1. Heat transfer external flows Rudolf Žitný, Ústav procesní a zpracovatelské techniky ČVUT FS 2010 HEAT PROCESSES HP6 Heat transfer at outer flows around sphere, cylinder and pipe bundle (derived asymptotic formula Nu=2 for sphere, paradox of cylinder). Experiment: hot air blown from hair drier to metallic cylinder with thermocouple; air flowrate calculated from temperature differences. Correlations VDI Warmeatlas. Heat exchangers: powerpoint presentation of HE design.

2. HEAT TRANSFER EXTERNAL FLOWS HP6 TwTw TT Thermal boundary layer~1/  Re Wake Nu~Re 2/3 Free stream temperature (it was mean calorific temperature at internal flows ) Example: cross flow - bundle Re=200 Re=800

3. HEAT TRANSFER EXTERNAL FLOWS HP6 Parallel flow at plate (thermal boundary layer - Laminar flow) x 

4. HEAT TRANSFER EXTERNAL FLOWS HP6 0,71  Pr  380 3,5  Re  7,6. 10 4. 0,67  Pr  300 1  Re  10 5. Flow around a sphere (Whitaker) Cross flow around a cylinder (Sparrow 2004) Cross flow around a plate (Sparrow 2004) See next slide Front side Rear side (wake) Important for heat transfer from droplets… Important for shell&tube and fin-tube heat exchangers

5. HEAT TRANSFER EXTERNAL FLOWS HP6 Cross flow around a cylinder according to VDI Wärmeatlas is based upon modified definition of characteristic length Laminar flow (theoretical correlation for parallel flow at plate) Turbulent flow D Blended correlation

6. HEAT TRANSFER tutorial HP6 Compare correlations for the cross flow around a cylinder according to VDI Wärmeatlas and Sparrow D Graph calculated for Pr=1. Nu,Re defined by diameter D

7. HEAT TRANSFER EXTERNAL FLOWS HP6 Heat transfer from a sphere. Limiting case for Re=0 TwTw TT D r TwTw T  =T w r D Heat transfer from a cylinder. Limiting case for Re=0 Infinitely long cylinder is so powerful heat source that it can heat the whole space to its surface temperature!! Cylinder is really something extraordinary. There doesn’t exist for example something similar to a linear relationship between velocity and the drag force on sphere (F=6  Ru).

8. Example EXTERNAL FLOWS HP6 How to determine heat transfer coefficient experimentally Thermal resistance of body has to be much less than the thermal resistance of thermal boundary layer s is thermal conductivity of solid (not fluid) T TT 35.1 0 C D Procedure: 1.Record temperature T(t) 2.Evaluate time constant  3.Evaluate 

9. HEAT PROCESSES tutorial HP6 Identify heat transfer coefficient (cross flow around cylinder) Pt100 T [C] FAN (hot air) OMEGA data logger (thermocouples) T 1,T 2, T 3 Watt meter Measured 1.3.2011 1200 W Cylinder H=0.075, D=0.07 [m] Aluminium c p =910, rho=2800 kg/m 3 Air c p =1000,  =1 kg/m 3, =0.03 W/m/K D f =0.05m 19 0 C 140 0 C

10. HEAT PROCESSES tutorial HP6 Example: velocity of air calculated from the enthalpy balance is 5 m/s (T nozzle =140 0 C, mass flowrate of air 0.01 kg/s) Corresponding Reynolds number (kinematic viscosity 2.10 -5 ) is Re=17500 Nusselt number calculated for Pr=0.7 is therefore Experiment 1.3.2011  =585 s T 0 =19.2, T  =81 C This is result from the heat transfer correlation More than 2times less is predicted from the time constant Probable explanation of this discrepancy: Velocity of air (5m/s) was calculated at the nozzle of hair dryer. Velocity at the cylinder will be much smaller. As soon as this velocity will be reduced 5-times (1 m/s at cylinder) the heat transfer coefficient will be the same as that predicted from the time constant (76 W/m/K)

