Effect of Temperature Dependent Properties on the Applicability of the Heat Conduction Equations for Rapid Heat Deposition Applications

2016 ◽  
Author(s):  
John G. Michopoulos ◽  
Andrew Birnbaum ◽  
Athanasios P. Iliopoulos
Keyword(s):  
Differential Equation ◽  
Thermal Properties ◽  
Heat Conduction ◽  
Effect Of Temperature ◽  
Temperature Dependent ◽  
Proper Form ◽  
Heat Deposition ◽  
Hyperbolic Form ◽  
Parabolic Form ◽  
Temperature Dependent Properties

Despite significant efforts examining the suitability of the proper form of the heat transfer partial differential equation (PDE) as a function of the time scale of interest (e.g. seconds, picoseconds, femtoseconds, etc.), very little work has been done to investigate the millisecond-microsecond regime. This paper examines the differences between the parabolic and one of the hyber-bolic forms of the heat conduction PDE that govern the thermal energy conservation on these intermediate timescales. Emphasis is given to the types of problems where relatively fast heat flux deposition is realized. Specifically, the classical parabolic form is contrasted against the lesser known Cattaneo-Vernotte hyperbolic form. A comparative study of the behavior of these forms over various pulsed conditions are applied at the center of a rectangular plate. Further emphasis is given to the variability of the solutions subject to constant or temperature-dependent thermal properties. Additionally, two materials, Al-6061 and refractory Nb1Zr, with widely varying thermal properties, were investigated.

Sensitivity Analysis for Nonlinear Heat Conduction

2000 ◽  
Vol 123 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Kevin J. Dowding ◽  
Bennie F. Blackwell
Keyword(s):  
Heat Conduction ◽  
General Procedure ◽  
Model Parameters ◽  
Nonlinear Heat Conduction ◽  
Temperature Dependent ◽  
Sensitivity Equations ◽  
Verification Problem ◽  
Temperature Variable ◽  
Numerical Solver ◽  
Temperature Dependent Properties

Parameters in the heat conduction equation are frequently modeled as temperature dependent. Thermal conductivity, volumetric heat capacity, convection coefficients, emissivity, and volumetric source terms are parameters that may depend on temperature. Many applications, such as parameter estimation, optimal experimental design, optimization, and uncertainty analysis, require sensitivity to the parameters describing temperature-dependent properties. A general procedure to compute the sensitivity of the temperature field to model parameters for nonlinear heat conduction is studied. Parameters are modeled as arbitrary functions of temperature. Sensitivity equations are implemented in an unstructured grid, element-based numerical solver. The objectives of this study are to describe the methodology to derive sensitivity equations for the temperature-dependent parameters and present demonstration calculations. In addition to a verification problem, the design of an experiment to estimate temperature variable thermal properties is discussed.

Multiquadric Collocation Method for Time-Dependent Heat Conduction Problems With Temperature-Dependent Thermal Properties

2006 ◽  
Vol 129 (2) ◽  
pp. 109-113 ◽  
Author(s):  
Somchart Chantasiriwan
Keyword(s):  
Thermal Properties ◽  
Heat Conduction ◽  
Collocation Method ◽  
Heat Conduction Problem ◽  
Piecewise Linear ◽  
Linear Functions ◽  
Time Dependent ◽  
Piecewise Linear Functions ◽  
Temperature Dependent ◽  
Kirchhoff Transformation

Abstract The multiquadric collocation method is a meshless method that uses multiquadrics as its basis function. Problems of nonlinear time-dependent heat conduction in materials having temperature-dependent thermal properties are solved by using this method and the Kirchhoff transformation. Variable transformation is simplified by assuming that thermal properties are piecewise linear functions of temperature. The resulting nonlinear equation is solved by an iterative scheme. The multiquadric collocation method is tested by a heat conduction problem for which the exact solution is known. Results indicate satisfactory performance of the method.

