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John Crepeau - One of the best experts on this subject based on the ideXlab platform.

  • On the Stefan Problem With Internal Heat Generation and Prescribed Heat Flux Conditions at the Boundary
    ASME 2019 Heat Transfer Summer Conference, 2019
    Co-Authors: Lyudmyla L. Barannyk, John Crepeau, Sidney D. V. Williams, Olufolahan Irene Ogidan, Alexey Sakhnov
    Abstract:

    Abstract We study the evolution of the solid-liquid interface during melting and solidification of a material with constant Internal Heat Generation and prescribed Heat flux at the boundary for a plane wall and a cylinder. The equations are solved by splitting them into transient and steady-state components and then using separation of variables. This results in an ordinary differential equation for the interface that involves infinite series. The initial value problem is solved numerically, and solutions are compared to the previously published quasi-static solutions. We show that when the Internal Heat Generation and the Heat flux at the boundary are close in value to each other, the motion of the phase change front takes longer to reach steady-state than when the values are farther apart. As the difference between the Internal Heat Generation and the Heat flux increases, the transient solutions become more dominant and the numerical solution of the phase change front does not reach steady-state before the outer boundary or centerline is reached. The difference between the Internal Heat Generation and the Heat flux at the boundary can be used to control the motion and speed of the interface. The problem has applications for a nuclear fuel rod during meltdown.

  • Analytical solutions to the Stefan problem with Internal Heat Generation
    Applied Thermal Engineering, 2016
    Co-Authors: David Mccord, John Crepeau, Ali Siahpush, João Angelo Ferres Brogin
    Abstract:

    Abstract A first-order, ordinary differential equation modeling the Stefan problem (solid–liquid phase change) with Internal Heat Generation in a plane wall is derived and the solutions are compared to the results of a computational fluid dynamics analysis. The Internal Heat Generation term makes the governing equations non-homogeneous so the principle of superposition is used to separate the transient from steady-state portions of the Heat equation, which are then solved separately. There is excellent agreement between the solutions to the differential equation and the CFD results for the movement of both the solidification and melting fronts. The solid and liquid temperature profiles show a distinct difference in slope along the interface early in the phase change process. As time increases, the changes in slope decrease and the temperature profiles become parabolic. The system reaches steady-state faster for larger Stefan numbers and inversely, the time to steady-state increases as the Stefan number decreases.

  • Numerical and experimental investigation of melting with Internal Heat Generation within cylindrical enclosures
    Applied Thermal Engineering, 2014
    Co-Authors: Amber Shrivastava, Ali Siahpush, Brian G. Williams, Bruce M. Savage, John Crepeau
    Abstract:

    There have been significant efforts by the Heat transfer community to investigate the melting phenomenon of materials. These efforts have included the analytical development of equations to represent melting, numerical development of computer codes to assist in modeling the phenomena, and collection of experimental data. The understanding of the melting phenomenon has application in several areas of interest, for example, the melting of a Phase Change Material (PCM) used as a thermal storage medium as well as the melting of the fuel bundle in a nuclear power plant during an accident scenario. The objective of this research is two-fold. First a numerical investigation, using computational fluid dynamics (CFD), of melting with Internal Heat Generation for a vertical cylindrical geometry is presented. Second, to the best of authors knowledge, there are very limited number of engineering experimental results available for the case of melting with Internal Heat Generation (IHG). An experiment was performed to produce such data using resistive, or Joule, Heating as the IHG mechanism. The numerical results are compared against the experimental results and showed favorable correlation. Uncertainties in the numerical and experimental analysis are discussed. Based on the numerical and experimental analysis, recommendations are made for future work.

  • Scale/Analytical Analyses of Freezing and Convective Melting With Internal Heat Generation
    Volume 2: Heat Transfer Enhancement for Practical Applications; Heat and Mass Transfer in Fire and Combustion; Heat Transfer in Multiphase Systems; He, 2013
    Co-Authors: Ali Siahpush, John Crepeau, Piyush Sabharwall
    Abstract:

    Using a scale/analytical analysis approach, we model phase change (melting) for pure materials which generate constant Internal Heat Generation for small Stefan numbers (approximately one). The analysis considers conduction in the solid phase and natural convection, driven by Internal Heat Generation, in the liquid regime. The model is applied for a constant surface temperature boundary condition where the melting temperature is greater than the surface temperature in a cylindrical geometry. The analysis also consider constant Heat flux (in a cylindrical geometry). We show the time scales in which conduction and convection Heat transfer dominate.Copyright © 2013 by ASME

  • Solid–liquid phase change driven by Internal Heat Generation
    Comptes Rendus Mécanique, 2012
    Co-Authors: John Crepeau, Ali Siahpush
    Abstract:

    Abstract This article presents results of solid–liquid phase change, the Stefan Problem, where melting is driven Internal Heat Generation, in a cylindrical geometry. The comparison between a quasi-static analytical solution for Stefan numbers less than one and numerical solutions shows good agreement. The computational results of phase change with Internal Heat Generation show how convection cells form in the liquid region. A scale analysis of the same problem shows four distinct regions of the melting process.

