Robert McMasters | Virginia Military Institute (original) (raw)

Papers by Robert McMasters

Journal of Thermophysics and Heat Transfer, 2016

45th AIAA Thermophysics Conference, 2015

ABSTRACT The time duration for processes involving transient thermal diffusion can be a critical ... more ABSTRACT The time duration for processes involving transient thermal diffusion can be a critical piece of information related to thermal processes in engineering applications. Analytical solutions must be used to calculate these types of time durations since the boundary conditions in such cases can be effectively like semi-infinite conditions. This research involves an investigation into analytical solutions for five geometries including one-dimensional cases for Cartesian, cylindrical and spherical coordinates. The fourth case involves two-dimensional conduction from a point heat source on the surface of a slab subjected to insulated boundary conditions elsewhere. The mathematical modeling for this case is done in cylindrical coordinates. The fifth case involves a heated surface on the inside of a hole bored through an infinite body, which is a one-dimensional problem in radial coordinates. A sixth case is also mentioned, which is the only two-dimensional configuration discussed, having to do with point heating on a flat plate. For each geometric configuration, a relationship is developed to determine the time required for a temperature rise to occur at a non-heated point in the body in response to a sudden change at a heated boundary. A range of time values is computed for each configuration based on the amount of temperature rise used as a criterion. Plots are given for each case showing the relationships between the temperature rise of interest and the amount of time required to reach that temperature.

11th AIAA/ASME Joint Thermophysics and Heat Transfer Conference, 2014

Volume 2: Heat Transfer Enhancement for Practical Applications; Fire and Combustion; Multi-Phase Systems; Heat Transfer in Electronic Equipment; Low Temperature Heat Transfer; Computational Heat Transfer, 2012

ABSTRACT A well-established method for determining the thermal diffusivity of materials is the la... more ABSTRACT A well-established method for determining the thermal diffusivity of materials is the laser flash method. The work presented here compares two analysis methods for flash heating tests on anisotropic carbon bonded carbon fiber (CBCF). This material exhibits a higher conductivity in the direction in which the fibers are oriented than in the direction perpendicular to the fiber orientation.The two analysis methods being compared in this experiment use different portions of the data in obtaining results. One method utilizes the temperature data from the entire surface of the sample by examining 201 temperature histories simultaneously, with each temperature history originating from an individual pixel within a line across the middle of the sample. The other analysis method utilizes only the temperature history from a single pixel in the center of the sample, similar to the data which is traditionally generated using the classical flash diffusivity method. Both analysis methods include accommodations for modeling the penetration of the laser flash into the porous surface of the CBCF material. Additionally, both models include a parameter which accounts for the non-uniform heating of the sample surface from the flash. Although the sample surface is ostensibly heated uniformly in flash diffusivity experiments, the heating has been found to be somewhat non-uniform, with more energy deposited more heavily in the center of the sample. This affects the analysis results, particularly in tests on anisotropic materials. The results in this work show very little difference between the thermal parameters arising from the two methods. The robustness of the method using the single-pixel temperature history shows that anisotropic thermal diffusivity can be measured using standard flash diffusivity instruments, avoiding the additional complexity associated with a thermal imaging camera.

Page 109. Analysis of Flash Diffusivity Experiments Performed on Semi-Porous Materials R. L McMAS... more Page 109. Analysis of Flash Diffusivity Experiments Performed on Semi-Porous Materials R. L McMASTERS and RB DINWIDDIE ABSTRACT Data from thermal diffusivity measurements using the laser flash method are analyzed using several mathematical models. ...

