation and fastens the convergence of the solution. In order to examine the effectiveness of this approach under severe test conditions, the unknown strength $G({\tau})$ is chosen in the form of rectangular, triangular and sinusoidal functions.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
• /
• v.18 no.8
• /
• pp.672-677
• /
• 2006

The steady cooling characteristics of a cryochamber for infrared (IR) detector have been investigated analytically, considering radiation shields. The thermal modeling considers the conduction heat transfer through cold finger, the gaseous conduction due to out-gassing, and the radiation heat transfer. The cooling load of the cryochamber is obtained by using a fin equation. The results obtained indicate that the gaseous conduction plays an important role in determining the steady cooling load. The steady cooling load is increased as the gas pressure is increased. It is also found that the cooling load is substantially decreased with a radiation shield. The most thermal load of a cryochamber occurs through the cold finger.

• Tribology and Lubricants
• /
• v.32 no.1
• /
• pp.1-8
• /
• 2016

This paper focuses on the thermal deformation induced preload change in the tilting pad journal bearing, using a three-dimensional (3D) thermo-hydro-dynamic (THD) approach. Preload is considered as a critical factor in designing the tilting pad journal bearing. The initial preload measured under nil external load and nil thermal gradient is influenced by two factors, namely, the thermal deformation and elastic deformation. Thermal deformation is due to a temperature distribution in the bearing pads, whereas the elastic deformation is due to fluid forces acting on the pads. This study focuses on the changes induced in preload and film clearance due to thermal deformation. The generalized Reynolds equation is used to evaluate the force of the fluid and the 3D energy equation is used to calculate the temperature of the lubricant. The abovementioned equations are combined by establishing a relationship between viscosity and temperature. The heat transfer within the bearing pads, the lubricant, and the spinning journal is calculated using the heat flux boundary condition. The 3D Finite Element Method (FEM) is used in modeling the (1) heat conduction in the spinning journal and bearing pads, (2) thermal gradient induced thermal distortion of the spinning journal and pads, and (3) viscous shearing, and heat conduction and convection in a thin film. This evaluation method has an increased fidelity, and it can prove to be a cost-effective tool that can be used by designers to predict the dynamic behavior of a bearing.

• Tribology and Lubricants
• /
• v.33 no.3
• /
• pp.112-118
• /
• 2017

Tilting pad journal bearings(TPJBs) are widely used for high speed rotating machinery owing to their rotordynamic stability and thermal management feature. With increase in the rotating speed of such machinery, an increasingly important aspect of TPJB design is the prediction of their thermal behaviors. Researchers have conducted detailed investigations in the last two decades, which provided design tools for the TPJBs. Based on these previous studies, this paper presents a thermohydrodynamic(THD) analysis model for TPJBs. To calculate pressure distribution, we solve the generalized Reynolds equation and to predict the lubricant temperature, we solve the 3D energy equation. We employ the oil mixing theory to calculate pad inlet temperature; further, to consider heat conduction via the pad, we solve the heat conduction equation for the pads. We assume the shaft temperature as the averaged oil film temperature and apply natural convection boundary conditions to the pad side and back surfaces. To validate the analysis model, we compare the predicted pad temperatures with those from previous research. The results show good agreement with previous research. In addition, we conduct parametric studies on a TPJB which was used in a gas turbine simulator system. The predicted results show that film temperature largely depends on the rotating speed and oil supply condition.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.13 no.1
• /
• pp.37-49
• /
• 2000

This paper is for the first essential study on the development of unified finite element formulations for solving problems related to the dynamics/thermoelastics behavior of solids. In the first part of formulations, the finite element method is based on the introduction of a new quantity defined as heat displacement, which allows the heat conduction equations to be written in a form equivalent to the equation of motion, and the equations of coupled thermoelasticity to be written in a unified form. The equations obtained are used to express a variational formulation which, together with the concept of generalized coordinates, yields a set of differential equations with the time as an independent variable. Using the Laplace transform, the resulting finite element equations are described in the transform domain. In the second, the Laplace transform is applied to both the equation of heat conduction derived in the first part and the equations of motions and their corresponding boundary conditions, which is referred to the transformed equation. Selections of interpolation functions dependent on only the space variable and an application of the weighted residual method to the coupled equation result in the necessary finite element matrices in the transformed domain. Finally, to prove the validity of two approaches, a comparison with one finite element equation and the other is made term by term.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.30 no.10 s.253
• /
• pp.950-956
• /
• 2006

A mathematical heat transfer model for the prediction of heat flux on the slab surface and temperature distribution in the slab has been developed by considering the thermal radiation in the furnace and transient conduction governing equations in the slab, respectively. The furnace is modeled as radiating medium with spatially varying temperature and constant absorption coefficient. The slab is moved with constant speed through non-firing, charging, preheating, heating, and soaking zones in the furnace. Radiative heat flux which is calculated from the radiative heat exchange within the furnace modeled using the FVM by considering the effect of furnace wall, slab, and combustion gases is applied as the boundary condition of the transient conduction equation of the slab. Heat transfer characteristics and temperature behavior of the slab is investigated by changing such parameters as absorption coefficient and emissivity of the slab. Comparison with the experimental work shows that the present heat transfer model works well for the prediction of thermal behavior of the slab in the reheating furnace.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.14 no.2
• /
• pp.276-287
• /
• 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
• /
• v.24 no.1
• /
• pp.93-102
• /
• 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.

• Journal of Power System Engineering
• /
• v.2 no.3
• /
• pp.27-33
• /
• 1998

The room temperature and air conditioning load in the underground space have been investigated numerically by the unsteady heat conduction equation. The model room has 3 m in height and 10 m in width, and it's position in the underground depth are 0.5 m to 5 m. When the room was located around surface, the room temperatures were strongly influenced by the atmosphere. But the underground depth is more than 2 m, the yearly temperature amplitude was small and the temperature phase was delayed. Up to 5 m of the depth, the cooling and heating load was decreased rapidly, but over 10 m of the depth, the air conditioning load was constant.

• Journal of applied mathematics & informatics
• /
• v.35 no.5_6
• /
• pp.439-447
• /
• 2017

This paper investigates the inverse problem of determining an unknown heat radiative coefficient, which is only time-dependent. This is an ill-posed problem, that is, small errors in data may cause huge deviations in determining solution. In this paper, the existence and uniqueness of the problem is established by the second Volterra integral equation theory, and the method of trace-type functional formulation combined with finite difference scheme is studied. One typical numerical example using the proposed method is illustrated and discussed.