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2018 | OriginalPaper | Buchkapitel

1. Macroscopic Heat Conduction Formulation

verfasst von : Leandro A. Sphaier, Jian Su, Renato Machado Cotta

Erschienen in: Handbook of Thermal Science and Engineering

Verlag: Springer International Publishing

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Abstract

In this chapter, mathematical formulations of macroscopic heat conduction are derived from the First Law of Thermodynamics. Specific forms of the heat conduction equation in isotropic media are given in Cartesian, Cylindrical, and Spherical coordinates systems, as well as in a general orthogonal coordinate system. Heat conduction equations in anisotropic media and in heterogeneous media are then derived. Mathematical formulations of one-dimensional transient heat conduction with phase change and in multilayered composite media are presented. Finally, classical and improved lumped parameter formulations for transient heat conduction problems are analyzed more closely. The so-called Coupled Integral Equations Approach (CIEA) is reviewed as a problem reformulation and simplification tool in heat and mass diffusion. The averaged temperature and heat flux, in one or more space coordinates, are approximated by Hermite formulae for integrals, yielding analytic relations between boundary and average temperatures, to be used in place of the usual plain equality assumed in the classical lumped system analysis. The accuracy gains achieved through the improved lumped-differential formulations are then illustrated through a few typical examples.

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Nächstes Kapitel Analytical Methods in Heat Transfer

English translation reprint in (Fourier 1878).

Alves LSB, Sphaier LA, Cotta RM (2000) Error analysis of mixed lumped-differential formulations in diffusion problems. Hybrid Methods Eng 2(4):409–435CrossRef

An C, Su J (2011) Improved lumped models for transient combined convective and radiative cooling of multi-layer composite slabs. Appl Therm Eng 31(14–15):2508–2517CrossRef

An C, Su J (2013) Lumped parameter model for one-dimensional melting in a slab with volumetric heat generation. Appl Therm Eng 60(1–2):387–396CrossRef

An C, Su J (2015) Lumped models for transient thermal analysis of multilayered composite pipeline with active heating. Appl Therm Eng 87:749–759CrossRef

Aparecido JB, Cotta RM (1990) Improved one-dimensional fin solutions. Heat Transf Eng 11(1):49–59CrossRef

Aparecido JB, Cotta RM, Özişik MN (1989) Analytical solutions to two-dimensional diffusion type problems in irregular geometries. J Franklin Inst 326:421–434MathSciNetMATHCrossRef

Arpaci VS (1966) Conduction heat transfer. Addison-Wesley, ReadingMATH

Aziz A, Kraus AD (1995) Transient heat transfer in extended surfaces. Appl Mech Rev 48(7):317–350CrossRef

Barbosa Mota JP, Rodrigues AE, Saatdjian E, Tondeur D (1997) Charge dynamics of methane adsorption storage system: intraparticle diffusional effects. Adsorption 3(2):117–125CrossRef

Barbuto FAA, Cotta RM (1997) Integral transformation of elliptic problems within irregular domains: fully developed channel flow. Int J Numer Methods Heat Fluid Flow 7(8):778–793MathSciNetMATHCrossRef

Barozzi GS, Pagliarini G (1985) A method to solve conjugate heat-transfer problems – the case of fully-developed laminar-flow in a pipe. J Heat Transf Trans ASME 107(1):77–83CrossRef

Bastos-Neto M, Torres AEB, Azevedo DCS, Cavalcante CL Jr (2005) A theoretical and experimental study of charge and discharge cycles in a storage vessel for adsorbed natural gas. Adsorption 11(2):147–157CrossRef

Benther JD, Sphaier LA (2015) One-dimensional formulation for heat and mass transfer in solid desiccant dehydration of natural gas. Heat Transf Eng 36(11):952–962CrossRef

Bird RB, Stewart WE, Lightfoot EN (2002) Transport phenomena, 2nd edn. Wiley, New York

Campo A, Schuler C (1988) Heat-transfer in laminar-flow through circular tubes accounting for two-dimensional wall conduction. Int J Heat Mass Transf 31(11):2251–2259CrossRef

Carslaw HS, Jaeger JC (1959) Conduction of heat in solids. Clarendon Press, LondonMATH

Cattaneo C (1958) Sur une forme de l’équation de la chaleur éliminant le paradoxe d’une propagation instantanée. Comptes Rendus 247(4):431–433MATH

Cengel YA, Boles MA (1998) Thermodynamics: an engineering approach, 3rd edn. WCB/McGraw-Hill, Hightstown