Journal of Heat Transfer, 2014

ABSTRACT There are many applications for problems involving thermal conduction in two-dimensional... more ABSTRACT There are many applications for problems involving thermal conduction in two-dimensional cylindrical objects. Experiments involving thermal parameter estimation are a prime example, including cylindrical objects suddenly placed in hot or cold environments. In a parameter estimation application, the direct solution must be run iteratively in order to obtain convergence with the measured temperature history by changing the thermal parameters. For this reason, commercial conduction codes are often inconvenient to use. It is often practical to generate numerical solutions for such a test, but verification of custom-made numerical solutions is important in order to assure accuracy. The present work involves the generation of an exact solution using Green’s functions where the principle of superposition is employed in combining a one-dimensional cylindrical case with a one-dimensional Cartesian case to provide a temperature solution for a two-dimensional cylindrical. Green’s functions are employed in this solution in order to simplify the process, taking advantage of the modular nature of these superimposed components. The exact solutions involve infinite series of Bessel functions and trigonometric functions but these series sometimes converge using only a few terms. Eigenvalues must be determined using Bessel functions and trigonometric functions. The accuracy of the solutions generated using these series is extremely high, being verifiable to eight or ten significant digits. Two examples of the solutions are shown as part of this work for a family of thermal parameters. The first case involves a uniform initial condition and homogeneous convective boundary conditions on all of the surfaces of the cylinder. The second case involves a nonhomogeneous convective boundary condition on a part of one of the planar faces of the cylinder and homogeneous convective boundary conditions elsewhere with zero initial conditions.

45th AIAA Thermophysics Conference, 2015

ABSTRACT The time duration for processes involving transient thermal diffusion can be a critical ... more ABSTRACT The time duration for processes involving transient thermal diffusion can be a critical piece of information related to thermal processes in engineering applications. Analytical solutions must be used to calculate these types of time durations since the boundary conditions in such cases can be effectively like semi-infinite conditions. This research involves an investigation into analytical solutions for five geometries including one-dimensional cases for Cartesian, cylindrical and spherical coordinates. The fourth case involves two-dimensional conduction from a point heat source on the surface of a slab subjected to insulated boundary conditions elsewhere. The mathematical modeling for this case is done in cylindrical coordinates. The fifth case involves a heated surface on the inside of a hole bored through an infinite body, which is a one-dimensional problem in radial coordinates. A sixth case is also mentioned, which is the only two-dimensional configuration discussed, having to do with point heating on a flat plate. For each geometric configuration, a relationship is developed to determine the time required for a temperature rise to occur at a non-heated point in the body in response to a sudden change at a heated boundary. A range of time values is computed for each configuration based on the amount of temperature rise used as a criterion. Plots are given for each case showing the relationships between the temperature rise of interest and the amount of time required to reach that temperature.

An interactive computer based learning tool for undergraduate students enrolled in Heat Transfer ... more An interactive computer based learning tool for undergraduate students enrolled in Heat Transfer courses has been significantly expanded. A previous version of the program provided graphical depictions of two-dimensional steady state conduction solutions for cases where temperature boundary conditions were prescribed. The present research expands the features of the program to include prescribed heat flux boundary conditions as well as convective boundary conditions. Moreover, the expanded program also handles transient cases so that students can watch temperature changes in a material on a real-time basis. The addition of these boundary conditions also now allows one dimensional problems to be solved by specifying a zero heat flux condition on opposing sides of the body.

Traditional flash diffusivity testing as outlined by Parker et al. [1] has been used as a method ... more Traditional flash diffusivity testing as outlined by Parker et al. [1] has been used as a method for determining the thermal diffusivity for many years. In Parker’s method, a thin sample of material is heated on one side by a short duration pulse. The resulting temperature rise on the opposite side of the sample is recorded by means of optical temperature measurement. This method, as validated by Taylor [2], determines the diffusivity of the heated sample from the correlation between the sample’s thickness and the time it takes for the measured temperature to reach a known percentage of its maximum value. Flash diffusivity testing is routinely performed on samples of 12-13 mm diameter, which are kept in place by a holder that contacts a low percentage of the sample’s surface area. This reduces heat conduction into the holder, making its effects negligible during the calculation of the sample’s thermal diffusivity. However, not all situations allow for the testing of samples that are...

IEEE Power Engineering Review, 2002

A method for establishing unit costs of delivered steam and electrical energy is presented. This ... more A method for establishing unit costs of delivered steam and electrical energy is presented. This method employs the use of least squares, based on a linear model of electrical energy generation and delivered steam as functions of generated boiler steam. The model is based on a plant design that allows steam to be extracted from between stages of the generating turbines at a reduced pressure to be used to serve heating loads. Alternatively, the steam can be run through lower pressure stages in the turbine to generate additional electrical power, and be exhausted at a vacuum, as dictated by external steam and electrical demand. A discussion of the accuracy of the method is presented as well as an example of the use of the method using two years of actual plant production.

