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Chap 16 & 18

Unit Operation & Transfer Phenomena. Chap 16 & 18. Unsteady State Conduction. U O T P. First law of thermodynamics. Through a cycle system,. syatem. surrounding. U O T P. First law of thermodynamics. Through a cycle system,. P. 2. a. a. b. 1. ρ. U O T P.

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Chap 16 & 18

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  1. Unit Operation & TransferPhenomena Chap 16 & 18 Unsteady State Conduction

  2. UOTP First law of thermodynamics • Through a cycle system, syatem surrounding

  3. UOTP First law of thermodynamics • Through a cycle system, P 2 a a b 1 ρ

  4. UOTP Conservation of energy Stream line II III I Boundary of system At time t+Δt Boundary of system At time t

  5. UOTP Conservation of energy Stream line dA v θ n

  6. UOTP Stream line S dA v θ n Work

  7. UOTP Fourier field equation-Unsteady State-1 • 切一塊下來討論 若時間 t 溫度為T，經過 dt 後,時間 t+dt 溫度為 T+dT, 熱傳әQ

  8. UOTP Fourier field equation Unsteady State-2

  9. UOTP Fourier field equation-Unsteady State-3

  10. UOTP Special Forms of Fourier field equation 熱擴散係數 α = k / (ρ cP)

  11. UOTP Special Forms of Fourier field equation 熱擴散係數 α = k / (ρ cP)

  12. Steady state qx at plate

  13. Prob-16-1

  14. Prob-16-6

  15. UOTP ey ex ez Appendix B y er eθ y r ez 單位向量 θ x x z

  16. UOTP Differential Continuity Equation質量不滅

  17. UOTP Incompressible flow液體流動相關方程式(牛頓流體) 連續方程式 動量方程式 Navier-Stokes equation 能量方程式

  18. UOTP Fourier field equation單向(x)其他導法 • 切一塊(面積A厚度dx)下來討論 若時間 t 溫度為T，經過 dt 後 時間 t+dt 溫度為 T+dT 則此塊固體吸熱 dq dq = V ρ Cp dT = dqin-dqout 又 Q = dq/dt dq = Q * dt T A dqout 熱擴散係數 α = k / (ρ cP) dqin dx

  19. UOTP Tc Th 塊狀(lump)固體受熱convection ,conduction皆不可忽略 metallic hot oil Bi大 :convection阻力小h大 Bi小 :conduction阻力小k大 Tc Th

  20. UOTP Examp-1 通常先分析Bi，<0.1，可估算h最大值 310K Copper wire 280-297K D=0.635cm

  21. UOTP Tc Th 塊狀(lump)固體受熱convection 阻力可忽略Th

  22. UOTP Examp-2convection 阻力可忽略Th Concrete D=0.1m,L=0.1m h= k=

  23. UOTP Ts Ts Heat Flow Q Q 2s x dx 無限大平板--不穩定熱傳 • 無限大平板之不穩定熱傳 • 平板初溫Ta，由兩外邊加熱， 經過tT後，平板平均溫度 • 弗立葉數(Fourier Number) NFo= αtT/s2 t=0 板溫 Ta t= tT板溫 a1 = (π/2)2 *若 NFo 大於0.1，第二項以後可省略

  24. UOTP 圓柱(無限長 半徑rm)與圓球(半徑rm)--不穩定熱傳 • 圓柱(半徑rm) • 圓球(半徑rm) *NFo= tT/rm2

  25. UOTP Examp-3 • 一塑膠板厚1in ，初溫70oF， 由兩面皆為250 oF 之穴道加溫， 經過多久可加至平均 210 oF • k=0.075Btu/ft-h- oF ρ=56.2lb/ft3 Cp=0.4Btu/lb- oF *NFo= tT/rm2 tT =16.24min

  26. UOTP Differential Continuity Equation

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