Cheroto S, Guigon SMS, Ribeiro JW, Cotta RM (1997) Lumped-differential formulations for drying in capillary porous media. Dry Technol 15(3):811–835CrossRef

Chester M (1963) Second sound in solids. Phys Rev 131(5):2013CrossRef

Corrêa EJ, Cotta RM (1998) Enhanced lumped-differential formulations of diffusion problems. Appl Math Model 22(3):137–152MATHCrossRef

Cotta RM (1998) Improved lumped-differential formulations in heat transfer, Chapter 10. In: Sun-den B, Faghri M (eds) Modelling of engineering heat transfer phenomena, vol 2. Computational Mechanics Publications, Southampton, pp 293–325

Cotta RM, Mikhailov MD (1997) Heat conduction – lumped analysis, integral transforms, symbolic computation. Wiley, Chichester

Cotta RM, Ozisik MN, Mennig J (1990) Coupled integral-equation approach for solving phase-change problems in a finite slab. J Franklin Inst 327(2):225–234MATHCrossRef

Cotta RM, Ungs MJ, Mikhailov MD (2003) Contaminant transport in finite fractured porous medium: integral transforms and lumped-differential formulations. Ann Nucl Energy 30(3):261–285CrossRef

Cotta RM, Knupp DC, Naveira-Cotta CP (2016) Analytical heat and fluid flow in microchannels and microsystems. Mechanical engineering series. Springer, ChamMATHCrossRef

da Silva MJM, Sphaier LA (2010) Dimensionless lumped formulation for performance assessment of adsorbed natural gas storage. Appl Energy 87(5):1572–1580CrossRef

Dantas LB, Orlande HRB, Cotta RM (2002) Estimation of dimensionless parameters of Luikov’s system for heat and mass transfer in capillary porous media. Int J Therm Sci 41(3):217–227CrossRef

Dantas LB, Orlande HRB, Cotta RM (2003) An inverse problem of parameter estimation for heat and mass transfer in capillary porous media. Int J Heat Mass Transf 46(9):1587–1598MATHCrossRef

Dantas LB, Orlande HRB, Cotta RM (2007) Improved lumped-differential formulations and hybrid solution methods for drying in porous media. Int J Therm Sci 46(9):878–889CrossRef

De Souza JRB, Lisboa KM, Cerqueira IG, Zotin JLZ, Naveira-Cotta CP, Cotta RM (2015) Conjugated heat transfer analysis of heated aeronautical pitot probes with flight tests experimental validation. Heat Transf Eng 36(11):991–1000CrossRef

de Souza JRB, Lisboa KM, Allahyarzadeh AB, de Andrade GJA, Loureiro JBR, Naveira-Cotta CP, Freire APS, Orlande HRB, Silva GAL, Cotta RM (2016) Thermal analysis of anti-icing systems in aeronautical velocity sensors and structures. J Braz Soc Mech Sci Eng 38(5):1489–1509CrossRef

Fourier JBJ (1822) Théorie analytique de la chaleur. Chez Firmin Didot, père et fils

Fourier JBJ (1878) The analytical theory of heat (English translation reprint). Cambridge University Press, Cambridge

Grattan-Guinness I, Ravetz J (1972) Joseph Fourier, 1768–1830: a survey of his life and work. The MIT Press, Cambridge, MAMATH

Gregg SJ, Sing KSW (1982) Adsorption, surface area and porosity, 2nd edn. Academic, London

Guedes ROC, Cotta RM, Brum NCL (1991) Heat transfer in laminar flow with wall axial conduction and external convection. J Thermophys Heat Transf 5(4):508–513CrossRef

Guedes ROC, Ozisik MN, Cotta RM (1994) Conjugated periodic turbulent forced-convection in a parallel-plate channel. J Heat Transf Trans ASME 116(1):40–46CrossRef

Guigon SMS, Dantas LB, Scofano Neto F, Cotta RM (1999) Exact solution of Luikov’s equations for drying in capillary porous media. Hybrid Methods Eng 1(4):365–387CrossRef

Hermite MC (1878) Sur la formule d’interpolation de Lagrange. J Crelle 84

Hirata SC, Couto P, Lara LG, Cotta RM (2009) Modeling and hybrid simulation of slow discharge process of adsorbed methane tanks. Int J Therm Sci 48(6):1176–1183CrossRef

Hsu CT (1999) A closure model for transient heat conduction in porous media. J Heat Transf Trans ASME 121(3):733–739CrossRef

Kays WM, Crawford ME, Weigand B (2004) Convective heat and mass transfer, 4th edn. McGraw-Hill, New York