Risk Analysis, 2004

Food safety objectives (FSOs) are established in order to minimize the risk of foodborne illnesse... more Food safety objectives (FSOs) are established in order to minimize the risk of foodborne illnesses to consumers, but these have not yet been incorporated into regulatory policy. An FSO states the maximum frequency and/or concentration of a microbiological hazard in a food at the time of consumption that provides an acceptable level of protection to the public and leads to a performance criterion for industry. However, in order to be implemented as a regulation, this criterion has to be achievable by the affected industry. In order to determine an FSO, the steps to produce and store that food need to be known, especially where they have an impact on contamination, growth, and destruction. This article uses existing models for growth of Listeria monocytogenes in conjunction with calculations of FSOs to approximate the outcome of more than one introduction of the foodborne organism throughout the food-processing path from the farm to the consumer. Most models for the growth and reduction of foodborne illnesses are logarithmic in nature, which fits the nature of the growth of microorganisms, spanning many orders of magnitude. However, these logarithmic models are normally limited to a single introduction step and a single reduction step. The model presented as part of this research addresses more than one introduction of food contamination, each of which can be separated by a substantial amount of time. The advantage of treating the problem this way is the accommodation of multiple introductions of foodborne pathogens over a range of time durations and conditions.

Numerical Heat Transfer, Part B: Fundamentals, 2002

This article describes the development of accurate solutions for transient three-dimensional cond... more This article describes the development of accurate solutions for transient three-dimensional conductive heat transfer in Cartesian coordinates for a parallelepiped which is homogeneous and has constant thermal properties. The intended use of these solutions is for verification of numerical computer programs which are used for solving transient heat conduction problems. Verification is a process to ensure that a computer code

Journal of Thermophysics and Heat Transfer, 2009

ABSTRACT The laser flash method for measuring thermal diffusivity is well established and has bee... more ABSTRACT The laser flash method for measuring thermal diffusivity is well established and has been in use for many years. Early analysis methods employed a simple model, in which one dimensional transient conduction was assumed, with insulated surfaces during the time subsequent to the flash. More recently, models of grater sophistication have been applied to flash diffusivity experiments. These models have been matched to experimental data using nonlinear regression and assume one-dimensional conduction. The advanced models have achieved highly accurate agreement with experimental data taken from thin samples, on the order of one millimeter in thickness. As samples become thicker, models which neglect edge losses can lose some conformity to the experimental data. The present research involves the application of a two dimensional model which allows for penetration of the laser flash into the sample. The accommodation of the flash penetration is important for porous materials, where the coarseness of the porosity is more than one percent of the sample thickness. Variability of the area of incidence of the flash is also investigated to determine the effect on the model and the results. Statistical methods are used in order to make a determination as to the validity of the two dimensional model, as compared with the one dimensional analysis method.

Journal of Thermophysics and Heat Transfer, 2002

ABSTRACT An analytical solution is provided to the nonlinear diffusion equation, with the thermal... more ABSTRACT An analytical solution is provided to the nonlinear diffusion equation, with the thermal conductivity given as a linear function of temperature. The derivation of the solution, and implications of it, are presented. The boundary and initial conditions associated with the solution provide applicability to specific cases. The solution is useful for verifying numerical (computer) solutions to thermal diffusion with temperature-dependent thermal conductivity. The (nonlinear) analytical solution is compared to a numerical solution from a finite element code to verify the accuracy of the code and to establish the order of convergence for the spatial discretization error.

Journal of Thermophysics and Heat Transfer, 2007

ABSTRACT Estimating the thermal conductivity of a film on a substrate of known thermal properties... more ABSTRACT Estimating the thermal conductivity of a film on a substrate of known thermal properties is examined in this research. The laser flash method, commonly used in the measurement of thermal diffusivity, is applied to a composite sample, which has a film deposited on a substrate. The laser flash is applied to the substrate and subsequent temperature measurements are recorded from the film side of the sample. Both the thermal conductivity and the volumetric heat capacity of the substrate must be known. Additionally, the volumetric heat capacity of the film must be known. The parameter estimation method used includes nonlinear regression of a transient conduction model in the solid material, which includes allowance for convective heat losses. The thermal conductivity is estimated simultaneously with the magnitude of the flash and the convection coefficient. The direct solution model is a two-layer exact solution which brings about very rapid computation, in contrast to numerical solutions. Several experiments are analyzed, with samples having various values of thermal conductivity, demonstrating the range over which the method can be used.

