热流科学与工程西步文源大学E教育部重点实验室NumericalHeatTransferChapter3NumericalMethodsforSolvingDiffusionEquationandtheirApplications(1)(Chapter4ofTextbook)roInstructorTao,Wen-QuanKeyLaboratoryofThermo-FluidScience&EngineeringInt.JointResearchLaboratoryofThermalScience&EngineeringXi'an Jiaotong UniversityInnovativeHarborofWestChina,Xian2022-Sept-20CFD-NHT-EHTG1/55CENTER
Instructor Tao, Wen-Quan Key Laboratory of Thermo-Fluid Science & Engineering Int. Joint Research Laboratory of Thermal Science & Engineering Xi’an Jiaotong University Innovative Harbor of West China, Xian 2022-Sept-20 Numerical Heat Transfer Chapter 3 Numerical Methods for Solving Diffusion Equation and their Applications (1) (Chapter 4 of Textbook) 1/55
热流科学与工程西步文源大堂G教育部重点实验室Contents(Chapter4of Textbook)Remarks: Chapter3 in the textbook will be studiedlaterfor the students'convenience of understanding3.11-D Heat Conduction Equation3.2Fully Implicit Scheme of Multi-dimensionalHeat ConductionEguation3.3TreatmentsofSourceTermandB.C3.4TDMA&ADIMethodsforSolvingABEs3.5FullyDevelopedHTinCircularTubes3.6*FullyDevelopedHTinRectangleDuctsCFD-NHT-EHTΦ2/55CENTER
2/55 3.1 1-D Heat Conduction Equation 3.2 Fully Implicit Scheme of Multi-dimensional Heat Conduction Equation 3.3 Treatments of Source Term and B.C. Contents (Chapter 4 of Textbook) 3.4 TDMA & ADI Methods for Solving ABEs 3.6* Fully Developed HT in Rectangle Ducts 3.5 Fully Developed HT in Circular Tubes Remarks: Chapter 3 in the textbook will be studied later for the students’ convenience of understanding
热流科学与工程西步文源大堂G教育部重点实验室3.1 1-D Heat Conduction Equation3.1.1 General equation of 1-D steadyheatconduction3.1.2 Discretization of G.G.E. by CV method3.1.3 Determination of interface thermalconductivity3.1.4Discretizationof 1-Dunsteadyheatconductionequation3.1.5Mathematical stability can't guaranteesolutionphysicallymeaningful（有意义的）中CFD-NHT-EHT3/55CENTER
3/55 3.1 1-D Heat Conduction Equation 3.1.1 General equation of 1-D steady heat conduction 3.1.3 Determination of interface thermal conductivity 3.1.4 Discretization of 1-D unsteady heat conduction equation 3.1.2 Discretization of G.G.E. by CV method 3.1.5 Mathematical stability can’t guarantee solution physically meaningful (有意义的)
热流科学与工程西步文源大堂E教育部重点实验室3.11-D HeatConduction Equation3.1.1G.E.of 1-D steadyheat conduction1.Two ways of codingfor solving engineeringproblemsSpecial code(专用程序)：FLOWTHERN,POLYFLOW.....Having some generality within itsapplicationrange.General code(通用程序):HT,FF,CombustionMT, Reaction, Thermal radiation, etc.; PHOENICS.FLUENT, CFX. STAR-CDDifferent codes tempt to have some generality(通用性)Generality includes: Coordinates; G.E.; B.Ctreatment; Source term treatment; Geometry...CFD-NHT-EHTΦ4/55CENTER
4/55 3.1 1-D Heat Conduction Equation 1. Two ways of coding for solving engineering problems Special code(专用程序): FLOWTHERN， POLYFLOW.Having some generality within its application range. Different codes tempt to have some generality(通用性）. Generality includes：Coordinates；G.E.；B.C. treatment；Source term treatment；Geometry. General code(通用程序): HT, FF, Combustion, MT, Reaction, Thermal radiation, etc.；PHOENICS, FLUENT, CFX, STAR-CD , . 3.1.1 G.E. of 1-D steady heat conduction
热流科学与工程西步文源大堂G教育部重点实验室2.General governing equations of 1-D steadyheatconductionproblemdT1dI+S=0[aA(x)dxA(x) dxT----Temperature,x----Independent spacevariable（独立空间变量）normal to cross section;A(x)----Area factor, normal to heat conductiondirection;a----Thermal conductivity;S---- Source term, may be a function of both x and T.ΦCFD-NHT-EHT5/55CENTER
5/55 2. General governing equations of 1-D steady heat conduction problem 1 [ ( ) ] 0 ( ) d dT A x S A x dx dx x-Independent space variable (独立空间变量), normal to cross section; A(x)-Area factor, normal to heat conduction direction; -Thermal conductivity; S- Source term, may be a function of both x and T. T-Temperature;