Dissertations / Theses: 'Heat equation'

1

Carroll, Andrew. "The stochastic nonlinear heat equation." Thesis, University of Hull, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.310216.

Full text

APA, Harvard, Vancouver, ISO, and other styles

2

Jumarhon, Bartur. "The one dimensional heat equation and its associated Volterra integral equations." Thesis, University of Strathclyde, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.342381.

Full text

APA, Harvard, Vancouver, ISO, and other styles

3

Wang, Jun. "Integral Equation Methods for the Heat Equation in Moving Geometry." Thesis, New York University, 2017. http://pqdtopen.proquest.com/#viewpdf?dispub=10618746.

Full text

Abstract:

Many problems in physics and engineering require the solution of the heat equation in moving geometry. Integral representations are particularly appropriate in this setting since they satisfy the governing equation automatically and, in the homogeneous case, require the discretization of the space-time boundary alone. Unlike methods based on direct discretization of the partial differential equation, they are unconditonally stable. Moreover, while a naive implementation of this approach is impractical, several efforts have been made over the past few years to reduce the overall computational cost. Of particular note are Fourier-based methods which achieve optimal complexity so long as the time step Δt is of the same order as Δx, the mesh size in the spatial variables. As the time step goes to zero, however, the cost of the Fourier-based fast algorithms grows without bound. A second difficulty with existing schemes has been the lack of efficient, high-order local-in-time quadratures for layer heat potentials.

In this dissertation, we present a new method for evaluating heat potentials that makes use of a spatially adaptive mesh instead of a Fourier series, a new version of the fast Gauss transform, and a new hybrid asymptotic/numerical method for local-in-time quadrature. The method is robust and efficient for any Δt, with essentially optimal computational complexity. We demonstrate its performance with numerical examples and discuss its implications for subsequent work in diffusion, heat flow, solidification and fluid dynamics.

APA, Harvard, Vancouver, ISO, and other styles

4

Xie, Shuguang School of Mathematics UNSW. "Stochastic heat equations with memory in infinite dimensional spaces." Awarded by:University of New South Wales. School of Mathematics, 2005. http://handle.unsw.edu.au/1959.4/24257.

Full text

Abstract:

This thesis is concerned with stochastic heat equation with memory and nonlinear energy supply. The main motivation to study such systems comes from Thermodynamics, see [85]. The main objective of this work is to study the existence and uniqueness of solutions to such equations and to investigate some fundamental properties of solutions like continuous dependence on initial conditions. In our approach we follow the seminal papers by Da Prato and Clement [10], where the stochastic heat equation with memory is tranformed into an integral equation in a function space and the so-called mild solutions are studied. In the aforementioned papers only linear equations with additive noise were investigated. The main contribution of this work is the extension of this approach to nonlinear equations. Our main tools are the theory of stochastic convolutions as developed in [33] and the theory of resolvent kernels for deterministic linear heat equations with memory, see[10]. Since the solution at time t depends on the whole history of the process up to time t, the resolvent kernel does not define a semigroup of operators in the state space of the process and therefore a ???standard??? theory of stochastic evolution equations as presented in the monograph [33] does not apply. A more delicate analysis of the resolvent kernles and the associated stochastic convolutions is needed. We will describe now content of this thesis in more detail. Introductory Chapters 1 and 2 collect some basic and essentially well known facts about the Wiener process, stochastic integrals, stochastic convolutions and integral kernels. However, some results in Chapter 2 dealing with stochastic convolution with respect to non-homogenous Wiener process are extensions of the existing theory. The main results of this thesis are presented in Chapters 3 and 4. In Chapter 3 we prove the existence and uniqueness of solutions to heat equations with additive noise and either Lipschitz or dissipative nonlinearities. In both cases we prove the continuous dependence of solutions on initial conditions. In Chapter 4 we prove the existence and uniqueness of solutions and continuous dependence on initial conditions for equations with multiplicative noise. The diffusion coefficients defined by unbounded operators are allowed.

APA, Harvard, Vancouver, ISO, and other styles

5

COMI, GIULIA. "Two Fractional Stochastic Problems: Semi-Linear Heat Equation and Singular Volterra Equation." Doctoral thesis, Università degli studi di Pavia, 2019. http://hdl.handle.net/11571/1292026.

Full text

APA, Harvard, Vancouver, ISO, and other styles

6

Thompson, Jeremy R. (Jeremy Ray). "Physical Motivation and Methods of Solution of Classical Partial Differential Equations." Thesis, University of North Texas, 1995. https://digital.library.unt.edu/ark:/67531/metadc277898/.

Full text

Abstract:

We consider three classical equations that are important examples of parabolic, elliptic, and hyperbolic partial differential equations, namely, the heat equation, the Laplace's equation, and the wave equation. We derive them from physical principles, explore methods of finding solutions, and make observations about their applications.

APA, Harvard, Vancouver, ISO, and other styles

7

Zhang, Junchi. "GPU computing of Heat Equations." Digital WPI, 2015. https://digitalcommons.wpi.edu/etd-theses/515.

Full text

Abstract:

There is an increasing amount of evidence in scientific research and industrial engineering indicating that the graphic processing unit (GPU) has a higher efficiency and a stronger ability over CPUs to process certain computations. The heat equation is one of the most well-known partial differential equations with well-developed theories, and application in engineering. Thus, we chose in this report to use the heat equation to numerically solve for the heat distributions at different time points using both GPU and CPU programs. The heat equation with three different boundary conditions (Dirichlet, Neumann and Periodic) were calculated on the given domain and discretized by finite difference approximations. The programs solving the linear system from the heat equation with different boundary conditions were implemented on GPU and CPU. A convergence analysis and stability analysis for the finite difference method was performed to guarantee the success of the program. Iterative methods and direct methods to solve the linear system are also discussed for the GPU. The results show that the GPU has a huge advantage in terms of time spent compared with CPU in large size problems.

