Novel Two-Dimensional Transient Heat Conduction Calculation in a Cooled Rotor: Ventilation Preheating—Blow-Down Flux

2009 ◽  
Vol 131 (8) ◽  
Author(s):  
J. P. Solano ◽  
G. Paniagua
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Data Reduction ◽  
Transient Heat Conduction ◽  
Element Model ◽  
Rotor Blades ◽  
Wall Heat Flux ◽  
Two Dimensional ◽  
Blow Down ◽  
Cross Sectional

This contribution presents an alternative to classical data reduction techniques to measure the heat transfer using thin-film gauges. A finite-element model of the two-dimensional unsteady heat conduction equation is solved in the cross-sectional area of a metallic airfoil bounded with a polyamide sheet on which thermal sensors are deposited. This novel methodology allows capturing all 2D heat conduction effects that are irremediably neglected with the 1D data reduction technique. The application of this technique in a compression tube facility allows an exact evaluation of the initial wall heat flux into cooled rotor blades. During the spinning-up period, the rotor is spun up to nearly its nominal speed (from 0 rpm to 6200 rpm) resulting in preheating due to drag losses. The long duration of this experiment (∼450 s) and the magnitude of the wall temperature increase result in significant 2D conduction effects that are not accounted for using the 1D approach. In addition, short-duration experiments confirm the existence of 2D effects at smaller time scales (∼0.5 s), as well as the influence of the initial nonuniform temperature distribution in the rotor blade. The resulting flux with such an initial condition appears to be the superposition of the wall heat flux at the end of the spinning up before the test and the flux due to the blow-down itself.

Novel 2D Transient Heat Conduction Calculation in a Cooled Rotor: Ventilation Preheating — Blowdown Flux

2008 ◽  
Author(s):  
J. P. Solano ◽  
G. Paniagua ◽  
A. de la Loma
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Short Duration ◽  
Data Reduction ◽  
Transient Heat Conduction ◽  
Element Model ◽  
Wall Heat Flux ◽  
Transient Temperature ◽  
Blow Down ◽  
Cross Sectional

An alternative to classical data reduction techniques for thin film gauges in short duration facilities is presented. A finite element model of the two-dimensional unsteady heat conduction equation is solved in the cross-sectional area of a metallic airfoil bounded with a polyamide sheet, on which thermal sensors are deposited. As a result, the transient temperature field in the multilayered substrate and the experimental wall heat flux distribution are derived. The methodology allows for capuring all 2D heat conduction effects that are irremediably neglected with the 1D data reduction technique. The application of this technique in a compression tube facility allows an exact evaluation of the initial wall heat flux into cooled rotor blades. During the spinning up period, the rotor of this type of fully rotating transient facilities is spun up to nearly its nominal speed (from 0 RPM to 6200 RPM) resulting in preheating due to drag losses. The long duration of this experiment (∼450 s) and the magnitude of the wall temperature increase result in significant 2D conduction effects that are not accounted for using the 1D approach. In addition, short duration experiments confirm the existence of 2D effects at smaller time scales (∼0.5 s), as well as the influence of the initial non-uniform temperature distribution in the rotor blade. The resulting flux with such an initial condition appears to be the superposition of the wall heat flux at the end of the spinning up before the test and the flux due to the blow-down itself.

Generalized Solution for Two-Dimensional Transient Heat Conduction Problems With Partial Heating Near a Corner

2019 ◽  
Vol 141 (7) ◽  
Author(s):  
Robert L. McMasters ◽  
Filippo de Monte ◽  
James V. Beck
Keyword(s):  
Boundary Condition ◽  
Heat Flux ◽  
Heat Conduction ◽  
Steady State ◽  
Separation Of Variables ◽  
Transient Heat Conduction ◽  
Generalized Solution ◽  
Convective Heating ◽  
Two Dimensional ◽  
Partial Heating