Effect of Temperature-Dependent Properties on Cyclic Plasticity of Bond Coat in Thermal Barrier Systems

2013 ◽  
Vol 535-536 ◽  
pp. 193-196
Author(s):  
Luo Chuan Su ◽  
Jian Guo Li ◽  
Wei Xu Zhang ◽  
Tie Jun Wang
Keyword(s):  
Bond Coat ◽  
Thermally Grown Oxide ◽  
Cyclic Plasticity ◽  
Effect Of Temperature ◽  
Thermal Barrier ◽  
Temperature Dependent ◽  
Barrier Coating ◽  
Thermal Growth ◽  
Key Factor ◽  
Temperature Dependent Properties

The accumulation of cyclic plasticity in bond coat (BC) is a key factor controlling the displacement instability of the thermally grown oxide (TGO) in thermal barrier systems. The cyclic plasticity is affected by the component material properties, which vary observably with the service temperature. A numerical model with the behavior of creep and thermal growth in TGO under thermal cycling is used to explore the effect of temperature-dependent properties on cyclic plasticity in BC. The influence of temperature-dependent Young's modulus of thermal barrier coating (TBC), TGO, BC and substrate, thermal expansion coefficient of TBC, BC and substrate, and the yield strength of BC on cyclic plasticity in BC is discussed respectively.

Behavior of a Compressible Magnetorheological Fluid Damper at High Temperatures

2011 ◽  
Author(s):  
Micheal McKee ◽  
Xiaojie Wang ◽  
Faramarz Gordaninejad
Keyword(s):  
Theoretical Model ◽  
Bulk Modulus ◽  
Yield Stress ◽  
Magnetorheological Fluid ◽  
Effect Of Temperature ◽  
Temperature Dependent ◽  
Bingham Plastic ◽  
Shear Yield ◽  
Fluid Dampers ◽  
Temperature Dependent Properties

This study focuses on the effect of temperature on the performance of compressible magnetorheological fluid dampers (CMRDs). In addition to change of properties in the presence of a magnetic field, magnetorheological fluids (MRFs) are temperature-dependent materials that their compressibility and rheological properties change with temperature, as well. A theoretical model that incorporates the temperature-dependent properties of MRF is developed to predict the behavior of a CMRD. An experimental study is also conducted using an annular flow CMRD with varying temperatures, motion frequencies, and magnetic fields. The experimental results are used to verify the theoretical model. The effect of temperature on the MRF properties, such as, the bulk modulus, yield stress and viscosity, are explored. It is found that the shear yield stress of the MRF remains unchanged within the testing range while both the plastic viscosity, using the Bingham plastic model, and the bulk modulus of the MRF decrease as temperature increases. In addition, it is observed that both the stiffness and the energy dissipation decrease with an increase in temperature.

Numerical Solution of Heat Conduction in a Heterogeneous Multiscale Material With Temperature-Dependent Properties

2016 ◽  
Vol 138 (6) ◽  
Author(s):  
James White
Keyword(s):  
Heat Conduction ◽  
Numerical Solution ◽  
Time Scales ◽  
Thermal Energy ◽  
Energy Equation ◽  
Three Dimensional ◽  
Homogeneous Material ◽  
Time Level ◽  
Temperature Dependent ◽  
Temperature Dependent Properties

Numerical solution of heat conduction in a heterogeneous material with small spatial and time scales can lead to excessive compute times due to the dense computational grids required. This problem is avoided by averaging the energy equation over the small-scales, which removes the appearance of the short spatial and time scales while retaining their effect on the average temperature. Averaging does, however, increase the complexity of the resulting thermal energy equation by introducing mixed spatial derivatives and six different averaged conductivity terms for three-dimensional analysis. There is a need for a numerical method that efficiently and accurately handles these complexities as well as the other details of the averaged thermal energy equation. That is the topic of this paper as it describes a numerical solution for the averaged thermal energy equation based on Fourier conduction reported recently in the literature. The solution, based on finite difference techniques that are second-order time-accurate and noniterative, is appropriate for three-dimensional time-dependent and steady-state analysis. Speed of solution is obtained by spatially factoring the scheme into an alternating direction sequence at each time level. Numerical stability is enhanced by implicit algorithms that make use of the properties of tightly banded matrices. While accurately accounting for the nonlinearity introduced into the energy equation by temperature-dependent properties, the numerical solution algorithm requires only the consideration of linear systems of algebraic equations in advancing the solution from one time level to the next. Computed examples are included and compared with those for a homogeneous material.

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