APA, Harvard, Vancouver, ISO, and other styles

8

Zähle, Henryk. "Stochastic heat equation and catalytic super Brownian motion." [S.l.] : [s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=972728163.

Full text

APA, Harvard, Vancouver, ISO, and other styles

9

Huntul, Mousa Jaar M. "Determination of unknown coefficients in the heat equation." Thesis, University of Leeds, 2018. http://etheses.whiterose.ac.uk/22491/.

Full text

Abstract:

The purpose of this thesis is to find the numerical solutions of one or multiple unknown coefficient identification problems in the governing heat transfer parabolic equations. These inverse problems are numerically solved subject to various types of overdetermination conditions such as the heat flux, nonlocal observation, mass/energy specification, additional temperature measurement, Cauchy data, general integral type over-determination, Stefan condition and heat momentum of the first, second and third order. The main difficulty associated with solving these inverse problems is that they are ill-posed since small changes in the input data can result in enormous changes in the output solution, therefore traditional techniques fail to provide accurate and stable solutions. Throughout this thesis, the finite-difference method (FDM) with the Crank-Nicolson (C-N) scheme is mainly used as a direct solver except in Chapters 8 and 9 where an alternating direction explicit (ADE) method is employed in order to deal with the two-dimensional heat equation. An explicit forward time central space (FTCS) method is also employed in Chapter 2 for the extension to higher dimensions. The treatment for solving a degenerate parabolic equation, which vanishes at the initial moment of time is discussed in Chapter 6. The inverse problems investigated are discretised using FDM or ADE and recast as nonlinear least-squares minimization problems with lower and upper simple bounds on the unknown coefficients. The resulting optimization problems are numerically solved using the \emph{lsqnonlin} routine from MATLAB optimization toolbox. The stability of the numerical solutions is investigated by introducing random noise into the input data which yields unstable results if no regularization is employed. The regularization method is included (where necessary) in order to reduce the influence of measurement errors on the numerical results. The choice of the regularization parameter(s) is based on the L-curve method, on the discrepancy principle criterion or on trial and error.

APA, Harvard, Vancouver, ISO, and other styles

10

Hayman, Kenneth John. "Finite-difference methods for the diffusion equation." Title page, table of contents and summary only, 1988. http://web4.library.adelaide.edu.au/theses/09PH/09phh422.pdf.

Full text

APA, Harvard, Vancouver, ISO, and other styles

11

Riahi, Ardeshir. "The use of an approximate integral method to account for intraparticle conduction in gas-solid heat exchangers." Thesis, University of British Columbia, 1985. http://hdl.handle.net/2429/25137.

Full text

Abstract:

The mathematical equations describing transient heat transfer between the fluid flowing through a fixed bed and a moving bed of packing were formulated. The resistance to heat transfer within the packing due to its finite thermal conductivity was taken into account. An approximate integral method was applied to obtain an analytical solution to transient response of the bed packing. Results for two cases of fixed and moving bed were obtained. The validity of the approximate method was checked against the more exact method employed by Handley and Heggs who obtained the results for a fixed bed of packing with a step change in fluid inlet temperature. It was concluded that the approximate method gives results that agree well with the more exact methods. The method considered here provides a quick determination of the packing mean temperature in order to obtain the effectiveness. The other peculiarity of this method is that the effect of packing thermal conductivity can be examined very quickly since the solution is in analytical form. The analysis of the results revealed that as the thermal conductivity of the packing decreases the difference between its surface and mean temperature increases. A series of charts showing the comparison between the packing surface and mean temperatures for different thermal conductivities are presented. The approximate method was a moving bed of packing. It was packing thermal conductivity is series of charts representing versus dimensionless length conductivities are presented. then applied to the case of concluded that the effect of more severe than expected. A the moving bed effectiveness for different thermal
Applied Science, Faculty of
Mechanical Engineering, Department of
Graduate

APA, Harvard, Vancouver, ISO, and other styles

12

Knaub, Karl R. "On the asymptotic behavior of internal layer solutions of advection-diffusion-reaction equations /." Thesis, Connect to this title online; UW restricted, 2001. http://hdl.handle.net/1773/6772.

Full text

APA, Harvard, Vancouver, ISO, and other styles

13

Gilkey, Peter B., Klaus Kirsten, Jeong Hyeong Park, Dmitri Vassilevich, and vassil@itp uni-leipzig de. "Asymptotics of the Heat Equation with `Exotic' Boundary Conditions or." ESI preprints, 2001. ftp://ftp.esi.ac.at/pub/Preprints/esi1027.ps.

Full text

APA, Harvard, Vancouver, ISO, and other styles

14

Kaya, Mujdat. "Inverse Problems For A Semilinear Heat Equation With Memory." Phd thesis, METU, 2005. http://etd.lib.metu.edu.tr/upload/12606106/index.pdf.