Journal of Heat Transfer, 1999

ABSTRACT Since the early 1960s, the laser flash method of thermal diffusivity measurement has bee... more ABSTRACT Since the early 1960s, the laser flash method of thermal diffusivity measurement has been used on a large variety of materials. Several parameter estimation methods have also been used in analyzing such experiments, employing various levels of sophistication. Estimation of thermal parameters, using the models developed as part of this research, is performed on experimental data from the Oak Ridge National Laboratory in Oak Ridge, TN. The material used is carbon bonded carbon fiber (CBCF) which is designed as an insulating material for atmosphere re-entry applications. Ambient temperatures in the experiments range from 800 degrees C to 1200 degrees C. The approximate thermal diffusivity of the material is 0.3 mm(2)/sec. This research investi gates the penetration of the laser flash beyond the surface of the material being heated. Three heat transfer models are presented, each with different assumptions about the initial temperature distribution inside the material. An evaluation is made of the response of the methods to factors which may enter into the experimental process. This is done in quantitative terms so as to assess the adequacy of the models in comparison to one another.

Journal of Heat Transfer, 2008

ABSTRACT The analytical solution for the problem of transient thermal conduction with solid body ... more ABSTRACT The analytical solution for the problem of transient thermal conduction with solid body movement is developed for a parallelepiped with convective boundary conditions. An effective transformation scheme is used to eliminate the flow terms. The solution uses Green’s functions containing convolution-type integrals, which involve integration over a dummy time, referred to as “cotime.” Two types of Green’s functions are used: one for short cotimes comes from the Laplace transform and the other for long cotimes from the method of separation of variables. A primary advantage of this method is that it incorporates internal verification of the numerical results by varying the partition time between the short and long components. In some cases, the long time solution requires a zeroth term in the summation, which does not occur when solid body motion is not present. The existence of this zeroth term depends upon the magnitude of the heat transfer coefficient associated with the convective boundary condition. An example is given for a two-dimensional case involving both prescribed temperature and convective boundary conditions. Comprehensive tables are also provided for the nine possible combinations of boundary conditions in each dimension.

Journal of Thermophysics and Heat Transfer, 2016

45th AIAA Thermophysics Conference, 2015

ABSTRACT The time duration for processes involving transient thermal diffusion can be a critical ... more ABSTRACT The time duration for processes involving transient thermal diffusion can be a critical piece of information related to thermal processes in engineering applications. Analytical solutions must be used to calculate these types of time durations since the boundary conditions in such cases can be effectively like semi-infinite conditions. This research involves an investigation into analytical solutions for five geometries including one-dimensional cases for Cartesian, cylindrical and spherical coordinates. The fourth case involves two-dimensional conduction from a point heat source on the surface of a slab subjected to insulated boundary conditions elsewhere. The mathematical modeling for this case is done in cylindrical coordinates. The fifth case involves a heated surface on the inside of a hole bored through an infinite body, which is a one-dimensional problem in radial coordinates. A sixth case is also mentioned, which is the only two-dimensional configuration discussed, having to do with point heating on a flat plate. For each geometric configuration, a relationship is developed to determine the time required for a temperature rise to occur at a non-heated point in the body in response to a sudden change at a heated boundary. A range of time values is computed for each configuration based on the amount of temperature rise used as a criterion. Plots are given for each case showing the relationships between the temperature rise of interest and the amount of time required to reach that temperature.

11th AIAA/ASME Joint Thermophysics and Heat Transfer Conference, 2014

Volume 2: Heat Transfer Enhancement for Practical Applications; Fire and Combustion; Multi-Phase Systems; Heat Transfer in Electronic Equipment; Low Temperature Heat Transfer; Computational Heat Transfer, 2012

