Numerical HeatTransfer（数值传热学）Chapter1 Introduction1/62
Numerical Heat Transfer (数值传热学) Chapter 1 Introduction 1/62
ContentsofChapter1(数学描述）of1.1 Mathematical formulationheattransferandfluidflow(HT&FF)problems（NHT基本概念）,its1.2BasicconceptsofNHTimportance andapplicationexamples1.3MathematicalandphysicalclassificationofHT & FF problems（问题分类）and itseffects on numerical solution2/62
1.1 Mathematical formulation （数学描述）of heat transfer and fluid flow (HT & FF) problems 1.2 Basic concepts of NHT（NHT 基本概念）, its importance and application examples 1.3 Mathematical and physical classification of HT & FF problems （ 问 题 分 类 ） and its effects on numerical solution Contents of Chapter 1 2/62
1.1 Mathematical formulation of heat transfer and fluidflow(HT&FF)problems1.1.1 Governing equationsand their general form（控制方程）（质量守恒）1.Massconservation（动量守恒）2.Momentum conservation（能量守恒）3.Energy conservation4.Generalform(一般形式)2.Conditions for unique solution （唯一解）3.Exampleof mathematical formulation3/62
1.1 Mathematical formulation of heat transfer and fluid flow (HT & FF) problems 3/62 1.1.1 Governing equations （控制方程）and their general form 2. Conditions for unique solution（唯一解） 3. Example of mathematical formulation 1. Mass conservation （质量守恒） 2. Momentum conservation （动量守恒） 3. Energy conservation （能量守恒） 4. General form （一般形式）
1.1 Mathematical formulation of heat transfer andfluidflow(HT&FF)problemsAll macro-scale（宏观）HT&FFproblemsaregoverned(控制) by three conservation laws:mass,momentum andenergyconservationlaw（守恒定律）The differences between different problems are in:conditions for the unique solution （唯一解）：（1） initial（初始的）&boundaryconditions，（2）physicalpropertiesand (3） source terms（(源项)1.1.1 Governing equations and their general form1. Mass conservationapa(pu)a(pv)a(pw)0atOzaxdy4/62
4/62 1.1 Mathematical formulation of heat transfer and fluid flow (HT & FF) problems All macro-scale （宏观）HT & FF problems are governed （控制）by three conservation laws：mass, momentum and energy conservation law (守恒定律). The differences between different problems are in: conditions for the unique solution（唯一解）：（1）initial （初始的）& boundary conditions, （2）physical properties and （3）source terms （源项）. 1.1.1 Governing equations and their general form 1. Mass conservation + (u) + (v) + (w) = 0 t x y z
u,v,w are three components (分量) of UR + div(pU) = 0dyat“div”(bold type,粗体is the mathematicalsymbol fordivergence（散度）：div(pU)- a(pu + (p) + 2(em)InCartesiancoordinateOzaxdy(直角坐标系）For incompressible fluid1（不可压缩流体），densityisconstantou+av+ow- 0div(U) =0Ox y Ozflowwithoutsourceandsink（没有源与汇的流动.Forexampleflow of water in a pipe)。5/62
+ div(U) = 0 t For incompressible fluid（不可压缩流体），density is constant, div(U ) =0 flow without source and sink (没有源与汇的流动. For example, flow of water in a pipe)。 div(U )= (u) + (v) + (w) x y z u + v + w = 0 x y z “div”（bold type,粗体） is the mathematical symbol for divergence（散度）： In Cartesian coordinate (直角 坐标系） u,v,w are three components (分量) of U. 5/62