Full text

Abstract:

ABSTRACT INVERSE PROBLEMS FOR A SEMILINEAR HEAT EQUATIONS WITH MEMORY Kaya, Mü
jdat Ph.D, Department of Mathematics Supervisor: Prof. Dr. A. Okay Ç
elebi Co-Supervisor: Prof. Dr. Varga Kalantarov May 2005, 79 pages In this thesis, we study the existence and uniqueness of the solutions of the inverse problems to identify the memory kernel k and the source term h, derived from First, we obtain the structural stability for k, when p=1 and the coefficient p, when g( )= . To identify the memory kernel, we find an operator equation after employing the half Fourier transformation. For the source term identification, we make use of the direct application of the final overdetermination conditions.

APA, Harvard, Vancouver, ISO, and other styles

15

Oliveira, Ana Carolina Carius de. "Hierarchical modelling for the heat equation in a heterogeneous." Laboratório Nacional de Computação Científica, 2006. http://www.lncc.br/tdmc/tde_busca/arquivo.php?codArquivo=68.

Full text

Abstract:

In this dissertation, we study the stationary heat equation in a heterogeneous tridimensional plate, using a "dimension reduction" techinique called hierarchical modelling and we generate model the original problem in a two-dimensional domain. To estimate the error modelling, we develop an asymptotic expansion for the original problem solution and for the aproximate solution. Comparing both solutions with their own asymptotic expansions, we obtain an estimative of the error modelling. We perform some computational experiments, using the Residual Free Bubbles (RFB) Method and the Multiscale Finite Element Method for the diffusion problem and for the diffusion-reaction problem in a two-dimensional domain, with small parameters. Finally, we extend the numeric solutions found the original tridimensional problem.
Neste trabalho, estudamos a equação do calor estacionária em uma placa heterogênea tridimensional. Para a modelagem deste problema, utilizamos uma técnica de redução de dimensão conhecida por Modelagem Hierárquica. Desta forma, geramos um modelo para o problema original em um domínio bidimensional. Com o objetivo de estimar o erro de modelagem, desenvolvemos a expansão assintótica da solução do problema original e da solução aproximada. Comparando as soluções com suas respectivas expansões assintóticas, obtemos uma estimativa para o erro de modelagem. Realizamos alguns experimentos computacionais, desenvolvendo o método Residual Free Bubbles (RFB) e o método de Elementos Finitos Multiescala (MEFM) para o problema de difusão e para o problema de difusão-reação em um domínio bidimensional, com parâmetros pequenos. Com base nestes experimentos, encontramos algumas soluções numéricas para o problema da placa tridimensional.

APA, Harvard, Vancouver, ISO, and other styles

16

Lun, Chin Hang. "A multi-layer extension of the stochastic heat equation." Thesis, University of Warwick, 2016. http://wrap.warwick.ac.uk/78989/.

Full text

Abstract:

The KPZ universality class is expected to contain a large class of random growth processes. In some of these models, there is an additional structure provided by multiple non-intersecting paths and utilisation of this additional structure has led to derivations of exact formulae for the distribution of quantities of interest. Motivated by this we study the multi-layer extension of the stochastic heat equation introduced by O'Connell and Warren in [OW11] which is the continuum analogue of the above mentioned structure. We also show that a multi-layer Cole-Hopf solution to the KPZ equation is well defined.

APA, Harvard, Vancouver, ISO, and other styles

17

Roxanas, Dimitrios. "Long-time dynamics for the energy-critical harmonic map heat flow and nonlinear heat equation." Thesis, University of British Columbia, 2017. http://hdl.handle.net/2429/61612.

Full text

Abstract:

The main focus of this thesis is on critical parabolic problems, in particular, the harmonic map heat from the plane to S2, and nonlinear focusing heat equations with an algebraic nonlinearity. The focus of this work has been on long-time dynamics, stability and singularity formation, and the investigation of the role of special, soliton-like, solutions to the asymptotic behaviour of solutions. Harmonic Map Heat Flow: Flow: we consider m-corotational solutions to the harmonic map heat flow from R2 to S2. We first work in a class of maps with trivial topology and energy of the initial data below two times the energy of the stationary harmonic map solutions. We give a new proof of global existence and decay. The proof is based on the "concentration-compactness plus rigidity" approach of Kenig and Merle and relies on the dissipation of the energy and a profile decomposition. We also treat m-corotational maps (m greater than 3) with non-trivial topology and energy of the initial data less than three times the energy of the stationary harmonic map solutions. Through a new stability argument we rule out finite-time blow-up and show that the global solution asymptotically converges to a harmonic map. Nonlinear Heat Equation: we also study solutions of the focusing energy-critical nonlinear heat equation. We show that solutions emanating from initial data with energy and kinetic energy below those of the stationary solutions are global and decay to zero. To prove that global solutions dissipate to zero we rely on a refined small data theory, L2-dissipation and an approximation argument. We then follow the "concentration-compactness plus rigidity" roadmap of Kenig and Merle (and in particular the approach taken by Kenig and Koch for Navier-Stokes) to exclude finite-time blow-up.
Science, Faculty of
Mathematics, Department of
Graduate

APA, Harvard, Vancouver, ISO, and other styles

18

Duthil, Eric Patxi. "Thermoacoustic heat pumping study : experimental and numerical approaches /." View Abstract or Full-Text, 2003. http://library.ust.hk/cgi/db/thesis.pl?MECH%202003%20DUTHIL.

Full text

Abstract:

Thesis (Ph. D.)--Hong Kong University of Science and Technology, 2003.
Includes bibliographical references (leaves 122-129). Also available in electronic version. Access restricted to campus users.