ABSTRACT A well-established method for determining the thermal diffusivity of materials is the la... more ABSTRACT A well-established method for determining the thermal diffusivity of materials is the laser flash method. The work presented here compares two analysis methods for flash heating tests on anisotropic carbon bonded carbon fiber (CBCF). This material exhibits a higher conductivity in the direction in which the fibers are oriented than in the direction perpendicular to the fiber orientation.The two analysis methods being compared in this experiment use different portions of the data in obtaining results. One method utilizes the temperature data from the entire surface of the sample by examining 201 temperature histories simultaneously, with each temperature history originating from an individual pixel within a line across the middle of the sample. The other analysis method utilizes only the temperature history from a single pixel in the center of the sample, similar to the data which is traditionally generated using the classical flash diffusivity method. Both analysis methods include accommodations for modeling the penetration of the laser flash into the porous surface of the CBCF material. Additionally, both models include a parameter which accounts for the non-uniform heating of the sample surface from the flash. Although the sample surface is ostensibly heated uniformly in flash diffusivity experiments, the heating has been found to be somewhat non-uniform, with more energy deposited more heavily in the center of the sample. This affects the analysis results, particularly in tests on anisotropic materials. The results in this work show very little difference between the thermal parameters arising from the two methods. The robustness of the method using the single-pixel temperature history shows that anisotropic thermal diffusivity can be measured using standard flash diffusivity instruments, avoiding the additional complexity associated with a thermal imaging camera.

Page 109. Analysis of Flash Diffusivity Experiments Performed on Semi-Porous Materials R. L McMAS... more Page 109. Analysis of Flash Diffusivity Experiments Performed on Semi-Porous Materials R. L McMASTERS and RB DINWIDDIE ABSTRACT Data from thermal diffusivity measurements using the laser flash method are analyzed using several mathematical models. ...

Journal of Heat Transfer, 2014

ABSTRACT There are many applications for problems involving thermal conduction in two-dimensional... more ABSTRACT There are many applications for problems involving thermal conduction in two-dimensional cylindrical objects. Experiments involving thermal parameter estimation are a prime example, including cylindrical objects suddenly placed in hot or cold environments. In a parameter estimation application, the direct solution must be run iteratively in order to obtain convergence with the measured temperature history by changing the thermal parameters. For this reason, commercial conduction codes are often inconvenient to use. It is often practical to generate numerical solutions for such a test, but verification of custom-made numerical solutions is important in order to assure accuracy. The present work involves the generation of an exact solution using Green’s functions where the principle of superposition is employed in combining a one-dimensional cylindrical case with a one-dimensional Cartesian case to provide a temperature solution for a two-dimensional cylindrical. Green’s functions are employed in this solution in order to simplify the process, taking advantage of the modular nature of these superimposed components. The exact solutions involve infinite series of Bessel functions and trigonometric functions but these series sometimes converge using only a few terms. Eigenvalues must be determined using Bessel functions and trigonometric functions. The accuracy of the solutions generated using these series is extremely high, being verifiable to eight or ten significant digits. Two examples of the solutions are shown as part of this work for a family of thermal parameters. The first case involves a uniform initial condition and homogeneous convective boundary conditions on all of the surfaces of the cylinder. The second case involves a nonhomogeneous convective boundary condition on a part of one of the planar faces of the cylinder and homogeneous convective boundary conditions elsewhere with zero initial conditions.

45th AIAA Thermophysics Conference, 2015

ABSTRACT The time duration for processes involving transient thermal diffusion can be a critical ... more ABSTRACT The time duration for processes involving transient thermal diffusion can be a critical piece of information related to thermal processes in engineering applications. Analytical solutions must be used to calculate these types of time durations since the boundary conditions in such cases can be effectively like semi-infinite conditions. This research involves an investigation into analytical solutions for five geometries including one-dimensional cases for Cartesian, cylindrical and spherical coordinates. The fourth case involves two-dimensional conduction from a point heat source on the surface of a slab subjected to insulated boundary conditions elsewhere. The mathematical modeling for this case is done in cylindrical coordinates. The fifth case involves a heated surface on the inside of a hole bored through an infinite body, which is a one-dimensional problem in radial coordinates. A sixth case is also mentioned, which is the only two-dimensional configuration discussed, having to do with point heating on a flat plate. For each geometric configuration, a relationship is developed to determine the time required for a temperature rise to occur at a non-heated point in the body in response to a sudden change at a heated boundary. A range of time values is computed for each configuration based on the amount of temperature rise used as a criterion. Plots are given for each case showing the relationships between the temperature rise of interest and the amount of time required to reach that temperature.

