NumericalHeatTransfer（数值传热学）Chapter11ApplicationExamplesoftheGeneral Codefor2DEllipticalFF&HTProblems1/91
1/91 Numerical Heat Transfer (数值传热学) Chapter 11 Application Examples of the General Code for 2D Elliptical FF & HT Problems
11.1 2D steadyheat conduction without sourceterminCartesiancoordinate11.2SteadyheatconductioninahollowcylinderConduction11.3Fully-developedheattransferina squareduct11.4Fullydevelopedheattransferinannularspacewithstraightfinatinnerwall11.5Fluidflowandheattransferina2-Dsuddenexpansion11.6ComplicatedfullydevelopedfluidflowandConvectiveheat transferin square duct11.7Impingingflowona rotatingdisc11.8 Turbulentflow and heat transfer in duct with acentraljet2/91
2/91 11.1 2D steady heat conduction without source term in Cartesian coordinate 11.2 Steady heat conduction in a hollow cylinder 11.3 Fully-developed heat transfer in a square duct 11.4 Fully developed heat transfer in annular space with straight fin at inner wall 11.5 Fluid flow and heat transfer in a 2-D sudden expansion 11.6 Complicated fully developed fluid flow and heat transfer in square duct 11.7 Impinging flow on a rotating disc 11.8 Turbulent flow and heat transfer in duct with a central jet Conduction Convective
ReviewofTeachingCodeMAINTeaching CodeSUPPLYSETUPUSERUGRIDGRIDMainSETUP1USERSTARTProgramDENSEENDBOUNDPRINTOUTPUTVariedtodealBlackbox,noIYwith a specificUSERDIFLOWmoneedtochangeproblemCaseGAMSORSETUP2dependentUSER:IncludesmodulesGRID,START,DENSESOLVEBOUND,OUTPUT,GAMSOR3/91
Teaching Code Main Program USER Black box, no need to change Varied to deal with a specific problem Review of Teaching Code USER ? 3/91 Case dependent USER: Includes modules GRID, START, DENSE, BOUND, OUTPUT, GAMSOR
11-12DsteadyheatconductionwithoutsourceterminCartesiancoordinate-KnowingUsERstructure11-1-1PhysicalproblemanditsmathformulationKnown:Steady heat conduction ofconstant properties without source termshown in Fig. 1 has following temperatureTemperatures ofdistribution onfour boundaries:the four boundariesaregivenT=x+y+xyFind: Temp. distribution within the regionRemarks: In all examples, physical quantities areFig.1 Computationalgiven by their numerical values without units. It isdomainassumed that all units are homogeneous (单位和谐)4/91
11-1-1 Physical problem and its math formulation 11-1 2D steady heat conduction without source term in Cartesian coordinate －Knowing USER structure Known: Steady heat conduction of constant properties without source term shown in Fig. 1 has following temperature distribution on four boundaries： T = x + y + xy Find: Temp. distribution within the region. Remarks: In all examples, physical quantities are given by their numerical values without units. It is assumed that all units are homogeneous (单位和谐). 4/91 Fig.1 Computational domain
appSolution: GGE+ div(p'tio) = div(Tμgradの)+dt2D, steady state, conductionconstant property, no source termV.(T,V@) = 0Laplace equation:Compared with the standard form, it is a diffusion problem with Iand sourceterm asfollows:I,==1, S, = 0at four boundariesBoundary conditions:T=x+y+xy5/91
* * * ( ) div u div grad ( ) ( ) S t + = + Solution: GGE (Γ ) 0 Laplace equation: = 2D, steady state, conduction constant property, no source term Compared with the standard form, it is a diffusion problem with and source term as follows: * = =1, 0 S = Boundary conditions: at four boundaries 5/91 T = x + y + xy