APA, Harvard, Vancouver, ISO, and other styles

19

Srisatkunarajah, Sivakolundu. "On the asymptotics of the heat equation for polygonal domains." Thesis, Heriot-Watt University, 1988. http://hdl.handle.net/10399/1001.

Full text

APA, Harvard, Vancouver, ISO, and other styles

20

Cao, Kai. "Inverse problems for the heat equation using conjugate gradient methods." Thesis, University of Leeds, 2018. http://etheses.whiterose.ac.uk/22611/.

Full text

Abstract:

In many engineering systems, e.g., in heat exchanges, reflux condensers, combustion chambers, nuclear vessels, etc. concerned with high temperatures/pressures/loads and/or hostile environments, certain properties of the physical medium, geometry, boundary and initial conditions are not known and their direct measurement can be very inaccurate or even inaccessible. In such a situation, one can adopt an inverse approach and try to infer the unknowns from some extra accessible measurements of other quantities that may be available. The purpose of this thesis is to determine the unknown space-dependent coefficients and/or initial temperature in inverse problems of heat transfer, especially to simultaneously reconstruct several unknown quantities. These inverse problems are investigated from additional pieces of information, such as internal temperature observations, final measured temperature and time-integral temperature measurement. The main difficulty involved in the solution of these inverse problems is that they are typically ill-posed. Thus, their solutions are unstable under small perturbations of the input data and classical numerical techniques fail to provide accurate and stable numerical results. Throughout this thesis, the inverse problems are transformed into optimization problems, and their minimizers are shown to exist. A variational method is employed to obtain their Fréchet gradients with respect to the unknown quantities. Based on this gradient, the conjugate gradient method (CGM) is established together with the adjoint and sensitivity problems. The stability of the numerical solution is investigated by introducing Gaussian random noise into the input measured data. Accurate and stable numerical solutions are obtained when using the CGM regularized by the discrepancy principle.

APA, Harvard, Vancouver, ISO, and other styles

21

Reinarz, Anne. "Sparse space-time boundary element methods for the heat equation." Thesis, University of Reading, 2015. http://centaur.reading.ac.uk/49315/.

Full text

Abstract:

The goal of this work is the efficient solution of the heat equation with Dirichlet or Neumann boundary conditions using the Boundary Elements Method (BEM). Efficiently solving the heat equation is useful, as it is a simple model problem for other types of parabolic problems. In complicated spatial domains as often found in engineering, BEM can be beneficial since only the boundary of the domain has to be discretised. This makes BEM easier than domain methods such as finite elements and finite differences, conventionally combined with time-stepping schemes to solve this problem. The contribution of this work is to further decrease the complexity of solving the heat equation, leading both to speed gains (in CPU time) as well as requiring smaller amounts of memory to solve the same problem. To do this we will combine the complexity gains of boundary reduction by integral equation formulations with a discretisation using wavelet bases. This reduces the total work to O(hₓ-(d-1)), when the solution of the linear system is performed with linear complexity. We show that the discretisation with a wavelet basis leads to a numerically sparse matrix. Further, we show that this matrix can be compressed without losing accuracy of the underlying Galerkin scheme. This matrix compression reduces the number of non-zero matrix entries from O(N2) to O(N). Thus, we can indeed solve the linear system in linear time. It has been shown theoretically that using sparse grid methods leads to considerably higher convergence rates in the energy norm of the problem. In this work we will show that the convergence can be further improved for some choices of polynomial degrees by using more general sparse grid spaces. We also give numerical results to verify the theoretical bounds from [Chernov, Schwab, 2013].

APA, Harvard, Vancouver, ISO, and other styles

22

Wilkinson, Rebecca L. "Numerical explorations of cake baking using the nonlinear heat equation." View electronic thesis, 2008. http://dl.uncw.edu/etd/2008-1/wilkinsonr/rebeccawilkinson.pdf.

Full text

APA, Harvard, Vancouver, ISO, and other styles

23

Hulsing, Kevin P. "Methods of Computing Functional Gains for LQR Control of Partial Differential Equations." Diss., Virginia Tech, 1999. http://hdl.handle.net/10919/30139.

Full text

Abstract:

This work focuses on a comparison of numerical methods for linear quadratic regulator (LQR) problems defined by parabolic partial differential equations. In particular, we study various methods for computing functional gains to boundary control problems for the heat equation. These methods require us to solve various equations including the algebraic Riccati equation, the Riccati partial differential equation and the Chandrasekhar partial differential equations. Numerical results are presented for control of a one-dimensional and a two-dimensional heat equation with Dirichlet or Robin boundary control.
Ph. D.

APA, Harvard, Vancouver, ISO, and other styles

24

Debrecht, Johanna M. "Plane Curves, Convex Curves, and Their Deformation Via the Heat Equation." Thesis, University of North Texas, 1998. https://digital.library.unt.edu/ark:/67531/metadc278501/.

Full text

Abstract:

We study the effects of a deformation via the heat equation on closed, plane curves. We begin with an overview of the theory of curves in R3. In particular, we develop the Frenet-Serret equations for any curve parametrized by arc length. This chapter is followed by an examination of curves in R2, and the resultant adjustment of the Frenet-Serret equations. We then prove the rotation index for closed, plane curves is an integer and for simple, closed, plane curves is ±1. We show that a curve is convex if and only if the curvature does not change sign, and we prove the Isoperimetric Inequality, which gives a bound on the area of a closed curve with fixed length. Finally, we study the deformation of plane curves developed by M. Gage and R. S. Hamilton. We observe that convex curves under deformation remain convex, and simple curves remain simple.