Kern DQ, Kraus AD (1972) Extended surface heat transfer. McGraw-Hill, New York

Knupp DC, Naveira-Cotta CP, Cotta RM (2012) Theoretical analysis of conjugated heat transfer with a single domain formulation and integral transforms. Int Commun Heat Mass Transf 39(3):355–362CrossRef

Knupp DC, Cotta RM, Naveira-Cotta CP (2015) Fluid flow and conjugated heat transfer in arbitrarily shaped channels via single domain formulation and integral transforms. Int J Heat Mass Transf 82:479–489CrossRef

Lobo PD, Mikhailov MD, Ozisik MN (1987) On the complex eigenvalues of Luikov system of equations. Dry Technol 5(2):273–286CrossRef

Luikov AV (1966) Heat and mass transfer in capillary-porous bodies. Pergamon Press, Oxford/New YorkMATHCrossRef

Luikov AV (1968) Analytical heat diffusion theory. Academic, New York/London

Luikov AV (1975) Systems of differential equations of heat and mass-transfer in capillary-porous bodies (review). Int J Heat Mass Transf 18(1):1–14MATHCrossRef

Luikov AV (1980) Heat and mass transfer. Mir Publishers; Distributed by Imported Publications, Moscow/ChicagoMATH

Luikov AV, Aleksash VA, Aleksash AA (1971) Analytical methods of solution of conjugated problems in convective heat transfer. Int J Heat Mass Transf 14(8):1047–1056CrossRef

Mennig J, Özişik MN (1985) Coupled integral equation approach for solving melting or solidification. Int J Heat Mass Transf 28(8):1481–1485MATHCrossRef

Mikhailov MD, Özişik MN (1984) Unified analysis and solutions of heat and mass diffusion. Wiley, New York

Moreira DC, Telles MCD, Nunes LCS, Sphaier LA (2015) Analysis of improved-lumped models for property estimation from temperature field data using a fin model. J Porous Media 18(10):985–996CrossRef

Mori S, Tsuji M, Takahashi K, Tanimoto A, Sakakibara M (1994) Coupling of laminar-flow heat-transfer in a vertical circular tube with external free-convection. Chem Eng J Biochem Eng J 55(3):103–114CrossRef

Myers GE (1998) Analytical methods in conduction heat transfer, 2nd edn. AMCHT Publications, Madison

Narasimhan TN (1999) Fourier’s heat conduction equation: history, influence, and connections. Rev Geophys 37(1):151–172CrossRef

Naveira CP, Lachi M, Cotta RM, Padet J (2009) Hybrid formulation and solution for transient conjugated conduction–external convection. Int J Heat Mass Transf 52(1–2):112–123MATHCrossRef

Naveira-Cotta CP, Lachi M, Rebay M, Cotta RM (2010) Experiments and simulations in transient conjugated conduction-convection-radiation. Heat Transf Res 41(3):209–231CrossRef

Nunes JS, Cotta RM, Avelino MR, Kakac S (2010) Conjugated heat transfer in microchannels. In: Kakac S, Kosoy B, Li D, Pramuanjaroenkij A (eds) Microfluidics based microsystems: fundamentals and applications. NATO science for peace and security series a: chemistry and biology. Springer, Dordrecht, pp 61–82

Özişik MN (1968) Boundary value problems of heat conduction. International Textbook Company, Scranton

Özişik MN (1993) Heat conduction, 2nd edn. Wiley Interscience, New York

Perelman TL (1961) On conjugated problems of heat transfer. Int J Heat Mass Transf 3(4):293–303CrossRef

Pérez Guerrero JS, Quaresma JNN, Cotta RM (2000) Simulation of laminar flow inside ducts of irregular geometry using integral transforms. Comput Mech 25(4):413–420MATHCrossRef

Pontedeiro AC, Cotta RM, Su J (2008) Improved lumped model for thermal analysis of high burn-up nuclear fuel rods. Prog Nucl Energy 50(7):767–773CrossRef

Poulikakos D (1993) Conduction heat transfer. International Textbook Company, Scranton

Regis CR, Cotta RM, Su J (2000) Improved lumped analysis of transient heat conduction in a nuclear fuel rod. Int Commun Heat Mass Transf 27(3):357–366CrossRef

Reis MCL, Macêdo EN, Quaresma JNN (2000) Improved lumped-differential formulations in hyperbolic heat conduction. Int Commun Heat Mass Transf 27(7):965–974CrossRef