A generalized solution for a two-dimensional (2D) transient heat conduction problem with a partial-heating boundary condition in rectangular coordinates is developed. The solution accommodates three kinds of boundary conditions: prescribed temperature, prescribed heat flux and convective. Also, the possibility of combining prescribed heat flux and convective heating/cooling on the same boundary is addressed. The means of dealing with these conditions involves adjusting the convection coefficient. Large convective coefficients such as 1010 effectively produce a prescribed-temperature boundary condition and small ones such as 10−10 produce an insulated boundary condition. This paper also presents three different methods to develop the computationally difficult steady-state component of the solution, as separation of variables (SOV) can be less efficient at the heated surface and another method (non-SOV) is more efficient there. Then, the use of the complementary transient part of the solution at early times is presented as a unique way to compute the steady-state solution. The solution method builds upon previous work done in generating analytical solutions in 2D problems with partial heating. But the generalized solution proposed here contains the possibility of hundreds or even thousands of individual solutions. An indexed numbering system is used in order to highlight these individual solutions. Heating along a variable length on the nonhomogeneous boundary is featured as part of the geometry and examples of the solution output are included in the results.

Study on the Analytic Solution of Two-Dimensional Transient Heat Conduction

2016 ◽  
Author(s):  
Youzhen Yang ◽  
Hu Wang ◽  
Hailong Ma ◽  
Wenguo Ma ◽  
Shenhu Ding ◽  
...  
Keyword(s):  
Heat Conduction ◽  
Analytic Solution ◽  
Transient Heat Conduction ◽  
Two Dimensional

Enhanced Explicit Scheme to Solve Transient Heat Conduction Problem

2007 ◽  
Vol 2 (1) ◽  
Author(s):  
Ganesh Hegde ◽  
Madhu Gattumane
Keyword(s):  
Heat Conduction ◽  
Correction Factor ◽  
Truncation Error ◽  
Transient Heat Conduction ◽  
Explicit Scheme ◽  
Stability And Convergence ◽  
Two Dimensional ◽  
Time Step ◽  
One Dimensional ◽  
Partial Derivatives

Improvement in accuracy without sacrificing stability and convergence of the solution to unsteady diffusion heat transfer problems by computational method of enhanced explicit scheme (EES), has been achieved and demonstrated, through transient one dimensional and two dimensional heat conduction. The truncation error induced in the explicit scheme using finite difference technique is eliminated by optimization of partial derivatives in the Taylor series expansion, by application of interface theory developed by the authors. This theory, in its simple terms gives the optimum values to the decision vectors in a redundant linear equation. The time derivatives and the spatial partial derivatives in the transient heat conduction, take the values depending on the time step chosen and grid size assumed. The time correction factor and the space correction factor defined by step sizes govern the accuracy, stability and convergence of EES. The comparison of the results of EES with analytical results, show decreased error as compared to the result of explicit scheme. The paper has an objective of reducing error in the explicit scheme by elimination of truncation error introduced by neglecting the higher order terms in the expansion of the governing function. As the pilot examples of the exercise, the implementation is aimed at solving one-dimensional and two-dimensional problems of transient heat conduction and compared with the results cited in the referred literature.

Finite Element Formulation for Two-Dimensional Inverse Heat Conduction Analysis

1992 ◽  
Vol 114 (3) ◽  
pp. 553-557 ◽  
Author(s):  
T. R. Hsu ◽  
N. S. Sun ◽  
G. G. Chen ◽  
Z. L. Gong
Keyword(s):  
Heat Flux ◽  
Finite Element ◽  
Heat Conduction ◽  
Surface Heat Flux ◽  
Surface Heat ◽  
Element Formulation ◽  
Two Dimensional ◽  
Inverse Heat Conduction ◽  
Discrete Point ◽  
Element Algorithm

This paper presents a finite element algorithm for two-dimensional nonlinear inverse heat conduction analysis. The proposed method is capable of handling both unknown surface heat flux and unknown surface temperature of solids using temperature histories measured at a few discrete point. The proposed algorithms were used in the study of the thermofracture behavior of leaking pipelines with experimental verifications.

scholarly journals Optimization of Geometric Parameters of Thermal Insulation of Pre-Insulated Double Pipes