APA, Harvard, Vancouver, ISO, and other styles

25

Andersen, Arden Bruce. "Validation of the USF Safe Exposure Time Equation for Heat Stress." Scholar Commons, 2011. http://scholarcommons.usf.edu/etd/2985.

Full text

Abstract:

Heat stress conditions are prevalent in the working environment around the world. Often they are not readily engineered out. Administrative controls and, in extreme/toxic environments, personal protective gear are the means available to protect workers. For every combination of metabolic work rate, clothing ensemble and environmental WBGT, there is a time of exposure threshold, beyond which the worker can no longer compensate for the heat stress, and signs and symptoms of heat strain appear. Increasingly, worker environments require specialty clothing either for worker protection or to maintain a clean/sanitary environment. Prior to the publication of the USF safe exposure time equation, no simple method was available for determining safe worker exposure time based on a clothing adjustment factor. To demonstrate the validity of the USF SET equation, both direct and indirect data from different environments, metabolic rates, and clothing ensembles were collected to compare observed tolerance times to the predicted safe exposure time. Statistical analysis was performed using the Kolmogorov-Smirnov test. The USF SET equation predicted an acceptable safe exposure time, 19 % of the trials. Based upon this data, the USF safe exposure time heat stress equation over estimates safe exposure time for workers in hot environments, in various clothing ensembles at various metabolic work rates.

APA, Harvard, Vancouver, ISO, and other styles

26

Maddipati, Sai Ratna Kiran. "Improving the Parallel Performance of Boltzman-Transport Equation for Heat Transfer." The Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1461334523.

Full text

APA, Harvard, Vancouver, ISO, and other styles

27

Macbeth, Tyler James. "Conjugate Heat Transfer and Average Versus Variable Heat Transfer Coefficients." BYU ScholarsArchive, 2016. https://scholarsarchive.byu.edu/etd/5801.

Full text

Abstract:

An average heat transfer coefficient, h_bar, is often used to solve heat transfer problems. It should be understood that this is an approximation and may provide inaccurate results, especially when the temperature field is of interest. The proper method to solve heat transfer problems is with a conjugate approach. However, there seems to be a lack of clear explanations of conjugate heat transfer in literature. The objective of this work is to provide a clear explanation of conjugate heat transfer and to determine the discrepancy in the temperature field when the interface boundary condition is approximated using h_bar compared to a local, or variable, heat transfer coefficient, h(x). Simple one-dimensional problems are presented and solved analytically using both h(x) and h_bar. Due to the one-dimensional assumption, h(x) appears in the governing equation for which the common methods to solve the differential equations with an average coefficient are no longer valid. Two methods, the integral equation and generalized Bessel methods are presented to handle the variable coefficient. The generalized Bessel method has previously only been used with homogeneous governing equations. This work extends the use of the generalized Bessel method to non-homogeneous problems by developing a relation for the Wronskian of the general solution to the generalized Bessel equation. The solution methods are applied to three problems: an external flow past a flat plate, a conjugate interface between two solids and a conjugate interface between a fluid and a solid. The main parameter that is varied is a combination of the Biot number and a geometric aspect ratio, A_1^2 = Bi*L^2/d_1^2. The Biot number is assumed small since the problems are one-dimensional and thus variation in A_1^2 is mostly due to a change in the aspect ratio. A large A_1^2 represents a long and thin solid whereas a small A_1^2 represents a short and thick solid. It is found that a larger A_1^2 leads to less problem conjugation. This means that use of h_bar has a lesser effect on the temperature field for a long and thin solid. Also, use of ¯ over h(x) tends to generally under predict the solid temperature. In addition is was found that A_2^2, the A^2 value for the second subdomain, tends to have more effect on the shape of the temperature profile of solid 1 and A_1^2 has a greater effect on the magnitude of the difference in temperature profiles between the use of h(x) and h_bar. In general increasing the A^2 values reduced conjugation.

APA, Harvard, Vancouver, ISO, and other styles

28

Gilkey, Peter B., Klaus Kirsten, Dmitri V. Vassilevich, and vassil@itp uni-leipzig de. "Heat Trace Asymptotics with Transmittal Boundary Conditions and Quantum." Nucl. Phys. B 601 (2001) 125-148, 2001. ftp://ftp.esi.ac.at/pub/Preprints/esi982.ps.

Full text

APA, Harvard, Vancouver, ISO, and other styles

29

Ashworth, Eileen. "Heat flow into underground openings: Significant factors." Diss., The University of Arizona, 1992. http://hdl.handle.net/10150/185768.

Full text

Abstract:

This project investigates the heat flow from the rock into ventilating airways by studying various parameters. Two approaches have been used: laboratory measurement of thermal properties to study their variation, and analytic and numerical models to study the effect of these variations on the heat flow. Access to a heat-flux system and special treatment of contact resistance has provided the opportunity to study thermal conductivity as a function of moisture contained in rock specimens. For porous sandstone, tuff, and concretes, thermal conductivity can double when the specimens are soaked; the functional dependence of conductivity on moisture for the first two cases is definitely non-linear. Five previous models for conductivity as a function of porosity are shown not to explain this new phenomenon. A preliminary finite element model is proposed which explains the key features. Other variations of conductivity with applied pressure, location, constituents, weathering or other damage, and anisotropy have been measured. In the second phase of the research, analytical and numerical methods have been employed to consider the effects of the variation in the thermal properties plus the use of insulation on the heat flow from the rock into the ventilated and cooled airways. Temperature measurements taken in drill holes at a local mine provide confirmation for some of the models. Results have been provided in a sensitivity analysis mode so that engineers working on other projects can see which parameters would require more detailed consideration. The thermal conductivity of the rock close to the airways is a key factor in affecting heat loads. Dewatering and the use of insulation, such as lightweight foamed shotcretes, are recommended.