Ribeiro JW, Cotta RM (1995) On the solution of nonlinear drying problems in capillary-porous media through integral transformation of Luikov equations. Int J Numer Methods Eng 38(6):1001–1020MATHCrossRef

Ribeiro JW, Cotta RM, Mikhailov MD (1993) Integral transform solution of Luikov equations for heat and mass-transfer in capillary-porous media. Int J Heat Mass Transf 36(18):4467–4475MATHCrossRef

Ruperti NJ, Cotta RM, Falkenberg CV, Su J (2004) Engineering analysis of ablative thermal protection for atmospheric reentry: improved lumped formulations and symbolic-numerical computation. Heat Transf Eng 25(6):101–111CrossRef

Ruthven DM (1984) Principles of adsorption and adsorption processes. Wiley, New York

Sacsa Diaz RP, Sphaier LA (2011) Development of dimensionless groups for heat and mass transfer in adsorbed gas storage. Int J Therm Sci 50(4):599–607CrossRef

Scofano Neto F, Cotta RM (1993) Improved hybrid lumped-differential formulation for double-pipe heat-exchanger analysis. J Heat Transf 115(4):921–927CrossRef

Shah RK, London AL (1978) Laminar flow forced convection in ducts: a source book for compact heat exchanger analytical data. In: Irvine TF Jr, Hartnet JP (eds) Advances in heat transfer. Academic, New York

Sontag RE, Van Wylen GJ (1991) Introduction to thermodynamics: classical and statistical, 3rd edn. Wiley, New York

Sphaier LA, Cotta RM (2000) Integral transform analysis of multidimensional eigenvalue problems within irregular domains. Numer Heat Transf B Fund 38(2):157–175CrossRef

Sphaier LA, Cotta RM (2002) Analytical and hybrid solutions of diffusion problems within arbitrarily shaped regions via integral transforms. Comput Mech 29(3):265–276MathSciNetMATHCrossRef

Sphaier LA, Jurumenha DS (2012) Improved lumped-capacitance model for heat and mass transfer in adsorbed gas discharge operations. Energy 44(1):978–985CrossRef

Sphaier LA, Worek WM (2004) Analysis of heat and mass transfer in porous sorbents used in rotary regenerators. Int J Heat Mass Transf 47(14–16):3415–3430MATHCrossRef

Sphaier LA, Worek WM (2009) Parametric analysis of heat and mass transfer regenerators using a generalized effectiveness-NTU method. Int J Heat Mass Transf 52(9–10):2265–2272MATHCrossRef

Su J (2001) Improved lumped models for asymmetric cooling of a long slab by heat convection. Int Commun Heat Mass Transf 28(7):973–983CrossRef

Su J (2004) Improved lumped models for transient radiative cooling of a spherical body. Int Commun Heat Mass Transf 31(1)MathSciNetCrossRef

Su J, Cotta RM (2001) Improved lumped parameter formulation for simplified LWR thermohydraulic analysis. Ann Nucl Energy 28(10):1019–1031CrossRef

Su G, Tan Z, Su J (2009) Improved lumped models for transient heat conduction in a slab with temperature-dependent thermal conductivity. Appl Math Model 33(1):274–283MATHCrossRef

Tan Z, Su G, Su J (2009) Improved lumped models for combined convective and radiative cooling of a wall. Appl Therm Eng 29(11–12):2439–2443CrossRef

Todreas NE, Kazimi MS (2012) Nuclear systems. Thermal hydraulic fundamentals, vol 1, 2nd edn. Taylor & Francis, Boca Raton

Traiano FML, Cotta RM, Orlande HRB (1997) Improved approximate formulations for anisotropic heat conduction. Int Commun Heat Mass Transf 24(6):869–878CrossRef

Vasiliev LL, Kanonchik L, Mishkinis D, Rabetsky M (2000) Adsorbed natural gas storage and transportation vessels. Int J Therm Sci 39(9–11):1047–1055CrossRef

Vernotte P (1958) Les paradoxes de la théorie continue de l’équation de la chaleur. Comptes Rendus 246(22):3154–3155MATH

Yener Y, Kakac S, Naveira-Cotta CP (2017) Heat conduction, 5th edn. Taylor & Francis, New York

Titel: Macroscopic Heat Conduction Formulation
verfasst von: Leandro A. Sphaier
Jian Su
Renato Machado Cotta
Verlag: Springer International Publishing
Buch: Handbook of Thermal Science and Engineering
Print ISBN: 978-3-319-26694-7

Electronic ISBN: 978-3-319-26695-4

Copyright-Jahr: 2018
DOI: https://doi.org/10.1007/978-3-319-26695-4_3

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