Ali Siahpush - One of the best experts on this subject based on the ideXlab platform.

  • Analytical solutions to the Stefan problem with Internal Heat Generation
    Applied Thermal Engineering, 2016
    Co-Authors: David Mccord, John Crepeau, Ali Siahpush, João Angelo Ferres Brogin
    Abstract:

    Abstract A first-order, ordinary differential equation modeling the Stefan problem (solid–liquid phase change) with Internal Heat Generation in a plane wall is derived and the solutions are compared to the results of a computational fluid dynamics analysis. The Internal Heat Generation term makes the governing equations non-homogeneous so the principle of superposition is used to separate the transient from steady-state portions of the Heat equation, which are then solved separately. There is excellent agreement between the solutions to the differential equation and the CFD results for the movement of both the solidification and melting fronts. The solid and liquid temperature profiles show a distinct difference in slope along the interface early in the phase change process. As time increases, the changes in slope decrease and the temperature profiles become parabolic. The system reaches steady-state faster for larger Stefan numbers and inversely, the time to steady-state increases as the Stefan number decreases.

  • Numerical and experimental investigation of melting with Internal Heat Generation within cylindrical enclosures
    Applied Thermal Engineering, 2014
    Co-Authors: Amber Shrivastava, Ali Siahpush, Brian G. Williams, Bruce M. Savage, John Crepeau
    Abstract:

    There have been significant efforts by the Heat transfer community to investigate the melting phenomenon of materials. These efforts have included the analytical development of equations to represent melting, numerical development of computer codes to assist in modeling the phenomena, and collection of experimental data. The understanding of the melting phenomenon has application in several areas of interest, for example, the melting of a Phase Change Material (PCM) used as a thermal storage medium as well as the melting of the fuel bundle in a nuclear power plant during an accident scenario. The objective of this research is two-fold. First a numerical investigation, using computational fluid dynamics (CFD), of melting with Internal Heat Generation for a vertical cylindrical geometry is presented. Second, to the best of authors knowledge, there are very limited number of engineering experimental results available for the case of melting with Internal Heat Generation (IHG). An experiment was performed to produce such data using resistive, or Joule, Heating as the IHG mechanism. The numerical results are compared against the experimental results and showed favorable correlation. Uncertainties in the numerical and experimental analysis are discussed. Based on the numerical and experimental analysis, recommendations are made for future work.

  • Scale/Analytical Analyses of Freezing and Convective Melting With Internal Heat Generation
    Volume 2: Heat Transfer Enhancement for Practical Applications; Heat and Mass Transfer in Fire and Combustion; Heat Transfer in Multiphase Systems; He, 2013
    Co-Authors: Ali Siahpush, John Crepeau, Piyush Sabharwall
    Abstract:

    Using a scale/analytical analysis approach, we model phase change (melting) for pure materials which generate constant Internal Heat Generation for small Stefan numbers (approximately one). The analysis considers conduction in the solid phase and natural convection, driven by Internal Heat Generation, in the liquid regime. The model is applied for a constant surface temperature boundary condition where the melting temperature is greater than the surface temperature in a cylindrical geometry. The analysis also consider constant Heat flux (in a cylindrical geometry). We show the time scales in which conduction and convection Heat transfer dominate.Copyright © 2013 by ASME

  • Solid–liquid phase change driven by Internal Heat Generation
    Comptes Rendus Mécanique, 2012
    Co-Authors: John Crepeau, Ali Siahpush
    Abstract:

    Abstract This article presents results of solid–liquid phase change, the Stefan Problem, where melting is driven Internal Heat Generation, in a cylindrical geometry. The comparison between a quasi-static analytical solution for Stefan numbers less than one and numerical solutions shows good agreement. The computational results of phase change with Internal Heat Generation show how convection cells form in the liquid region. A scale analysis of the same problem shows four distinct regions of the melting process.

  • SCALE ANALYSIS OF CONVECTIVE MELTING WITH Internal Heat Generation
    ASME JSME 2011 8th Thermal Engineering Joint Conference, 2011
    Co-Authors: Ali Siahpush, John Crepeau
    Abstract:

    Using a scale analysis approach, we model phase change (melting) for pure materials which generate Internal Heat for small Stefan numbers (approximately one). The analysis considers conduction in the solid phase and natural convection, driven by Internal Heat Generation, in the liquid regime. The model is applied for a constant surface temperature boundary condition where the melting temperature is greater than the surface temperature in a cylindrical geometry. We show the time scales in which conduction and convection Heat transfer dominate.Copyright © 2011 by ASME

A Aziz - One of the best experts on this subject based on the ideXlab platform.