APA, Harvard, Vancouver, ISO, and other styles

30

Manay, Siddharth. "Applications of anti-geometric diffusion of computer vision : thresholding, segmentation, and distance functions." Diss., Georgia Institute of Technology, 2003. http://hdl.handle.net/1853/33626.

Full text

APA, Harvard, Vancouver, ISO, and other styles

31

Rivera, Noriega Jorge. "Some remarks on certain parabolic differential operators over non-cylindrical domains /." free to MU campus, to others for purchase, 2001. http://wwwlib.umi.com/cr/mo/fullcit?p3025649.

Full text

APA, Harvard, Vancouver, ISO, and other styles

32

Tyler, Jonathan. "Analysis and implementation of high-order compact finite difference schemes /." Diss., CLICK HERE for online access, 2007. http://contentdm.lib.byu.edu/ETD/image/etd2177.pdf.

Full text

APA, Harvard, Vancouver, ISO, and other styles

33

Laurén, Fredrik. "Analysis of the energy exchange between atmosphere and ground using the compressible Navier-Stokes equations and the heat equation." Thesis, Uppsala universitet, Avdelningen för beräkningsvetenskap, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-304006.

Full text

Abstract:

In this paper the interface between the one dimensional compressible Navier-Stokes equation and the heat equation is analysed. For the linearized and symmetrized model, the energy method is used to derive interface conditions that bounds the solution. First, the characteristic far field boundary conditions are derived for the Navier-Stokes equation, second boundary conditions for a solid wall are derived and last interface condition with a heat equation. High order Summation-by-Parts operators are used for the spatial discretization. Boundary and interface conditions are weakly imposed using Simultaneous Approximation Terms. The implementation is stable and the method of manufactured solution is used to verify the implementation. An efficiency study showed that high order operators are superior in how much computer power is needed to get an accurate solution.

APA, Harvard, Vancouver, ISO, and other styles

34

Sawyer, Patrice. "The heat equation on the symmetric space associated with SL(n,R) /." Thesis, McGill University, 1989. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=74269.

Full text

Abstract:

The main topic of this thesis is the study of the fundamental solution of the heat equation for the symmetric spaces of positive definite matrices, Pos(n,R).
Our first step is to develop a "False Abel Inverse Transform" ${ cal G}$ which transforms functions of compact support on an euclidean space into integrable functions on the symmetric space. The transform ${ cal G}$ is shown to satisfy the relation $ Delta{ cal G}(f; cdot) = { cal G}( Gamma( Delta)f; cdot)$ $( Gamma( Delta)$ is the usual Laplacian with a constant drift).
Using this transform, we find explicit formulas for the heat kernel in the cases n = 2 and n = 3. These formulas allow us to give the asymptotic development for the heat kernal as t tends to infinity. Finally, we give an upper and lower bound of the same type for the heat kernel. In the case n = 3, the lower bound is completely new.

APA, Harvard, Vancouver, ISO, and other styles

35

Bales, Walter. "Asymptotic approximation of the free boundary for the American put near expiry." To access this resource online via ProQuest Dissertations and Theses @ UTEP, 2009. http://0-proquest.umi.com.lib.utep.edu/login?COPT=REJTPTU0YmImSU5UPTAmVkVSPTI=&clientId=2515.

Full text

APA, Harvard, Vancouver, ISO, and other styles

36

Allu, Pareekshith. "A Hybrid Ballistic-Diffusive Method to Solve the Frequency Dependent Boltzmann Transport Equation." The Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1451998769.

Full text

APA, Harvard, Vancouver, ISO, and other styles

37

Litaker, Eric T. "Finite volume element (FVE) discretization and multilevel solution of the axisymmetric heat equation." Thesis, Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 1994. http://handle.dtic.mil/100.2/ADA294750.

Full text

Abstract:

Thesis (M.S. in Mathematics) Naval Postgraduate School, December 1994.
Thesis advisor(s): David R. Canright, V.E. Henson. "December 1994." Includes bibliographical references. Also available online.

APA, Harvard, Vancouver, ISO, and other styles

38

Tzanetis, Dimitrios E. "Global existence and asymptotic behaviour of unbounded solutions for the semilinear heat equation." Thesis, Heriot-Watt University, 1986. http://hdl.handle.net/10399/1604.

Full text

APA, Harvard, Vancouver, ISO, and other styles

39

Chin, P. W. M. (Pius Wiysanyuy Molo). "Contribution to qualitative and constructive treatment of the heat equation with domain singularities." Thesis, University of Pretoria, 2011. http://hdl.handle.net/2263/28554.

Full text

APA, Harvard, Vancouver, ISO, and other styles

40

Davies, Kevin L. "Declarative modeling of coupled advection and diffusion as applied to fuel cells." Diss., Georgia Institute of Technology, 2014. http://hdl.handle.net/1853/51814.