11. HEAT TRANSFER EXTERNAL FLOWS HP6 Ephraim M. Sparrow, John P. Abraham, Jimmy C.K. Tong: Archival correlations for average heat transfer coefficients for non-circular and circular cylinders and for spheres in cross-flow. International Journal of Heat and Mass Transfer 47 (2004) 5285–5296 Equivalent diameter D h is replaced by width l in Nu and Re definition

12. HEAT TRANSFER EXTERNAL FLOWS HP6 S. Tiwari, D. Maurya, G. Biswas, V. Eswaran: Heat transfer enhancement in cross-flow heat exchangers using oval tubes and multiple delta winglets. International Journal of Heat and Mass Transfer 46 (2003) 2841–2856 Air flow in narrow gap of fin-tube heat exchanger is usually laminar Vortex shedding behind circular pipe increases pressure drop Flow behind an oval tube is almost steady and symmetric Nu enhancement by winglets

13. HEAT TRANSFER Bundle of tubes cross flow HP6 Delvaux

14. HEAT TRANSFER Bundle of tubes cross flow HP6 0,7  Pr  500 n=0 gases n=0,25 liquid Exponent m depends upon Re (increases from laminar value 0,4 up to 0,84 in fully turbulent flow), Coefficient c 1 depends upon Re and geometry. The coefficient c 2 depends upon number of tube rows in the bundle. Zhukauskas (1972)

15. HEAT TRANSFER Bundle of tubes HP6 Procedure recommended by VDI Warmeatlas Nussels number for 1 row of tubes calculated from correlation (e.g.Sparrow) for single tube using modified velocity in Re Nusselt number for N-rows of tubes in the direction of flow (Nu increases with number of rows because tubes act as a promotor of turbulence)

16. HEAT TRANSFER Film flow HP6 Wyeth

17. HEAT TRANSFER Film flow HP6 Free film of liquid falls down on a vertical heat transfer surface driven by gravity (water coolers, vertical shell&tube heat exchangers, falling film evaporators). Mass flow rate  (kg/s/m) is determined by a liquid distributor at the top of wall (usually a vertical tube).  (  =  u  ) determines the flowing film thickness  as follows from the force balances gravity Viscous force at wall  Parabolic velocity profile y Correlation for laminar film Re=  /  < 400 Turbulent film

18. HEAT TRANSFER Film flow HP6 Mass flowrate has to be high enough so that a uniform and stable liquid film covering the whole heat transfer surface of tubes will be formed. Stability and waviness of the film is affected by surface tension . Restriction on minimal flowrate (intensity of scrapping) can be expressed in terms of Weber number (ratio of kinetic and surface energy) Flow Distribution into tubes of evaporator calandria Falling film evaporators – liquid film flows down on inner surface of vertical tubes, heated from outside. Heat transfer coefficient is usually calculated as  = / . Consequence: the heat transfer coefficient cannot be greater than Very restrictive!! Nii S.et al: Membrane evaporators. Journal of membrane science, 201 (2002), 149-159

19. HEAT TRANSFER wiped film HP6 Scraped surface heat exchangers are applied for processing of highly viscous and fouling sensitive materials. Penetration depth Contact time corresponding to thermal boundary layer development N-number of blades, n-rotational frequency This is only an idea, more precise Azoory Boot correlation See also R. De Goede, E.J. De Jong: Heat transfer properties of a scraped-surface heat exchanger in the turbulent flow regime. Chemical Engineering Science, Volume 48, Issue 8, 1993, Pages 1393-1404Heat transfer properties of a scraped-surface heat exchanger in the turbulent flow regime Thickness of boundary layer 

20. HP6

21. EXAM HP6 Heat transfer external flows

22. What is important (at least for exam) HP6 sphere cylinder derive Nu=2 for Re=0 from equation heat transfer at falling film cross flow on bundle of tubes (N-rows)