  • entropy Generation in a hollow cylinder with temperature dependent thermal conductivity and Internal Heat Generation with convective radiative surface cooling
    International Communications in Heat and Mass Transfer, 2012
    Co-Authors: Mohsen Torabi, A Aziz
    Abstract:

    Abstract This article investigates entropy Generation in an asymmetrically cooled hollow cylinder with temperature dependent thermal conductivity and Internal Heat Generation. The inside surface of the cylinder is cooled by convection on its inside surface while the outside surface experiences simultaneous convective–radiative cooling. The thermal conductivity of the cylinder as well as the Internal Heat Generation within the cylinder are linear functions of temperature, introducing two nonlinearities in the one-dimensional steady state Heat conduction equation. A third nonlinearity arises due to radiative Heat loss from the outside surface of the cylinder. The nonlinear system is solved analytically using the differential transformation method (DTM) to obtain the temperature distribution which is then used to compute local and total entropy Generation rates in the cylinder. The accuracy of DTM is verified by comparing its predictions with the analytical solution for the case of constant thermal conductivity and constant Internal Heat Generation. The local and total entropy Generations depend on six dimensionless parameters: Heat Generation parameter Q, thermal conductivity parameter β, conduction–convection parameters Nc1 and Nc2, conduction–radiation parameter Nr, convection sink temperature δ and radiation sink temperature η.

  • entropy Generation in an asymmetrically cooled slab with temperature dependent Internal Heat Generation
    Heat Transfer Research, 2012
    Co-Authors: A Aziz, Waqar Ahmed Khan
    Abstract:

    The paper presents an entropy Generation analysis for steady conduction in a slab with temperature-dependent volumetric Internal Heat Generation. The slab experiences asymmetric convective cooling on its two faces. The exact analytical solution for the temperature distribution is used to compute dimensionless local and total entropy Generation rates in the slab. The total entropy Generation rate depends on five dimensionless parameters: reference Heat Generation temperature Q, the Heat Generation–temperature variation parameter a, the temperature asymmetry parameter λ, and Biot numbers Bi1 and Bi2. Graphs illustrating the effect of these five parameters on the local and total entropy Generation rates are presented and discussed. It is found that the total entropy Generation in the slab can be minimized with a suitable choice of the cooling parameters. The paper corrects the flawed entropy results published recently. The present results for the special case of uniform Internal Heat Generation confirm the results presented in a 2003 paper. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.20404

  • a least squares method for a longitudinal fin with temperature dependent Internal Heat Generation and thermal conductivity
    Energy Conversion and Management, 2011
    Co-Authors: A Aziz, M N Bouaziz
    Abstract:

    Approximate but highly accurate solutions for the temperature distribution, fin efficiency, and optimum fin parameter for a constant area longitudinal fin with temperature dependent Internal Heat Generation and thermal conductivity are derived analytically. The method of least squares recently used by the authors is applied to treat the two nonlinearities, one associated with the temperature dependent Internal Heat Generation and the other due to temperature dependent thermal conductivity. The solution is built from the classical solution for a fin with uniform Internal Heat Generation and constant thermal conductivity. The results are presented graphically and compared with the direct numerical solutions. The analytical solutions retain their accuracy (within 1% of the numerical solution) even when there is a 60% increase in thermal conductivity and Internal Heat Generation at the base temperature from their corresponding values at the sink temperature. The present solution is simple (involves hyperbolic functions only) compared with the fairly complex approximate solutions based on the homotopy perturbation method, variational iteration method, and the double series regular perturbation method and offers high accuracy. The simple analytical expressions for the temperature distribution, the fin efficiency and the optimum fin parameter are convenient for use by engineers dealing with the design and analysis of Heat generating fins operating with a large temperature difference between the base and the environment.

Lelio Luzzi - One of the best experts on this subject based on the ideXlab platform.

  • dynamic stability of natural circulation loops for single phase fluids with Internal Heat Generation
    Chemical Engineering Science, 2015
    Co-Authors: D E Ruiz, Antonio Cammi, Lelio Luzzi
    Abstract:

    Previous studies have investigated the dynamic stability of natural circulating flows inside closed loops. The systems considered have an external Heat source, and the circulating fluids do not generate Heat Internally. In this work, the effects of Internal Heat Generation on the stability of natural circulating flows are investigated for the first time. A semianalytical linear method and a numerical nonlinear method are applied in order to characterize the effects of Internal Heat Generation on the stability maps of different closed loop configurations. Results show that when Internal Heat Generation dominates the external Heat source, it can modify the shape and area of the stability regions. Among the different loop configurations studied, the Vertical Heater-Vertical Cooler (VHVC) configuration shows a better stability behavior.

