1、CHAPTER 4,College of Nuclear Science and Technology,Unsteady-state Conduction,1,2,4-1 INTRODUCTION,the temperature of the object changes over time.,Unsteady-state heat-transfer analysis is obviously of significant practical interest.,Definition,CHAPTER 4,College of Nuclear Science and Technology,CHA
2、PTER 4,College of Nuclear Science and Technology,3,Classification,CHAPTER 4,College of Nuclear Science and Technology,4,The transient unsteady heat conduction has two different regime:,difference,CHAPTER 4,College of Nuclear Science and Technology,5,The heat flow:,CHAPTER 4,College of Nuclear Scienc
3、e and Technology,6,Purpose,(1) The rules of the distribution of the temperature and the heat flow:,(2) Heat conduction differential equation:,CHAPTER 4,College of Nuclear Science and Technology,7,The Biot number,- surface-convection resistance,- internal-conduction resistance,Dimensionless number,CH
4、APTER 4,College of Nuclear Science and Technology,8,The influence of Bi on the temperature distribution,CHAPTER 4,College of Nuclear Science and Technology,9,4-2 LUMPED-HEAT-CAPACITY SYSTEM,The lumped-heat-capacity system is one analysis that assumes that the internal resistance of the body is negli
5、gible in comparison with the external resistance.The temperature will be nearly uniform throughout the solid.,Definition,zreo dimension,CHAPTER 4,College of Nuclear Science and Technology,10,The object of arbitrary shape,CHAPTER 4,College of Nuclear Science and Technology,11,Cooling process, accordi
6、ng to the law of conservation of energy:,excessive temperature:,Then:,Control equation,Initial condition,CHAPTER 4,College of Nuclear Science and Technology,12,The equation is changed:,excessive tem- perature ratio,CHAPTER 4,College of Nuclear Science and Technology,13,In this equation,the Fourier n
7、umber,Exponential distribution,CHAPTER 4,College of Nuclear Science and Technology,14,dimension of the index:,When,CHAPTER 4,College of Nuclear Science and Technology,15,Time constant,CHAPTER 4,College of Nuclear Science and Technology,16,Transient heat flow,In the transient heating process,whether
8、the equations are the same?,CHAPTER 4,College of Nuclear Science and Technology,17,CHAPTER 4,College of Nuclear Science and Technology,18,The greater Fo,thermal disturbance can more deeply spread to object interior,Bi is dimensionless thermal resistance. Fo is dimensionless time.,CHAPTER 4,College o
9、f Nuclear Science and Technology,19,Applicability,or,Dimensionless distant related to object geometry,Excessive temperature is less than 5% in any point.,CHAPTER 4,College of Nuclear Science and Technology,20,4-3 Transient heat flow in a semi-infinite solid,Semi-infinite body can be thought as one s
10、pecial situation of one dimensional plate.,CHAPTER 4,College of Nuclear Science and Technology,21,Analytical solutions for one-dimensional unsteady-state conduction,Differential equation,Initial condition,CHAPTER 4,College of Nuclear Science and Technology,22,Adiabatic boundary condition,The third k
11、ind of boundary condition,Bring in excessive temperature:,CHAPTER 4,College of Nuclear Science and Technology,23,CHAPTER 4,College of Nuclear Science and Technology,24,Analytical solution,CHAPTER 4,College of Nuclear Science and Technology,25,2.Cylinder,Analytical solution by separation variable met
12、hod:,CHAPTER 4,College of Nuclear Science and Technology,26,3. Sphere,CHAPTER 4,College of Nuclear Science and Technology,27,A simplified analytical solution in Regular regime,Plate:,Cylinder:,Sphere:,For plate:,CHAPTER 4,College of Nuclear Science and Technology,28,Heat transfer:,The maximal heat f
13、low,Make Q the heat flow in,CHAPTER 4,College of Nuclear Science and Technology,29,Plate:,Cylinder:,Sphere :,CHAPTER 4,College of Nuclear Science and Technology,30,4-5 Multidimensional systems,For the multidimensional problems,its possible to combine the solutions for the one-dimensional systems in
14、a very straightforward way.,CHAPTER 4,College of Nuclear Science and Technology,31,CHAPTER 4,College of Nuclear Science and Technology,32,4-6 Transient numerical method,Solving steps:,1. Establish control equation and definite condition,Control equation:,Definite conditions:,CHAPTER 4,College of Nuc
15、lear Science and Technology,33,2. Area discretization,Node: (m,n) Step: x,y Control volume,3. Establish discrete equation,x=y:,CHAPTER 4,College of Nuclear Science and Technology,34,4. Set up the iterative initial field,5. Solving algebraic equations,6. Solution analysis,CHAPTER 4,College of Nuclear
16、 Science and Technology,35,One-dimensional unsteady-state conduction,1. Time-space area discretization,CHAPTER 4,College of Nuclear Science and Technology,36,Forward difference:,Backward difference:,Central difference:,CHAPTER 4,College of Nuclear Science and Technology,37,Discrete method for differ
17、ential equations of one-dimensional unsteady-state conduction:,CHAPTER 4,College of Nuclear Science and Technology,38,Taylor series expansion method,Central difference,Forward difference,Explicit scheme,CHAPTER 4,College of Nuclear Science and Technology,39,Backward difference,Implicit scheme,Centra
18、l difference,CHAPTER 4,College of Nuclear Science and Technology,40,Heat balance method,CHAPTER 4,College of Nuclear Science and Technology,41,CHAPTER 4,College of Nuclear Science and Technology,42,Grid Fourier number,Grid Biot number,CHAPTER 4,College of Nuclear Science and Technology,43,CHAPTER 4,
19、College of Nuclear Science and Technology,44,4-7 Thermal resistance and capacity formulation,Steady-state conditions: the net energy transfer into the node is zero.,Unsteady-state conditions: the net energy transfer into the node must be evidenced as an increase in internal energy of the element.,CH
20、APTER 4,College of Nuclear Science and Technology,45,Node i, specific heat and temperature, then its rate of change with time is approximated by:,define: the thermal capacity,The energy balance by forward differences:,CHAPTER 4,College of Nuclear Science and Technology,46,The energy balance by backw
21、ard differences:,CHAPTER 4,College of Nuclear Science and Technology,47,Minimum stability requirement:,CHAPTER 4,College of Nuclear Science and Technology,48,4-8 Summary,Unsteady-state conduction,Basic conceptions or characteristics of unsteady-state conduction,Lumped-heat-capacity system,Semi-infinite solid,Convection boundary conditions,Multidimensional systems,Transient numerical method,CHAPTER 4,College of Nuclear Science and Technology,49,Thank you!,