Energies ◽  
2019 ◽  
Vol 12 (6) ◽  
pp. 1012 ◽  
Author(s):  
Dorota Krawczyk ◽  
Tomasz Teleszewski
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Cross Section ◽  
Thermal Insulation ◽  
Major Axis ◽  
Heat Losses ◽  
Sectional Area ◽  
Cross Sectional ◽  
Elliptical Shape ◽  
Half Axis

This paper presents the analysis of the heat conduction of pre-insulated double ducts and the optimization of the shape of thermal insulation by applying an elliptical shape. The shape of the cross-section of the thermal insulation is significantly affected by the thermal efficiency of double pre-insulated networks. The thickness of the insulation from the external side of the supply and return pipes affects the heat losses of the double pre-insulated pipes, while the distance between the supply and return pipes influences the heat flux exchanged between these ducts. An assumed elliptical shape with a ratio of the major axis to the minor half axis of an ellipse equaling 1.93 was compared to thermal circular insulation with the same cross-sectional area. All calculations were made using the boundary element method (BEM) using a proprietary computer program written in Fortran as part of the VIPSKILLS project.

A Comparison Between Three- and Two-Dimensional Thermal Finite Element Analysis of the Gas Metal Arc Welding Process

2003 ◽  
Author(s):  
Mohammad S. Davoud ◽  
Xiaomin Deng
Keyword(s):  
Finite Element ◽  
3D Model ◽  
Gas Metal Arc Welding ◽  
Welding Process ◽  
Element Model ◽  
Transient Temperature ◽  
Two Dimensional ◽  
Element Analysis ◽  
Cross Sectional ◽  
2D Model

Predictions of transient temperature distributions in welding can help the selection of welding process parameters that minimize residual stresses. A three-dimensional (3D) thermal finite element model of bead-on-plate gas metal are welding (GMAW) is presented and is used to evaluate a cross-sectional, two-dimensional (2D) counterpart model. While the thermomechanical problem of welding is 3D in nature, it is shown that the 2D model can provide temperature field predictions comparable to those of the 3D model, even though the 2D model tends to predict peak temperatures higher than those of the 3D model. Both types of model predictions are compared to welding test measurements.

Two-dimensional hybrid analytical approach for the investigation of thermal aspects in human tissue undergoing regional hyperthermia therapy

2020 ◽  
Vol 234 (20) ◽  
pp. 3951-3966
Author(s):  
Jaideep Dutta ◽  
Balaram Kundu
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Cancer Treatment ◽  
Thermal Response ◽  
Skin Tissue ◽  
Hyperbolic Heat Conduction ◽  
Two Dimensional ◽  
Regional Hyperthermia ◽  
Hyperthermia Therapy ◽  
The Impact

The formation of the present work is based on the development of the exact analytical solution of two-dimensional temperature response by employing the hyperbolic heat conduction bioheat model in a single-layered human skin tissue subjected to the regional hyperthermia therapy (RHT) for cancer treatment. The mathematical approach has been utilized as a hybrid form of ‘separation of variables’ and ‘finite integral transform’ method. Three kinds of surface heat fluxes (constant, sinusoidal and cosine) have been employed as an external heat source on the therapeutic surface of the square-shaped skin tissue of 100 mm × 100 mm. An innovative form of initial condition (spatially dependent) has been implemented in the present mathematical formulation as skin tissues are highly non-homogeneous and non-uniform in structure. The present research outcome indicates that cosine heat flux would be a suitable alternative for the sinusoidal heat flux. The impact of the relaxation time lag has been clearly noted in the thermal response with the waveform-like behaviour and it justifies the postulate of hyperbolic heat conduction. The two-dimensional temperature of the skin tissue has been observed in the range of 48.1 ℃–40 ℃ (in decreasing order). Estimated peak temperatures are in the proposed spectrum of hyperthermia therapy for an exposure time of 100 s, and this fact is true in an agreement with the medical protocol of the cancer treatment. The accuracy of the mathematical modelling and in-house computer codes are justified with the published numerical models and the maximum deviation of the thermal response has been noticed in order of 1.5–3%. The two-dimensional surface thermal contours have provided a glimpse of heat flow in the physical domain of skin tissue under different heating conditions and this research output may be beneficial to establish the theoretical standard of the regional hyperthermia treatment for cancer eradication.

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