  • A generalized approach to Heat transfer in pipe flow with Internal Heat Generation
    Chemical Engineering Science, 2010
    Co-Authors: Valentino Di Marcello, Antonio Cammi, Lelio Luzzi
    Abstract:

    Abstract In the last few years, there has been a renewed interest in the molten salt reactor (MSR), one of the “Generation IV International Forum” concepts, which adopts a circulating molten salt mixture as both Heat generator (fuel) and coolant. The Heat transfer of a fluid with Internal Heat Generation depends on the strength of the source whose influence on the Heat exchange process is significant enough to demand consideration. At present, few studies have been performed on the subject from either an experimental or a numerical point of view. This study considers fluids with a wide range of Reynolds numbers, flowing through smooth and straight circular tubes within which the flow is hydrodynamically developed but thermally developing (conditions of interest for MSR core channels). The study aims at an assessment of the Heat transfer modelling for a large variety of fluids (with Prandtl numbers in the range 0≤Pr≤10 4 ), in particular taking into account the influence of the Internal Heat Generation on the temperature distribution, which plays an important role in the case of molten salts for nuclear reactors. To this purpose, the general and unified solution of the Heat transfer equation is applied to the turbulent Graetz problem with boundary conditions of the third kind and arbitrary Heat source distribution, incorporating recent formulations for turbulent flow and convection. Computed results are shown to be in a good agreement with experimental data concerning Heat transfer evaluations for both fully developed and thermally developing flow conditions, over a large range of Prandtl numbers (10 −2 4 ). Finally, a preliminary correlation, which includes the Prandtl number range of interest for molten salts, is proposed for the Nusselt number predictions in the case of simultaneous uniform wall Heat flux and Internal Heat Generation.

Chetna M. Bhongade - One of the best experts on this subject based on the ideXlab platform.

  • Effect of Michell function on the thickness of circular plate with Internal Heat Generation
    IOSR Journal of Mathematics, 2014
    Co-Authors: Chetna M. Bhongade, H. Durge
    Abstract:

    The present paper deals with the determination of displacement and thermal transient stresses in a thick ( ) circular plate with Internal Heat Generation. External arbitrary Heat supply is applied at the upper surface of a thick ( ) circular plate, whereas the lower surface of a thick ( ) circular plate is insulated and the Heat is dissipated due to convection in surrounding through lateral surface. Here we compute the effect of Michell function on the thickness of circular plate with Internal Heat Generation. The governing Heat conduction equation has been solved by using integral transform method and the results are obtained in series form in terms of Bessel's functions and the results for temp erature change and stresses have been computed numerically and illustrated graphically. Keywords:Thick plate ( ) Thin plate ( ) , Internal Heat Generation, thermal stresses.

  • AN INVERSE STEADY STATE THERMAL STRESSES IN A LIMITING THICK CIRCULAR PLATE WITH Internal Heat Generation
    Asian Journal of Current Engineering and Maths, 2013
    Co-Authors: Chetna M. Bhongade, M. H. Durge
    Abstract:

    The present paper deals with the determination of temperature, displacement and thermal stresses in a limiting thick circular plate with Internal Heat Generation. A limiting thick circular plate is subjected to arbitrary known interior temperature under steady state, the fixed circular edge of limiting circular plate are thermally insulated and lower surface of limiting circular plate is kept at zero temperature. Here we compute the effects of Internal Heat Generation in terms of stresses along radial direction and modify Kulkarni V. S. (2008). The governing Heat conduction equation has been solved by the method of integral transform technique. The results are obtained in a series form in terms of Bessel’s functions. The results for stresses have been computed numerically and illustrated graphically.

  • Some study of Thermoelastic Steady State behavior of Thick annular disc with Internal Heat Generation
    IOSR Journal of Mathematics, 2013
    Co-Authors: Chetna M. Bhongade, M. H. Durge
    Abstract:

    The present paper deals with the determination of displacement and thermal stresses in a thick annular disc with Internal Heat Generation. Arbitrary Heat �� �� is applied on the upper surface of disc whereas lower surface dissipates Heat by convection and the fixed circular edge are thermally insulated. Here we compute the effects of Internal Heat Generation of a thick annular disc in terms of stresses along radial direction. The governing Heat conduction equation has been solved by the method of integral transform technique. The results are obtained in a series form in terms of Bessel's functions. The results for temperature change, displacement and stresses have been computed numerically and illustrated graphically.