《数值传热学》研究生课程教学资源（课件讲稿）Chapter 1 Introduction Numerical Heat Transfer

热流科学与工程西步文源大堂E教育部重点实验室(3)Center line :3.Boundary conditionsOuaT0, V=0(1) Inlet: specifyingdydy(说明)variations of u,y, T(4) Outlet: Mathematically thewithy ;distributions of u y T or their进口边界出口边界first-orderderivatives(导数))areTin中心线required.Actually,approximations must be madeCan we regardthis boundaryformulation as heat transfer andfluid flow over a backward step?超体边界(2）Solid B.C.:No slip（滑移）invelocity,no jump（跳跃）intempCFD-NHT-EHTΦ10/57CENTER

16/57 3. Boundary conditions x y （1）Inlet：specifying (说明）variations of u,v,T with y ； （2）Solid B.C.：No slip（滑移） in velocity, no jump（跳跃） in temp. (4）Outlet：Mathematically the distributions of u,v,T or their first-order derivatives(导数) are required. Actually， approximations must be made. Can we regard this boundary formulation as heat transfer and fluid flow over a backward step? （3）Center line： 0; 0 u T v y y       

热流科学与工程西步文源大堂E教育部重点实验室Notes to Section 1.1Inthe left hand sidea(puu) , a(puv) , a(puw)div(puu)axayOzThe right hand side :aaOvououowopaau(adivU+2n+pF01+nn++axOzaxayazaxaxaxdyr0aaua(Ooauauavowdu(idivu)nnQzazayaxaxCC02axaxaxaxOxSdiv(grad(u)ouQuouapgrad(u)PF= div(ngradu) + S,axOzayaxaaaouauOudiv(grad(u) :Thus we have:OzayaxayOzaxa(pu+ div(puu) = div(ngradu) + S,Navier-StokesatCFD-NHT-EHTG17/57CENTER

17/57 The right hand side : Thus we have: ( 2 ) [ ( )] [ ( )] x u u v w p divU F u x y x z x x x y z                                ( ) ( ) ( ) u div U div grad S u u u t         ( ) u u u grad u x y z          i j k ( ( )) ( ) ( ) ( ) u u u div grad u x x y y z z                ( ) u   div gradu S ( ) ( ) ( ) ( ) ( ) ( ) ( ) x u v w divU x x y x z u u u x x y y z x x z x p F                                            Navier-Stokes div grad u ( ( )) u S ( ) ( ) ( ) ( ) uu uv uw div uU x y z              In the left hand side Notes to Section 1.1

热流科学与工程亚步文源大堂E教育部重点实验室Gradientofascalar（标量的梯度） is a vector:Ou:Qu-uigrad(u):OxOz01Divergenceofavector（矢量的散度） is a scalar:OuOu217div(grad(u)) = divayazdxaaaouauOudiv(grad(u))OzaxayzOxO10auaC1OC1div(ngrad(u))az(maaxdxd1End of Notes to Section 1.1中CFD-NHT-EHT18/57CENTER

18/57 Gradient of a scalar (标量的梯度) is a vector： ( ) u u u grad u i j k x y z          Divergence of a vector (矢量的散度) is a scalar： ( ( )) ( ) u u u div grad u div i j k x y z          ( ( )) ( ) ( ) ( ) u u u div grad u x x y y z z                ( ( )) ( ) ( ) ( ) u u u div grad u x x y y z z                    End of Notes to Section 1.1

热流科学与工程西步文源大堂E教育部重点实验室1.2Basic concepts of NHT, its importance andapplicationexamples1.2.1Threefundamental approachesof scientificresearch and their relationships1.2.2 Basic concepts of numerical solutionsbasedoncontinuumassumption1.2.3Classificationofnumericalsolutionmethodsbasedoncontinuumassumption1.2.4Importanceandapplicationexamples1.2.5Stories of two celebrities(名人)in numericalsimulation1.2.6Some suggestions中CFD-NHT-EHT19/57CENTER

19/57 1.2 Basic concepts of NHT, its importance and application examples 1.2.1 Three fundamental approaches of scientific research and their relationships 1.2.2 Basic concepts of numerical solutions based on continuum assumption 1.2.3 Classification of numerical solution methods based on continuum assumption 1.2.4 Importance and application examples 1.2.5 Stories of two celebrities (名人) in numerical simulation 1.2.6 Some suggestions