Heat and Mass Transfer Heat Transfer Formula Sheet and Tables Heat Transfer from Extended Surfaces (Fins PDF

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Heat and Mass Transfer Heat Transfer Formula Sheet and Tables Heat Transfer from Extended Surfaces (Fins) Case I: very long fin Case II: fin with a finite length, L, and the end is insulated Case III: fin with a finite length, L, and losses heat by convection from its end Fin Efficiency: Convection ...

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Heat and Mass Transfer

Heat Transfer Formula Sheet and Tables Heat Transfer from Extended Surfaces (Fins) Case I: very long fin

Case II: fin with a finite length, L, and the end is insulated

Case III: fin with a finite length, L, and losses heat by convection from its end

Fin Efficiency:

Convection Dimensionless numbers 1. Reynolds number

Re D 

um Dh 4m   Dh 

2. Nusselt number

1

Pr 

3. Prandtl number

 C p   k

4. Grashof number 5. Rayleigh number

Ra = GrPr

Correlations used in External Forced Convection 1. Flat plate in parallel flow For laminar flow,

Tf 

Ts  :T 2

Nu x 

hx x  0.664 Re1x/ 2 Pr1/ 3 , Pr  0.6 k

Nu x 

hx x  0.565Re1x/ 2 Pr1 / 2 , Pr  0.05 k

For Turbulent flow.

Tf 

Ts : T 2

Nu x  0.0296 Re 4x / 5 Pr1/ 3 , 0.6  Pr  60 2. Cross flow around cylinders: a. Circular shapes hD 0.62 Re 0.5 Pr1/ 3 Nu   0 .3  2 / 3 1/ 4 k 1  0.4 / Pr 





  Re 5 / 8    1     282,000  

4/5

It correlates available data well for Re Pr > 0.2. The fluid properties are evaluated at the mean film temperature Ts  T

Tf 

2

b. Non-circular shapes

1/ 3 Nu D  C Re m D Pr

Where C and m are listed in the following table:

2

3. Cross flow around spheres:

Nu D 

 2  (0.4 Re1D/ 2  0.06 Re 2D/ 3 ) Pr 0.4 

  s

1/ 4

   

where properties are evaluated at T∞ , except µs which is evaluated at Ts 4. Flow across tube banks:

Where Nusult no:





Nu D  1.13C1 Re mD ,max Pr1/ 3 C2

2000  Re D ,max  4  104  valid for :    Pr  0.7 

Where: C1 and m are obtained from the following table:

C2 = 1 For N L  10 C2 = from the following table if N L  10

Re D,max  Where: Vmax

Vmax

Vmax D



ST For case (a) Aligned  V ST  D ST  V For case (b) staggered and 2( S D  D)

SD 

ST  D 2

3

Correlations used in Internal Forced Convection Tref  Tm 

1  Ti  To   Ts   2 2 

For turbulent flow

Re D 

um Dh  2300 

Dh 

4 Ac P

For uniform constant surface temperature:  PL  Ts  Tm ,o  exp  h  m C  Ts  Tm ,i p   To include the contributions due to convection at the tube inner and outer surfaces, and due to conduction across the tube wall:

 U As  To T  Tm ,o    exp   m c  Ti T  Tm ,i p   Nusselt Number for fully developed laminar flow in tubes of various cross sections

Nusselt Number for fully developed Turbulent flow hDh Nu   0.023Re 0.8 Pr n k where n= 0.4 for heating and 0.3 for cooling of the fluid flowing through the tube. The fluid properties are evaluated at the bulk mean fluid temperature Tb= (Ti + Te)/2.

4

Natural Convection: Geometry 1. Vertical plates

Recommended Equation  0.387 Ra1L/ 6  Nu L  0.825  1  (0.492 / Pr)9 / 16 



2. Inclined plates, (cold surface up or hot surface down)

  4/9  



 0.387 Ra1L/ 6 Nu L   0.825  1  (0.492 / Pr)9 / 16 



2

  4/9  

2



Where: g  g cos 3. Horizontal plates (Hot surface up or cold surface down) 4. Horizontal plates (Cold surface up or hot surface down) 5. Horizontal cylinder

Nu L  0.54 Ra1L/ 4

(104  Ra L  107 )

Nu L  0.15 Ra1L/ 3

(107  Ra L  1011 )

Nu L  0.27 Ra1L/ 4

(105  Ra L  1010 )

Ra D  1012

  0.387 Ra1D/ 6  Nu D   0.60  8 / 27 9 / 16   1  (0.559 / Pr)  



Ra D  1011

6. Sphere

Pr  0.7

2



 0.589 Ra1D/ 4 Nu D  2    1  (0.469 / Pr)9 / 16 



1/ 4

  4/9  



Heat Exchangers Log mean Temperature Difference

Tlm 

T2  T1 T ln 2 T1

For parallel flow:

Tlm  LMTD 

For counter flow:

Tlm  LMTD 

(Th,o  Tc ,o )  (Th,i  Tc ,i ) ln[(Th,o  Tc ,o ) /(Th,i  Tc ,i )] (Th,o  Tc ,i )  (Th,i  Tc ,o ) ln[(Th,o  Tc ,i ) /(Th,i  Tc ,o )]

Cross-flow & Multi-pass (shell & tube):

Tlm  LMTD  F

(Th,o  Tc ,i )  (Th,i  Tc ,o ) ln[(Th,o  Tc ,i ) /(Th,i  Tc ,o )]

Where: F = correction factor which can be obtained from the following figures: 5

Correction factor F charts for common shell-and-tube and cross-flow heat exchangers. 6

Heat Exchanger Effectiveness,  :

The heat capacity ratio:

Cr 



qact qmax

0   1

Cmin Cmax

The “Number of Transfer Units” (NTU):

NTU 

UA Cmin

Effectiveness for heat exchangers 7...