(传热英文课件)chapter 4(Unsteady-state Conduction).ppt

CHAPTER 4 College of Nuclear Science and Technology * CHAPTER 4 College of Nuclear Science and Technology * 4-6 Transient numerical method Solving steps: 1. Establish control equation and definite condition Control equation: Definite conditions: CHAPTER 4 College of Nuclear Science and Technology * 2. Area discretization Node: (m,n) Step: Δx,Δy Control volume 3. Establish discrete equation Δx=Δy: CHAPTER 4 College of Nuclear Science and Technology * 4. Set up the iterative initial field 5. Solving algebraic equations 6. Solution analysis CHAPTER 4 College of Nuclear Science and Technology * One-dimensional unsteady-state conduction 1. Time-space area discretization CHAPTER 4 College of Nuclear Science and Technology * Forward difference: Backward difference: Central difference: CHAPTER 4 College of Nuclear Science and Technology * Discrete method for differential equations of one-dimensional unsteady-state conduction: CHAPTER 4 College of Nuclear Science and Technology * Taylor series expansion method Central difference Forward difference Explicit scheme CHAPTER 4 College of Nuclear Science and Technology * Backward difference Implicit scheme Central difference CHAPTER 4 College of Nuclear Science and Technology * Heat balance method CHAPTER 4 College of Nuclear Science and Technology * CHAPTER 4 College of Nuclear Science and Technology * Grid Fourier number Grid Biot number CHAPTER 4 College of Nuclear Science and Technology * CHAPTER 4 College of Nuclear Science and Technology * 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. CHAPTER 4 College of Nuclear Science and Technology * Node i, specific heat and temperature, then its rate of change with time is approximated by: define: the thermal capacity The energy balance