LEADER 05640nam 2200721Ia 450 001 9910141300103321 005 20200520144314.0 010 $a1-280-59115-3 010 $a9786613620989 010 $a1-118-20722-X 010 $a1-118-20723-8 010 $a1-118-20720-3 035 $a(CKB)2670000000166847 035 $a(EBL)817872 035 $a(OCoLC)782877147 035 $a(SSID)ssj0000623126 035 $a(PQKBManifestationID)11926387 035 $a(PQKBTitleCode)TC0000623126 035 $a(PQKBWorkID)10655659 035 $a(PQKB)10579664 035 $a(MiAaPQ)EBC817872 035 $a(Au-PeEL)EBL817872 035 $a(CaPaEBR)ebr10546545 035 $a(CaONFJC)MIL362098 035 $a(EXLCZ)992670000000166847 100 $a20110902d2012 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aMathematical modeling in science and engineering$b[electronic resource] $ean axiomatic approach /$fIsmael Herrera, George F. Pinder 205 $a1st ed. 210 $aHoboken, N.J. $cWiley$d2012 215 $a1 online resource (259 p.) 300 $aDescription based upon print version of record. 311 $a1-118-08757-7 320 $aIncludes bibliographical references and index. 327 $aMATHEMATICAL MODELING IN SCIENCE AND ENGINEERING: An Axiomatic Approach; CONTENTS; Preface; 1 AXIOMATIC FORMULATION OF THE BASIC MODELS; 1.1 Models; 1.2 Microscopic and macroscopic physics; 1.3 Kinematics of continuous systems; 1.3.1 Intensive properties; 1.3.2 Extensive properties; 1.4 Balance equations of extensive and intensive properties; 1.4.1 Global balance equations; 1.4.2 The local balance equations; 1.4.3 The role of balance conditions in the modeling of continuous systems; 1.4.4 Formulation of motion restrictions by means of balance equations; 1.5 Summary; Exercises; References 327 $a2 MECHANICS OF CLASSICAL CONTINUOUS SYSTEMS2.1 One-phase systems; 2.2 The basic mathematical model of one-phase systems; 2.3 The extensive/intensive properties of classical mechanics; 2.4 Mass conservation; 2.5 Linear momentum balance; 2.6 Angular momentum balance; 2.7 Energy concepts; 2.8 The balance of kinetic energy; 2.9 The balance of internal energy; 2.10 Heat equivalent of mechanical work; 2.11 Summary of basic equations for solid and fluid mechanics; 2.12 Some basic concepts of thermodynamics; 2.12.1 Heat transport; 2.13 Summary; Exercises; References 327 $a3 MECHANICS OF NON-CLASSICAL CONTINUOUS SYSTEMS3.1 Multiphase systems; 3.2 The basic mathematical model of multiphase systems; 3.3 Solute transport in a free fluid; 3.4 Transport by fluids in porous media; 3.5 Flow of fluids through porous media; 3.6 Petroleum reservoirs: the black-oil model; 3.6.1 Assumptions of the black-oil model; 3.6.2 Notation; 3.6.3 Family of extensive properties; 3.6.4 Differential equations and jump conditions; 3.7 Summary; Exercises; References; 4 SOLUTE TRANSPORT BY A FREE FLUID; 4.1 The general equation of solute transport by a free fluid; 4.2 Transport processes 327 $a4.2.1 Advection4.2.2 Diffusion processes; 4.3 Mass generation processes; 4.4 Differential equations of diffusive transport; 4.5 Well-posed problems for diffusive transport; 4.5.1 Time-dependent problems; 4.5.2 Steady state; 4.6 First-order irreversible processes; 4.7 Differential equations of non-diffusive transport; 4.8 Well-posed problems for non-diffusive transport; 4.8.1 Well-posed problems in one spatial dimension; 4.8.2 Well-posed problems in several spatial dimensions; 4.8.3 Well-posed problems for steady-state models; 4.9 Summary; Exercises; References 327 $a5 FLOW OF A FLUID IN A POROUS MEDIUM5.1 Basic assumptions of the flow model; 5.2 The basic model for the flow of a fluid through a porous medium; 5.3 Modeling the elasticity and compressibility; 5.3.1 Fluid compressibility; 5.3.2 Pore compressibility; 5.3.3 The storage coefficient; 5.4 Darcy's law; 5.5 Piezometric level; 5.6 General equation governing flow through a porous medium; 5.6.1 Special forms of the governing differential equation; 5.7 Applications of the jump conditions; 5.8 Well-posed problems; 5.8.1 Steady-state models; 5.8.2 Time-dependent problems 327 $a5.9 Models with a reduced number of spatial dimensions 330 $aA powerful, unified approach to mathematical and computational modeling in science and engineering Mathematical and computational modeling makes it possible to predict the behavior of a broad range of systems across a broad range of disciplines. This text guides students and professionals through the axiomatic approach, a powerful method that will enable them to easily master the principle types of mathematical and computational models used in engineering and science. Readers will discover that this axiomatic approach not only enables them to systematically construct effective models, 606 $aSystem analysis$xMathematical models 606 $aScience$xMathematical models 606 $aEngineering$xMathematical models 608 $aElectronic books. 615 0$aSystem analysis$xMathematical models. 615 0$aScience$xMathematical models. 615 0$aEngineering$xMathematical models. 676 $a501/.51 686 $aTEC009000$2bisacsh 700 $aHerrera$b Ismael$054138 701 $aPinder$b George Francis$f1942-$021006 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910141300103321 996 $aMathematical modeling in science and engineering$92205230 997 $aUNINA