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heat transfer equations module 5

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module 5 coefficient of thermal expansion eq 5.5 (for an ideal gas) Grashof number eq 5.8 for D 3  or L 3 or δ 3   ‒  this is the gap for enclosed spaces or L 3 Rayleigh number eq 5.11a L = Area/Perimeter Rayleigh number sub in for Pr &  υ film temperature is an average local value of HT coefficient for eq 5.11b laminar natural convection vertical plate or cylinder  boundary layer thickne ss for same natural convection for eq 5.13 turbulent region vertical plate or cylinder Gr L  > 10 9 long plate angled (from vertical) eq 5.14 heated surface on bottom (or cooled from top) 10 5  < Gr L  Pr cosθ < 10 11 heated surface on top − use eq 5.13 (without cosθ) 0 ≤ θ ≤ 89º 10 5  ≤ Ra L  ≤ 10 7 horizontal plate top=hot or bottom=cool eq 5.15 10 7  ≤ Ra L  ≤ 10 10 horizontal plate top=hot or bottom=cool eq 5.16 10 5  ≤ Ra L  ≤ 10 10 horizontal plate top=cool or bottom=hot eq 5.17 L = surface area / perimeter transition L to T is Ra D  = 10 9 critical region for natural convection HT coefficient for single wires or pipes for horizontal Pr > 0.5 natural convection 10 3  < Gr < 10 9 laminar  based on chart fig 5.13 ∞ = β T 1 Pr D T g Ra 2 3 υ ∆ β =  − + 2 T T T air element air ( ) x k Pr 0.952 Gr  P r 508 . 0 h 4 1 4 1 x 2 1  x c + = ( ) 4 1 2 Gr Pr 0.56 Pr  x 3 . 4 x  + = δ ( ) 3 1 L c L  P r Gr 0.13 k L h u  N  = = ( ) 4 1 L cos P r Gr 56 . 0 uL  N  θ = 4 1 L L  Ra 54 . 0 u  N  = 3 1 L L  Ra 15 . 0 u  N  = 4 1 L L  Ra 27 . 0 u  N  = ( ) 4 1 D D Pr Gr 53 . 0 u  N  =  k c D T g Ra  p 2 3 µ ρ ∆ β =  D T g Gr 2 3 υ ∆ β =

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Page 1: HEAT TRANSFER Equations Module 5

8/12/2019 HEAT TRANSFER Equations Module 5

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Page 2: HEAT TRANSFER Equations Module 5

8/12/2019 HEAT TRANSFER Equations Module 5

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Page 3: HEAT TRANSFER Equations Module 5

8/12/2019 HEAT TRANSFER Equations Module 5

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