Full text

Abstract:

The goal of this research is to realize the advantages of declarative modeling for complex physical systems that involve both advection and diffusion to varying degrees in multiple domains. This occurs, for example, in chemical devices such as fuel cells. The declarative or equation-based modeling approach can provide computational advantages and is compatible with physics-based, object-oriented representations. However, there is no generally accepted method of representing coupled advection and diffusion in a declarative modeling framework. This work develops, justifies, and implements a new upstream discretization scheme for mixed advective and diffusive flows that is well-suited for declarative models. The discretization scheme yields a gradual transition from pure diffusion to pure advection without switching events or nonlinear systems of equations. Transport equations are established in a manner that ensures the conservation of material, momentum, and energy at each interface and in each control volume. The approach is multi-dimensional and resolved down to the species level, with conservation equations for each species in each phase. The framework is applicable to solids, liquids, gases, and charged particles. Interactions among species are described as exchange processes which are diffusive if the interaction is inert or advective if it involves chemical reactions or phase change. The equations are implemented in a highly modular and reconfigurable manner using the Modelica language. A wide range of examples are demonstrated—from basic models of electrical conduction and evaporation to a comprehensive model of a proton exchange membrane fuel cell (PEMFC). Several versions of the PEMFC model are simulated under various conditions including polarization tests and a cyclical electrical load. The model is shown to describe processes such as electro-osmotic drag and liquid pore saturation. It can be scaled in complexity from 4000 to 32,000 equations, resulting in a simulation times from 0.2 to 19 s depending on the level of detail. The most complex example is a seven-layer cell with six segments along the length of the channel. The model library is thoroughly documented and made available as a free, open-source software package.

APA, Harvard, Vancouver, ISO, and other styles

41

Weiß, Jan-Philipp. "Numerical analysis of lattice Boltzmann methods for the heat equation on a bounded interval." Karlsruhe : Univ.-Verl. Karlsruhe, 2006. http://www.uvka.de/univerlag/volltexte/2006/179/.

Full text

APA, Harvard, Vancouver, ISO, and other styles

42

Antoniouk, Alexandra, Oleg Kiselev, Vitaly Stepanenko, and Nikolai Tarkhanov. "Asymptotic solutions of the Dirichlet problem for the heat equation at a characteristic point." Universität Potsdam, 2012. http://opus.kobv.de/ubp/volltexte/2012/6198/.

Full text

Abstract:

The Dirichlet problem for the heat equation in a bounded domain is characteristic, for there are boundary points at which the boundary touches a characteristic hyperplane t = c, c being a constant. It was I.G. Petrovskii (1934) who first found necessary and sufficient conditions on the boundary which guarantee that the solution is continuous up to the characteristic point, provided that the Dirichlet data are continuous. This paper initiated standing interest in studying general boundary value problems for parabolic equations in bounded domains. We contribute to the study by constructing a formal solution of the Dirichlet problem for the heat equation in a neighbourhood of a characteristic boundary point and showing its asymptotic character.

APA, Harvard, Vancouver, ISO, and other styles

43

Govindaraj, Thavamani. "Optimal Control of a Stochastic Heat Equation with Control and Noise on the Boundary." Thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-76037.

Full text

Abstract:

In this thesis, we give a mathematical background of solving a linear quadratic control problem for the heat equation, which involves noise on the boundary, in a concise way. We use the semigroup approach for the solvability of the problem. To obtain optimal controls, we use optimization techniques for convex functionals. Finally we give a feedback form for the optimal control. In order to enhance understanding of linear quadratic problem, we first present the methods in deterministic cases and then extend to noisy systems.

APA, Harvard, Vancouver, ISO, and other styles

44

Kuang, Shilong. "Analysis of conjugate heat equation on complete non-compact Riemannian manifolds under Ricci flow." Diss., UC access only, 2009. http://proquest.umi.com/pqdweb?index=7&did=1907270831&SrchMode=2&sid=2&Fmt=2&VInst=PROD&VType=PQD&RQT=309&VName=PQD&TS=1270053784&clientId=48051.

Full text

Abstract:

Thesis (Ph. D.)--University of California, Riverside, 2009.
Includes abstract. Includes bibliographical references (leaves 74-76). Issued in print and online. Available via ProQuest Digital Dissertations.

APA, Harvard, Vancouver, ISO, and other styles

45

Ko, Kang-Hoon. "Heat transfer enhancement in a channel with porous baffles." Texas A&M University, 2004. http://hdl.handle.net/1969.1/1519.

Full text

Abstract:

An experimental and numerical investigation of heat transfer enhancement in a three dimensional channel using wall mounted porous baffles was conducted. The module average heat transfer coefficients were measured in a uniformly heated rectangular channel with staggered positioned porous baffles. A numerical procedure was implemented, in conjunction with a commercially available Navier-Stokes solver, to model the turbulent flow in porous media. The Brinkman-Forchheimer-Extended Darcy model was used for modeling fluid flow through the porous baffles. Conventional, oneequation, and two-equation models were used for heat transfer modeling. The accuracy and characteristics of each model were investigated and discussed. The results were compared with experimental data. Baffles were mounted alternatively on the top and bottom walls. Heat transfer coefficients and pressure loss for periodically fully developed flow and heat transfer were obtained for different pore densities (10, 20, and 40 pores per inch (PPI)) with two different baffle heights ( / h h B D = 1/3 and 2/3), and two baffle thicknesses ( / t h B D = 1/3 and 1/12). The Reynolds number (Re) was varied from 20,000 to 50,000. To compare the effect of foam metal baffles, the data for conventional solid-type baffles was obtained for ( / t h B D =1/3). The maximum uncertainties associated with the module Nusselt number and friction factor were 5.8% and 4.3%, respectively. The experimental procedure was validated by comparing the data for the straight channel without baffles ( / h h B D = 0) with those in the literature. The use of porous baffles resulted in heat transfer enhancement as high as 300% compared to heat transfer in straight channels without baffles. However, the heat transfer enhancement per unit increase in pumping power was less than one for the range of parameters studied in this work. Correlation equations were developed for the heat transfer enhancement ratio and the heat transfer enhancement per unit increase in pumping power in terms of Reynolds number. The conventional theoretical model, the dispersion conductivity model, and the modified two-phase model using the local thermal non-equilibrium theory were considered. The results from each model were compared against the experimental data, and compared to each other to investigate the efficiency of each model. Also, the characteristics of each model were discussed.

