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.

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.

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.

Evaluation of response characteristics of thin film gauge for conductive heat transfer mode

2020 ◽  
pp. 014233122096066
Author(s):  
Tanweer Alam ◽  
Rakesh Kumar
Keyword(s):  
Thin Film ◽  
Heat Transfer ◽  
Heat Flux ◽  
Short Duration ◽  
Temperature Data ◽  
Heat Transfer Analysis ◽  
Transient Temperature ◽  
Conductive Heat ◽  
Sensing Element ◽  
Element Analysis

Heat transfer analysis is the one of the most important designing aspects for many engineering systems. The design prospect in the preview of heat transfer focuses on the prediction of heat flux with the help of measured transient temperature data. Thin film gauges are one of the most predominant method for the heat flux prediction especially for short duration transient temperature measurement. Thin film gauges are usually exposed to the heated environment for the measurement purpose. However, there are some prominent research areas like ablation phenomenon met to spacecraft thermal shields during re-entry to the atmosphere, for which direct exposure of the thin film gauge to the heated environment causes the functional and working difficulties associated with the gauge. In the present study, it is aimed to investigate the suitability of thin film gauge for the conduction-based short duration measurement. An experimental set up is fabricated, which is used to supply the heat load to the hand-made thin film gauge using platinum as sensing element and quartz as a substrate. The transient temperature data is recorded during experiment is further compared with the simulated temperature histories obtained through finite element analysis. The heat flux estimation for both the analysis is made using measured transient temperature data by convolute integral of one- dimensional heat conduction equation. The estimated heat flux value for the experimental and numerical result is found to be in excellent agreement.

scholarly journals Analytic transient solutions of a cylindrical heat equation

Filomat ◽  
2021 ◽  
Vol 35 (8) ◽  
pp. 2617-2628
Author(s):  
K.Y. Kung ◽  
Man-Feng Gong ◽  
H.M. Srivastava ◽  
Shy-Der Lin
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Partial Differential Equation ◽  
Heat Conduction ◽  
Heat Equation ◽  
Heat Conduction Equation ◽  
Separation Of Variables ◽  
Transient Heat Conduction ◽  
Transient Temperature ◽  
Transient Solutions

The principles of superposition and separation of variables are used here in order to investigate the analytical solutions of a certain transient heat conduction equation. The structure of the transient temperature appropriations and the heat-transfer distributions are summed up for a straight mix of the results by means of the Fourier-Bessel arrangement of the exponential type for the investigated partial differential equation.

Mesoscopic Heat Conduction and Onset of Periodicity

2003 ◽  
Author(s):  
Kal Renganathan Sharma
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Time Domain ◽  
Heat Conduction Equation ◽  
Higher Order ◽  
Heat Propagation ◽  
Conduction Equation ◽  
Transient Temperature ◽  
Higher Order Terms ◽  
Fourier Heat Conduction

Mesoscopic approach deals with study that considers temporal fluctuations which is often averaged out in a macroscopic approach without going into the molecular or microscopic approach. Transient heat conduction cannot be fully described by Fourier representation. The non-Fourier effects or finite speed of heat propagation effect is accounted for by some investigators using the Cattaneo and Vernotte non-Fourier heat conduction equation: q=−k∂T/∂x−τr∂q/∂t(1) A generalized expression to account for the non-Fourier or thermal inertia effects suggested by Sharma (5) as: q=−k∂T/∂x−τr∂q/∂t−τr2/2!∂2q/∂t2−τr3/3!∂3q/∂t3−…(2) This was obtained by a Taylor series expansion in time domain. Manifestation of higher order terms in the modified Fourier’w law as periodicity in the time domain is considered in this study. When a CWT is maintained at one end of a medium of length L where L is the distance from the isothermal wall beyond which there is no appreciable temperature change from the initial condition during the duration of the study the transient temperature profile is obtained by the method of Laplace transforms. The space averaged heat flux is obtained and upon inversion from Laplace domain found to be a constant for the the case obeying Fourier’s law; 1 − exp(−τ) using the Cattaneo and Vernotte non-Fourier heat conduction equation, and upon introduction of the second derivative in time of the heat flux the expression becomes, 1 − exp(−τ)(Sin(τ) + Cos(τ)). Thus the periodicity in time domain is lost when the higher order terms in the generalized Fourier expression is neglected.

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.

The Inverse Problem in Transient Heat Conduction

1964 ◽  
Vol 31 (3) ◽  
pp. 369-375 ◽  
Author(s):  
E. M. Sparrow ◽  
A. Haji-Sheikh ◽  
T. S. Lundgren
Keyword(s):  
Heat Flux ◽  
Inverse Problem ◽  
Heat Conduction ◽  
Numerical Calculation ◽  
Initial Temperature ◽  
Transient Heat Conduction ◽  
Analytical Treatment ◽  
Initial Temperature Distribution ◽  
Plane Slab ◽  
Long Cylinder

A general theory is devised for determining the temperature and heat flux at the surface of a solid when the temperature at an interior location is a prescribed function of time. The theory is able to accommodate an initial temperature distribution which varies arbitrarily with position throughout the solid. Detailed analytical treatment is extended to the sphere, the plane slab, and the long cylinder; and it is additionally shown that the semi-infinite solid is a particular case of the general formulation. The accuracy of the method is demonstrated by a numerical example. In addition, a numerical calculation procedure is devised which appears to provide smooth, nonoscillatory results.

Heat Flux Estimation in a Nonlinear Inverse Heat Conduction Problem With Moving Boundary

2009 ◽  
Author(s):  
Hosein Molavi ◽  
Ali Hakkaki-Fard ◽  
Alireza Pourshaghaghy ◽  
Mehdi Molavi ◽  
Ramin K. Rahmani
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Measurement Errors ◽  
Moving Boundary ◽  
Heat Conduction Problem ◽  
Adjoint Problem ◽  
Inverse Heat Conduction Problem ◽  
Transient Temperature ◽  
Nonlinear Heat Conduction ◽  
Mechanical Removal

Estimation of heat flux in the nonlinear heat conduction problem becomes more challenging when the material at the boundary loses its mass due to phase change, chemical erosion, oxidation, or mechanical removal. In this paper, a new gradient-type method with adjoint problem is employed to predict the unknown time-varying heat flux at the receding surface in the nonlinear heat conduction problem. Particular features of this novel approach are discussed and examined. Results obtained by the new method for several test cases are benchmarked and analyzed using the numerical experiments with the simulated exact and noisy measurements. Exceedingly reliable estimation on the heat flux can be obtained from the knowledge of the transient temperature recordings, even in the case with measurement errors. In order to evaluate the performance characteristics of the present inverse scheme, simulations are conducted to analyze the effects of this technique with regard to conjugate gradient method with adjoint problem and variable metric method with adjoint problem. The obtained results show that the present inverse scheme distinguishably accelerates the convergence rate, which approve the well capability of the method for this type of heat conduction problems.

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