An interactive computer based learning tool for undergraduate students enrolled in Heat Transfer ... more An interactive computer based learning tool for undergraduate students enrolled in Heat Transfer courses has been significantly expanded. A previous version of the program provided graphical depictions of two-dimensional steady state conduction solutions for cases where temperature boundary conditions were prescribed. The present research expands the features of the program to include prescribed heat flux boundary conditions as well as convective boundary conditions. Moreover, the expanded program also handles transient cases so that students can watch temperature changes in a material on a real-time basis. The addition of these boundary conditions also now allows one dimensional problems to be solved by specifying a zero heat flux condition on opposing sides of the body.

Traditional flash diffusivity testing as outlined by Parker et al. [1] has been used as a method ... more Traditional flash diffusivity testing as outlined by Parker et al. [1] has been used as a method for determining the thermal diffusivity for many years. In Parker’s method, a thin sample of material is heated on one side by a short duration pulse. The resulting temperature rise on the opposite side of the sample is recorded by means of optical temperature measurement. This method, as validated by Taylor [2], determines the diffusivity of the heated sample from the correlation between the sample’s thickness and the time it takes for the measured temperature to reach a known percentage of its maximum value. Flash diffusivity testing is routinely performed on samples of 12-13 mm diameter, which are kept in place by a holder that contacts a low percentage of the sample’s surface area. This reduces heat conduction into the holder, making its effects negligible during the calculation of the sample’s thermal diffusivity. However, not all situations allow for the testing of samples that are...

IEEE Power Engineering Review, 2002

A method for establishing unit costs of delivered steam and electrical energy is presented. This ... more A method for establishing unit costs of delivered steam and electrical energy is presented. This method employs the use of least squares, based on a linear model of electrical energy generation and delivered steam as functions of generated boiler steam. The model is based on a plant design that allows steam to be extracted from between stages of the generating turbines at a reduced pressure to be used to serve heating loads. Alternatively, the steam can be run through lower pressure stages in the turbine to generate additional electrical power, and be exhausted at a vacuum, as dictated by external steam and electrical demand. A discussion of the accuracy of the method is presented as well as an example of the use of the method using two years of actual plant production.

Risk Analysis, 2004

Food safety objectives (FSOs) are established in order to minimize the risk of foodborne illnesse... more Food safety objectives (FSOs) are established in order to minimize the risk of foodborne illnesses to consumers, but these have not yet been incorporated into regulatory policy. An FSO states the maximum frequency and/or concentration of a microbiological hazard in a food at the time of consumption that provides an acceptable level of protection to the public and leads to a performance criterion for industry. However, in order to be implemented as a regulation, this criterion has to be achievable by the affected industry. In order to determine an FSO, the steps to produce and store that food need to be known, especially where they have an impact on contamination, growth, and destruction. This article uses existing models for growth of Listeria monocytogenes in conjunction with calculations of FSOs to approximate the outcome of more than one introduction of the foodborne organism throughout the food-processing path from the farm to the consumer. Most models for the growth and reduction of foodborne illnesses are logarithmic in nature, which fits the nature of the growth of microorganisms, spanning many orders of magnitude. However, these logarithmic models are normally limited to a single introduction step and a single reduction step. The model presented as part of this research addresses more than one introduction of food contamination, each of which can be separated by a substantial amount of time. The advantage of treating the problem this way is the accommodation of multiple introductions of foodborne pathogens over a range of time durations and conditions.

Numerical Heat Transfer, Part B: Fundamentals, 2002

This article describes the development of accurate solutions for transient three-dimensional cond... more This article describes the development of accurate solutions for transient three-dimensional conductive heat transfer in Cartesian coordinates for a parallelepiped which is homogeneous and has constant thermal properties. The intended use of these solutions is for verification of numerical computer programs which are used for solving transient heat conduction problems. Verification is a process to ensure that a computer code

Journal of Thermophysics and Heat Transfer, 2009

ABSTRACT The laser flash method for measuring thermal diffusivity is well established and has bee... more ABSTRACT The laser flash method for measuring thermal diffusivity is well established and has been in use for many years. Early analysis methods employed a simple model, in which one dimensional transient conduction was assumed, with insulated surfaces during the time subsequent to the flash. More recently, models of grater sophistication have been applied to flash diffusivity experiments. These models have been matched to experimental data using nonlinear regression and assume one-dimensional conduction. The advanced models have achieved highly accurate agreement with experimental data taken from thin samples, on the order of one millimeter in thickness. As samples become thicker, models which neglect edge losses can lose some conformity to the experimental data. The present research involves the application of a two dimensional model which allows for penetration of the laser flash into the sample. The accommodation of the flash penetration is important for porous materials, where the coarseness of the porosity is more than one percent of the sample thickness. Variability of the area of incidence of the flash is also investigated to determine the effect on the model and the results. Statistical methods are used in order to make a determination as to the validity of the two dimensional model, as compared with the one dimensional analysis method.