APA, Harvard, Vancouver, ISO, and other styles

46

Zaveri, Sona. "The second eigenfunction of the Neumann Laplacian on thin regions /." Thesis, Connect to this title online; UW restricted, 2006. http://hdl.handle.net/1773/5748.

Full text

APA, Harvard, Vancouver, ISO, and other styles

47

Vo, Thi Minh Nhat. "Construction of a control and reconstruction of a source for linear and nonlinear heat equations." Thesis, Orléans, 2018. http://www.theses.fr/2018ORLE2012/document.

Full text

Abstract:

Dans cette thèse, nous étudions un problème de contrôle et un problème inverse pour les équationsde la chaleur. Notre premier travail concerne la contrôlabilité à zéro pour une équation de la chaleur semi-linéaire. Il est à noter que sans contrôle, la solution est instable et il y aura en général explosion de la solution en un temps fini. Ici, nous proposons un résultat positif de contrôlabilité à zéro sous une hypothèse quantifiée de petitesse sur la donnée initiale. La nouveauté réside en la construction de ce contrôle pour amener la solution à l’état d’équilibre.Notre second travail aborde l’équation de la chaleur rétrograde dans un domaine borné et sous la condition de Dirichlet. Nous nous intéressons à la question suivante: peut-on reconstruire la donnée initiale à partir d’une observation de la solution restreinte à un sous-domaine et à un temps donné? Ce problème est connu pour être mal-posé. Ici, les deux principales méthodes proposées sont: une approche de filtrage des hautes fréquences et une minimisation à la Tikhonov. A chaque fois, nous reconstruisons de manière approchée la solution et quantifions l’erreur d’approximation
My thesis focuses on two main problems in studying the heat equation: Control problem and Inverseproblem.Our first concern is the null controllability of a semilinear heat equation which, if not controlled, can blow up infinite time. Roughly speaking, it consists in analyzing whether the solution of a semilinear heat equation, underthe Dirichlet boundary condition, can be driven to zero by means of a control applied on a subdomain in whichthe equation evolves. Under an assumption on the smallness of the initial data, such control function is builtup. The novelty of our method is computing the control function in a constructive way. Furthermore, anotherachievement of our method is providing a quantitative estimate for the smallness of the size of the initial datawith respect to the control time that ensures the null controllability property.Our second issue is the local backward problem for a linear heat equation. We study here the followingquestion: Can we recover the source of a linear heat equation, under the Dirichlet boundary condition, from theobservation on a subdomain at some time later? This inverse problem is well-known to be an ill-posed problem,i.e their solution (if exists) is unstable with respect to data perturbations. Here, we tackle this problem bytwo different regularization methods: The filtering method and The Tikhonov method. In both methods, thereconstruction formula of the approximate solution is explicitly given. Moreover, we also provide the errorestimate between the exact solution and the regularized one

APA, Harvard, Vancouver, ISO, and other styles

48

Anagurthi, Kumar. "Analytical solution for inverse heat conduction problem." Ohio : Ohio University, 1999. http://www.ohiolink.edu/etd/view.cgi?ohiou1176227397.

Full text

APA, Harvard, Vancouver, ISO, and other styles

49

Rao, Sachit Srinivasa. "Sliding mode control in mechanical, electrical and thermal distributed processes." Columbus, Ohio : Ohio State University, 2006. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1164817694.

Full text

APA, Harvard, Vancouver, ISO, and other styles

50

Siqueira, Sunni Ann. "Calculation of Time-Dependent Heat Flow in a Thermoelectric Sample." ScholarWorks@UNO, 2012. http://scholarworks.uno.edu/honors_theses/24.

Full text

Abstract:

In this project, the time-dependent one-dimensional heat equation with internal heating is solved using eigenfunction expansion, according to the thermoelectric boundary conditions. This derivation of the equation describing time-dependent heat flow in a thermoelectric sample or device yields a framework that scientists can use (by entering their own parameters into the equations) to predict the behavior of a system or to verify numerical calculations. Allowing scientists to predict the behavior of a system can help in decision making over whether a particular experiment is worthy of the time to construct and execute it. For experimentalists, it is valuable as a tool for comparison to validate the results of an experiment. The calculations done in this derivation can be applied to pulsed cooling systems, the analysis of Z-meter measurements, and other transient techniques that have yet to be invented. The vast majority of the calculations in this derivation were done by hand, but the parts that required numerical solutions, plotting, or powerful computation, were done using Mathematica 8. The process of filling in all the steps needed to arrive at a solution to the time-dependent heat equation for thermoelectrics yields many insights to the behavior of the various components of the system and provides a deeper understanding of such systems in general.

APA, Harvard, Vancouver, ISO, and other styles

Dissertations / Theses on the topic 'Heat equation'

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles