Relevant bibliographies by topics / Fractional order heat equation

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Fractional order heat equation'

Author: Grafiati
Published: 5 June 2025
Last updated: 2 August 2025

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

Select a source type:

Consult the lists of relevant articles, books, theses, conference reports, and other scholarly sources on the topic 'Fractional order heat equation.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Journal articles on the topic "Fractional order heat equation"

1

Kosmakova, M. T., S. A. Iskakov, and L. Zh Kasymova. "To solving the fractionally loaded heat equation." BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 101, no. 1 (2021): 65–77. http://dx.doi.org/10.31489/2021m1/65-77.

Full text
Abstract:
In this paper we consider a boundary value problem for a fractionally loaded heat equation in the class of continuous functions. Research methods are based on an approach to the study of boundary value problems, based on their reduction to integral equations. The problem is reduced to a Volterra integral equation of the second kind by inverting the differential part. We also carried out a study the limit cases for the fractional derivative order of the term with a load in the heat equation of the boundary value problem. It is shown that the existence and uniqueness of solutions to the integral
APA, Harvard, Vancouver, ISO, and other styles
2

Gundogdu, Hami, and Ömer Gozukizil. "On the approximate numerical solutions of fractional heat equation with heat source and heat loss." Thermal Science, no. 00 (2021): 321. http://dx.doi.org/10.2298/tsci210713321g.

Full text
Abstract:
In this paper, we are interested in obtaining an approximate numerical solution of the fractional heat equation where the fractional derivative is in Caputo sense. We also consider the heat equation with a heat source and heat loss. The fractional Laplace-Adomian decomposition method is applied to gain the approximate numerical solutions of these equations. We give the graphical representations of the solutions depending on the order of fractional derivatives. Maximum absolute error between the exact solutions and approximate solutions depending on the fractional-order are given. For the last
APA, Harvard, Vancouver, ISO, and other styles
3

Kochubei, Anatoly N., Yuri Kondratiev, and José Luís da Silva. "On fractional heat equation." Fractional Calculus and Applied Analysis 24, no. 1 (2021): 73–87. http://dx.doi.org/10.1515/fca-2021-0004.

Full text
Abstract:
Abstract In this paper, the long-time behavior of the Cesaro mean of the fundamental solution for fractional Heat equation corresponding to random time changes in the Brownian motion is studied. We consider both stable subordinators leading to equations with the Caputo-Djrbashian fractional derivative and more general cases corresponding to differential-convolution operators, in particular, distributed order derivatives.
APA, Harvard, Vancouver, ISO, and other styles
4

Verma, Ninny, and Dr Anil Kumar Menaria. "FRACTIONAL ORDER DISTRIBUTION ON HEAT FLUX FOR CRYSTALLINE CONCRETE MATERIAL." INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER RESEARCH 11, no. 02 (2023): 3268–72. http://dx.doi.org/10.47191/ijmcr/v11i2.08.

Full text
Abstract:
The present work devoted to analyse the impact of fractional order one dimensional heat equation on heat transfer in concrete substances, during conduction process. Throughout the evolution the thermal properties of substances are considered as constant parameters. Investigations were done through statistical phenomena with linear representation of curve.
APA, Harvard, Vancouver, ISO, and other styles
5

Alkhasov, A. B., R. P. Meilanov, and M. R. Shabanova. "Heat conduction equation in fractional-order derivatives." Journal of Engineering Physics and Thermophysics 84, no. 2 (2011): 332–41. http://dx.doi.org/10.1007/s10891-011-0477-9.

Full text
APA, Harvard, Vancouver, ISO, and other styles
6

Khan, Hassan, Rasool Shah, Poom Kumam, and Muhammad Arif. "Analytical Solutions of Fractional-Order Heat and Wave Equations by the Natural Transform Decomposition Method." Entropy 21, no. 6 (2019): 597. http://dx.doi.org/10.3390/e21060597.

Full text
Abstract:
In the present article, fractional-order heat and wave equations are solved by using the natural transform decomposition method. The series form solutions are obtained for fractional-order heat and wave equations, using the proposed method. Some numerical examples are presented to understand the procedure of natural transform decomposition method. The natural transform decomposition method procedure has shown that less volume of calculations and a high rate of convergence can be easily applied to other nonlinear problems. Therefore, the natural transform decomposition method is considered to b
APA, Harvard, Vancouver, ISO, and other styles
7

Blasiak, Slawomir. "Heat Transfer Analysis for Non-Contacting Mechanical Face Seals Using the Variable-Order Derivative Approach." Energies 14, no. 17 (2021): 5512. http://dx.doi.org/10.3390/en14175512.

Full text
Abstract:
This article presents a variable-order derivative (VOD) time fractional model for describing heat transfer in the rotor or stator in non-contacting mechanical face seals. Most theoretical studies so far have been based on the classical equation of heat transfer. Recently, constant-order derivative (COD) time fractional models have also been used. The VOD time fractional model considered here is able to provide adequate information on the heat transfer phenomena occurring in non-contacting face seals, especially during the startup. The model was solved analytically, but the characteristic featu
APA, Harvard, Vancouver, ISO, and other styles
8

Li, Shu-Nan, and Bing-Yang Cao. "Fractional-order heat conduction models from generalized Boltzmann transport equation." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378, no. 2172 (2020): 20190280. http://dx.doi.org/10.1098/rsta.2019.0280.

Full text
Abstract:
The relationship between fractional-order heat conduction models and Boltzmann transport equations (BTEs) lacks a detailed investigation. In this paper, the continuity, constitutive and governing equations of heat conduction are derived based on fractional-order phonon BTEs. The underlying microscopic regimes of the generalized Cattaneo equation are thereafter presented. The effective thermal conductivity κ eff converges in the subdiffusive regime and diverges in the superdiffusive regime. A connection between the divergence and mean-square displacement 〈|Δ x | 2 〉 ∼ t γ is established, namely
APA, Harvard, Vancouver, ISO, and other styles
9

Shammakh, Wafa, A. George Maria Selvam, Vignesh Dhakshinamoorthy, and Jehad Alzabut. "Stability of Boundary Value Discrete Fractional Hybrid Equation of Second Type with Application to Heat Transfer with Fins." Symmetry 14, no. 9 (2022): 1877. http://dx.doi.org/10.3390/sym14091877.

Full text
Abstract:
The development in the qualitative theory of fractional differential equations is accompanied by discrete analog which has been studied intensively in recent past. Suitable fixed point theorem is to be selected to study the boundary value discrete fractional equations due to the properties exhibited by fractional difference operators. This article aims at investigating the stability results in the sense of Hyers and Ulam with application of Mittag–Leffler function hybrid fractional order difference equation of second type. The symmetric structure of the operators defined in this article is vit
APA, Harvard, Vancouver, ISO, and other styles
10

Alharthi, Nadiyah Hussain, Abdon Atangana, and Badr S. Alkahtani. "Numerical analysis of some partial differential equations with fractal-fractional derivative." AIMS Mathematics 8, no. 1 (2022): 2240–56. http://dx.doi.org/10.3934/math.2023116.

Full text
Abstract:
<abstract> <p>In this study, we expanded the partial differential equation framework to which fractal-fractional differentiation can be applied. For this, we employed the generalized Mittag-Leffler function, and the fractal-fractional derivatives based on the power-law kernel. A general partial differential equation with the fractal-fractional derivative, the power law kernel and the generalized Mittag-Leffler function was thoroughly examined. There is almost no numerical scheme for solving partial differential equations with fractal-fractional derivatives, as less investigation ha
APA, Harvard, Vancouver, ISO, and other styles
More sources

Dissertations / Theses on the topic "Fractional order heat equation"

1

Tapdigoglu, Ramiz. "Inverse problems for fractional order differential equations." Thesis, La Rochelle, 2019. http://www.theses.fr/2019LAROS004/document.

Full text
Abstract:
Dans cette thèse, nous nous intéressons à résoudre certains problèmes inverses pour des équations différentielles aux dérivées fractionnaires. Un problème inverse est généralement mal posé. Un problème mal posé est un problème qui ne répond pas à l’un des trois critères de Hadamard pour être bien posé, c’est-à-dire, soit l’existence, l’unicité ou une dépendance continue aux données n'est plus vraie, à savoir, des petits changements dans les données de mesure entraînent des changements indéfiniment importants dans la solution. La plupart des difficultés à résoudre des problèmes mal posés sont c
APA, Harvard, Vancouver, ISO, and other styles
2

Farquhar, Megan Elizabeth. "Cardiac modelling with fractional calculus: An efficient computational framework for modelling the propagation of electrical impulses in the heart." Thesis, Queensland University of Technology, 2018. https://eprints.qut.edu.au/120682/1/__qut.edu.au_Documents_StaffHome_StaffGroupH%24_halla_Desktop_Megan_Farquhar_Thesis.pdf.

Full text
Abstract:
Heart failure is one of the most common causes of death in the western world. Many heart problems are linked to disturbances in cardiac electrical activity. Further understanding of how electrical impulses propagate through the heart may lead to new diagnosis and treatment options. Using our novel numerical scheme, we are able to conduct preliminary investigations into the effect of fixed and variable order fractional Laplacian operators for modelling propagation of electrical impulses through the heart. We implement our numerical framework to solve the coupled monodomain, Beeler-Reuter mod
APA, Harvard, Vancouver, ISO, and other styles
3

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
4

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
5

Tyler, Jonathan G. "Analysis and Implementation of High-Order Compact Finite Difference Schemes." BYU ScholarsArchive, 2007. https://scholarsarchive.byu.edu/etd/1278.

Full text
Abstract:
The derivation of centered compact schemes at interior and boundary grid points is performed and an analysis of stability and computational efficiency is given. Compact schemes are high order implicit methods for numerical solutions of initial and/or boundary value problems modeled by differential equations. These schemes generally require smaller stencils than the traditional explicit finite difference counterparts. To avoid numerical instabilities at and near boundaries and in regions of mesh non-uniformity, a numerical filtering technique is employed. Experiments for non-stationary linear p
APA, Harvard, Vancouver, ISO, and other styles
6

Atwell, Jeanne A. "Proper Orthogonal Decomposition for Reduced Order Control of Partial Differential Equations." Diss., Virginia Tech, 2000. http://hdl.handle.net/10919/26985.

Full text
Abstract:
Numerical models of PDE systems can involve very large matrix equations, but feedback controllers for these systems must be computable in real time to be implemented on physical systems. Classical control design methods produce controllers of the same order as the numerical models. Therefore, emph{reduced} order control design is vital for practical controllers. The main contribution of this research is a method of control order reduction that uses a newly developed low order basis. The low order basis is obtained by applying Proper Orthogonal Decomposition (POD) to a set of functional gains
APA, Harvard, Vancouver, ISO, and other styles
7

Talarcek, Steven C. "An Experimental Study of Disturbance Compensation and Control for a Fractional-Order System." University of Akron / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=akron1542303891784113.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

Abdelsheed, Ismail Gad Ameen. "Fractional calculus: numerical methods and SIR models." Doctoral thesis, Università degli studi di Padova, 2016. http://hdl.handle.net/11577/3422267.

Full text
Abstract:
Fractional calculus is ”the theory of integrals and derivatives of arbitrary order, which unify and generalize the notions of integer-order differentiation and n-fold integration”. The idea of generalizing differential operators to a non-integer order, in particular to the order 1/2, first appears in the correspondence of Leibniz with L’Hopital (1695), Johann Bernoulli (1695), and John Wallis (1697) as a mere question or maybe even play of thoughts. In the following three hundred years a lot of mathematicians contributed to the fractional calculus: Laplace (1812), Lacroix (1812), Fourier (1822
APA, Harvard, Vancouver, ISO, and other styles
9

Hejazi, Hala Ahmad. "Finite volume methods for simulating anomalous transport." Thesis, Queensland University of Technology, 2015. https://eprints.qut.edu.au/81751/1/Hala%20Ahmad_Hejazi_Thesis.pdf.

Full text
Abstract:
In this thesis a new approach for solving a certain class of anomalous diffusion equations was developed. The theory and algorithms arising from this work will pave the way for more efficient and more accurate solutions of these equations, with applications to science, health and industry. The method of finite volumes was applied to discretise the spatial derivatives, and this was shown to outperform existing methods in several key respects. The stability and convergence of the new method were rigorously established.
APA, Harvard, Vancouver, ISO, and other styles
10

Badía, José M., Peter Benner, Rafael Mayo, Enrique S. Quintana-Ortí, Gregorio Quintana-Ortí, and Jens Saak. "Parallel Order Reduction via Balanced Truncation for Optimal Cooling of Steel Profiles." Universitätsbibliothek Chemnitz, 2006. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200601566.

Full text
Abstract:
We employ two efficient parallel approaches to reduce a model arising from a semi-discretization of a controlled heat transfer process for optimal cooling of a steel profile. Both algorithms are based on balanced truncation but differ in the numerical method that is used to solve two dual generalized Lyapunov equations, which is the major computational task. Experimental results on a cluster of Intel Xeon processors compare the efficacy of the parallel model reduction algorithms.
APA, Harvard, Vancouver, ISO, and other styles
More sources

Books on the topic "Fractional order heat equation"

1

Hartley, T. T. A solution to the fundamental linear fractional order differential equation. National Aeronautics and Space Administration, Lewis Research Center, 1998.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
2

Povstenko, Yuriy. Linear Fractional Diffusion-Wave Equation for Scientists and Engineers. Birkhäuser, 2015.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
3

Povstenko, Yuriy. Linear Fractional Diffusion-Wave Equation for Scientists and Engineers. Birkhäuser, 2016.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
4

Povstenko, Yuriy. Linear Fractional Diffusion-Wave Equation for Scientists and Engineers. Birkhauser Verlag, 2015.

Find full text
APA, Harvard, Vancouver, ISO, and other styles

Book chapters on the topic "Fractional order heat equation"

1

Grubb, Gerd. "Fractional-Order Operators: Boundary Problems, Heat Equations." In Mathematical Analysis and Applications—Plenary Lectures. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-00874-1_2.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Obrączka, Anna, and Jakub Kowalski. "Heat Transfer Modeling in Ceramic Materials Using Fractional Order Equations." In Lecture Notes in Electrical Engineering. Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-00933-9_20.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Colombo, Fabrizio, and Jonathan Gantner. "The fractional heat equation using quaternionic techniques." In Quaternionic Closed Operators, Fractional Powers and Fractional Diffusion Processes. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-16409-6_9.

Full text
APA, Harvard, Vancouver, ISO, and other styles
4

Deya, Aurélien, and Samy Tindel. "Malliavin Calculus for Fractional Heat Equation." In Malliavin Calculus and Stochastic Analysis. Springer US, 2013. http://dx.doi.org/10.1007/978-1-4614-5906-4_16.

Full text
APA, Harvard, Vancouver, ISO, and other styles
5

Goldstein, Gisèle Ruiz, Jerome A. Goldstein, Davide Guidetti, and Silvia Romanelli. "The Fourth Order Wentzell Heat Equation." In Semigroups of Operators – Theory and Applications. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-46079-2_12.

Full text
APA, Harvard, Vancouver, ISO, and other styles
6

Atanacković, Teodor M., Sanja Konjik, and Stevan Pilipović. "Wave equation involving fractional derivatives of real and complex fractional order." In Fractional Differential Equations, edited by Anatoly Kochubei and Yuri Luchko. De Gruyter, 2019. http://dx.doi.org/10.1515/9783110571660-015.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

Pitolli, Francesca, and Laura Pezza. "A Fractional Spline Collocation Method for the Fractional-order Logistic Equation." In Approximation Theory XV: San Antonio 2016. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-59912-0_15.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

Povstenko, Yuriy. "Thermoelasticity Based on Space-Time-Fractional Heat Conduction Equation." In Solid Mechanics and Its Applications. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-15335-3_6.

Full text
APA, Harvard, Vancouver, ISO, and other styles
9

Povstenko, Yuriy. "Thermoelasticity Based on Space-Time-Fractional Heat Conduction Equation." In Solid Mechanics and Its Applications. Springer International Publishing, 2024. http://dx.doi.org/10.1007/978-3-031-64587-7_6.

Full text
APA, Harvard, Vancouver, ISO, and other styles
10

Atangana, Abdon, and Anum Shafiq. "Volterra Equation with Constant Fractional Order and Variable Order Fractal Dimension." In Advances in Mathematical Modelling, Applied Analysis and Computation. Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-0179-9_17.

Full text
APA, Harvard, Vancouver, ISO, and other styles

Conference papers on the topic "Fractional order heat equation"

1

Tseng, Chien-Cheng, and Su-Ling Lee. "Fractional Heat Kernel Smoothing Using Fractional Order Graph Laplacian Matrix." In 2024 IEEE 13th Global Conference on Consumer Electronics (GCCE). IEEE, 2024. https://doi.org/10.1109/gcce62371.2024.10760829.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Thangavelu and S. Padmasekaran. "The exact solutions of heat equation by RDTM for the fractional order." In PROCEEDINGS OF INTERNATIONAL CONFERENCE ON ADVANCES IN MATERIALS RESEARCH (ICAMR - 2019). AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0017176.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Dong, Guanqiang, Mingcong Deng, and Longguo Jin. "Modeling of a spiral heat exchanger using fractional order equation and GPU." In 2019 International Conference on Advanced Mechatronic Systems (ICAMechS). IEEE, 2019. http://dx.doi.org/10.1109/icamechs.2019.8861652.

Full text
APA, Harvard, Vancouver, ISO, and other styles
4

Sierociuk, Dominik, Andrzej Dzielin´ski, Grzegorz Sarwas, Ivo Petras, Igor Podlubny, and Tomas Skovranek. "Modeling Heat Transfer in Heterogeneous Media Using Fractional Calculus." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-47374.

Full text
Abstract:
The paper presents the results of modeling the heat transfer process in heterogeneous media with the assumption that part of the heat flux is dispersed in the air around the beam. The heat transfer process in solid material (beam) can be described by integer order partial differential equation. However, in heterogeneous media it can be described by sub- or hyperdiffusion equation which results in fractional order partial differential equation. Taking into consideration that the part of the heat flux is dispersed into the neighbouring environment we additionally modify the main relation between
APA, Harvard, Vancouver, ISO, and other styles
5

Mamatov, Mashrabzhon Shakhabutdinovich. "Differential games of pursuit for the two-dimensional heat equation with derivatives of fractional order." In International Conference "Optimal Control and Differential Games" dedicated to the 110th anniversary of L. S. Pontryagin. Steklov Mathematical Institute, 2018. http://dx.doi.org/10.4213/proc23006.

Full text
APA, Harvard, Vancouver, ISO, and other styles
6

Mesquita, Maximilian S., and Marcelo J. S. de Lemos. "Mass Transport Modeling for Turbulent Flow in Saturated Porous Media." In ASME 2003 Heat Transfer Summer Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/ht2003-47251.

Full text
Abstract:
This paper presents derivations of mass transport equations for turbulent flow in permeable structures. Equations are developed following two distinct procedures. The first method considers time averaging of the local instantaneous mass transport equation before the volume average operator is applied. The second methodology employs both averaging operators but in a reverse order. This work is intended to demonstrate that both approaches lead to equivalent equations when one takes into account both time fluctuations and spatial deviations of velocity and mass fraction. A modeled form for the fi
APA, Harvard, Vancouver, ISO, and other styles
7

Liu, Yaqing, Liancun Zheng, Xinxin Zhang, and Fenglei Zong. "The MHD Flows for a Heated Generalized Oldroyd-B Fluid With Fractional Derivative." In 2010 14th International Heat Transfer Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/ihtc14-22278.

Full text
Abstract:
In this paper, we present a circular motion of magnetohydrodynamic (MHD) flow for a heated generalized Oldroyd-B fluid. The fractional calculus approach is introduced to establish the constitutive relationship of a viscoelastic fluid. The velocity and temperature fields of the flow are described by fractional partial differential equations. Exact analytical solutions of velocity and temperature fields are obtained by using Hankel transform and Laplace transform for fractional calculus. Results for ordinary viscous flow are deduced by making the fractional order of differential tend to one and
APA, Harvard, Vancouver, ISO, and other styles
8

El-Shahed, Moustafa. "Fractional Calculus Model of the Semilunar Heart Valve Vibrations." In ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/detc2003/vib-48384.

Full text
Abstract:
The objective of this paper is to solve the equation of motion of semilunar heart valve vibrations. The vibrations of the closed semilunar valves were modeled with a Caputo hactional derivative of order α. With the help of Laplace transformation, closed-form solution is obtained for the equation of motion in terms of Mittag-Leffler function. An alternative Method for Semi-differential equation, when α = 0.5, is examined using MATHEMATICA. The simplicity of these solutions makes them ideal for testing the accuracy of numerical methods. This solution can be of some interest for a better fit of e
APA, Harvard, Vancouver, ISO, and other styles
9

Youssef, Hamdy M., Khaled A. Elsibai, and Alaa A. El-Bary. "Fractional Order Thermoelastic Waves of Cylindrical Gold Nano-Beam." In ASME 2013 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/imece2013-62876.

Full text
Abstract:
In this work, a mathematical model of cylindrical nano-beam with constant elastic parameters with fractional order heat conduction will be constructed. The governing equations of the mathematical model will be taken when the beam is quiescent first. Laplace transforms techniques will be used to get the general solution for any set of boundary conditions. The solution will be obtained for a certain model when the beam is subjected to thermal load. Inversion of Laplace transforms will be obtained numerically, and the results will be presented graphically with some comparisons to study the impact
APA, Harvard, Vancouver, ISO, and other styles
10

Li, Like, Renwei Mei, and James F. Klausner. "Heat Transfer in Thermal Lattice Boltzmann Equation Method." In ASME 2012 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/imece2012-87990.

Full text
Abstract:
The evaluation of the boundary heat flux and total heat transfer in the lattice Boltzmann equation (LBE) simulations is investigated. The boundary heat fluxes in the discrete velocity directions of the thermal LBE (TLBE) model are obtained directly from the temperature distribution functions at the lattice nodes. With the rectangular lattice uniformly spaced the effective surface area for the discrete heat flux is the unit spacing distance, thus the heat flux integration becomes simply a summation of all the discrete heat fluxes with constant surface areas. The present method for the evaluatio
APA, Harvard, Vancouver, ISO, and other styles
You might also be interested in the extended bibliographies on the topic 'Fractional order heat equation' for particular source types:
Journal articles Dissertations / Theses
We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!

To the bibliography