Journal of Thermophysics and Heat Transfer, 2002

ABSTRACT An analytical solution is provided to the nonlinear diffusion equation, with the thermal... more ABSTRACT An analytical solution is provided to the nonlinear diffusion equation, with the thermal conductivity given as a linear function of temperature. The derivation of the solution, and implications of it, are presented. The boundary and initial conditions associated with the solution provide applicability to specific cases. The solution is useful for verifying numerical (computer) solutions to thermal diffusion with temperature-dependent thermal conductivity. The (nonlinear) analytical solution is compared to a numerical solution from a finite element code to verify the accuracy of the code and to establish the order of convergence for the spatial discretization error.

Journal of Thermophysics and Heat Transfer, 2007

ABSTRACT Estimating the thermal conductivity of a film on a substrate of known thermal properties... more ABSTRACT Estimating the thermal conductivity of a film on a substrate of known thermal properties is examined in this research. The laser flash method, commonly used in the measurement of thermal diffusivity, is applied to a composite sample, which has a film deposited on a substrate. The laser flash is applied to the substrate and subsequent temperature measurements are recorded from the film side of the sample. Both the thermal conductivity and the volumetric heat capacity of the substrate must be known. Additionally, the volumetric heat capacity of the film must be known. The parameter estimation method used includes nonlinear regression of a transient conduction model in the solid material, which includes allowance for convective heat losses. The thermal conductivity is estimated simultaneously with the magnitude of the flash and the convection coefficient. The direct solution model is a two-layer exact solution which brings about very rapid computation, in contrast to numerical solutions. Several experiments are analyzed, with samples having various values of thermal conductivity, demonstrating the range over which the method can be used.

Journal of Heat Transfer, 1999

ABSTRACT Since the early 1960s, the laser flash method of thermal diffusivity measurement has bee... more ABSTRACT Since the early 1960s, the laser flash method of thermal diffusivity measurement has been used on a large variety of materials. Several parameter estimation methods have also been used in analyzing such experiments, employing various levels of sophistication. Estimation of thermal parameters, using the models developed as part of this research, is performed on experimental data from the Oak Ridge National Laboratory in Oak Ridge, TN. The material used is carbon bonded carbon fiber (CBCF) which is designed as an insulating material for atmosphere re-entry applications. Ambient temperatures in the experiments range from 800 degrees C to 1200 degrees C. The approximate thermal diffusivity of the material is 0.3 mm(2)/sec. This research investi gates the penetration of the laser flash beyond the surface of the material being heated. Three heat transfer models are presented, each with different assumptions about the initial temperature distribution inside the material. An evaluation is made of the response of the methods to factors which may enter into the experimental process. This is done in quantitative terms so as to assess the adequacy of the models in comparison to one another.

Journal of Heat Transfer, 2008

ABSTRACT The analytical solution for the problem of transient thermal conduction with solid body ... more ABSTRACT The analytical solution for the problem of transient thermal conduction with solid body movement is developed for a parallelepiped with convective boundary conditions. An effective transformation scheme is used to eliminate the flow terms. The solution uses Green’s functions containing convolution-type integrals, which involve integration over a dummy time, referred to as “cotime.” Two types of Green’s functions are used: one for short cotimes comes from the Laplace transform and the other for long cotimes from the method of separation of variables. A primary advantage of this method is that it incorporates internal verification of the numerical results by varying the partition time between the short and long components. In some cases, the long time solution requires a zeroth term in the summation, which does not occur when solid body motion is not present. The existence of this zeroth term depends upon the magnitude of the heat transfer coefficient associated with the convective boundary condition. An example is given for a two-dimensional case involving both prescribed temperature and convective boundary conditions. Comprehensive tables are also provided for the nine possible combinations of boundary conditions in each dimension.