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Convection Part1

Convection Part1. External Flow. Introduction. Recall: Convention is the heat transfer mode between a fluid and a solid or a 2 fluids of different phases In order to simplify the process we used Newton’s correlation

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Convection Part1

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  1. Convection Part1 External Flow

  2. Introduction Recall: Convention is the heat transfer mode between a fluid and a solid or a 2 fluids of different phases In order to simplify the process we used Newton’s correlation Where h is the convective heat transfer coefficient also called the film coefficient. h is a function of: Fluid flow Fluid properties Geometry of the solid

  3. There are four means to evaluate the heat transfer coefficient 1) Dimensional analysis 2) Exact analysis of boundary layer 3) Approximate integral analysis of the boundary layer 4) Analogy between energy and momentum transfer Significant Parameters: Nusselt Number Nu y x

  4. The heat transfer rate between the surface and the fluid is At the surface itself Where k is the thermal conductivity of the fluid. Therefore:

  5. Prandtl Number Pr Momentum Diffusivity Thermal Diffusivity The ratio of the momentum diffusivity over the thermal diffusivity is a combination of fluid properties and is also thougth of as a property (Named Prandtl Number Pr). Dependent on fluid and temperature

  6. Dimensional Analysis of Convective Heat Transfer Forced Convection: movement dictated by v

  7. Using the Buckingham method we group the variables in dimensionless number: This dimensional analysis for a forced convection in a circular conduit indicates the possibility of correlating the variables as Similarly we could have developed the Stanton number instead of the Nusselt

  8. Free Convection: movement dictated by buoyancy Given the coefficient of thermal expansion β:

  9. Using the Buckingham method we group the variables in dimensionless number: Define the Grashof number as This dimensional analysis for a forced convection in a circular conduit indicates the possibility of correlating the variables as

  10. Selected Dimensionless Groups

  11. Flat Plate in Parallel Flow Turbulent Flow Transition Region Laminar Flow δ(x) x L Properties of fluid evaluated at the film temperature Tf

  12. Forced Convection Flat Plate in Parallel Flow Laminar flow: Re<2 x 105 Prandtl number >0.6 The local Nusselt number is The average Nusselt number All Prandtl number and Pe >100 The local Nusselt number is The average Nusselt number x L

  13. Forced Convection Flat Plate in Parallel Flow Transition flow: Rec=5 x 105 60>Prandtl number >0.6 3 x 106 >Re > 2 x 105 The average Nusselt number L

  14. L Forced Convection Flat Plate in Parallel Flow Turbulent flow: Re>3x106 60>Prandtl number >0.6 107 >Re >3 x 106 The average Nusselt number The local Nusselt number

  15. Cylinder in a Cross Flow Transition Laminar Turbulent v D Separation Properties of fluid evaluated at the film temperature Tf v D Separation

  16. Forced Convection Cylinder in a Cross Flow The average Nusselt number If ReDPr>0.2

  17. Forced Convection Various Object in a Cross Flow The average Nusselt number D D D D D

  18. Sphere in a Cross Flow All properties of fluid evaluated at temperature , except μs at Ts Restrictions 0.71 < Pr < 380 3.5 < ReD < 7.6x104

  19. Bank of Tubes in a Cross Flow V Fluid in cross flow over tube bank

  20. Aligned Bank of Tubes in a Cross Flow SL D ST A1 Properties of fluid evaluated at the film temperature Tf

  21. SL Staggered Bank of Tubes in a Cross Flow D A1 ST Properties of fluid evaluated at the film temperature Tf If else

  22. Number of row (NL) greater or equal to 10 2000 < ReD,max < 40000 Pr > 0.7 C1 in table 7.5 If number of row is smaller than 10 C2 in table 7.6

  23. Number of row (NL) greater or equal to 20 1000 < ReD,max < 2x106 500 > Pr > 0.7 C in table 7.7 If number of row is smaller than 10 C2 in table 7.8 All properties of fluid evaluated at the average temperature except Prs at Ts

  24. In this case the temperature difference in the convective heat transfer equation is defined as the log-mean temperature difference ΔTlm Where Ti is the temperature of the fluid entering the bank To is the temperature of the fluid leaving the bank And the outlet temperature can be estimated using Where N is the total number of tube and NT the transverse number of tube. Finally the heat transfer rate per unit length is

  25. Packed Bed Properties of fluid evaluated at the the average temperature ε is the porosity or void fraction of the bed (0.3 to 0.5) Valid for gas flow

  26. Ap,T is the total area of the particles and Ab,c is the bed cross sectional area

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