HP 6 HEAT PROCESSES Heat transfer external flows

HP 6 HEAT PROCESSES Heat transfer external flows 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. Rudolf Žitný, Ústav procesní a zpracovatelské techniky ČVUT FS 2010

HEAT TRANSFER EXTERNAL FLOWS HP 6 Wake Nu~Re 2/3 Tw Free stream temperature (it was mean calorific temperature at internal flows ) T Thermal boundary layer~1/ Re Re=200 Example: cross flow - bundle Re=800

HP 6 HEAT TRANSFER EXTERNAL FLOWS Parallel flow at plate (thermal boundary layer - Laminar flow) x

HP 6 HEAT TRANSFER EXTERNAL FLOWS Flow around a sphere (Whitaker) Important for heat transfer from droplets… Front side See next slide 0, 71 Pr 380 3, 5 Re 7, 6. 104. Cross flow around a cylinder (Sparrow 2004) Important for shell&tube and fin-tube heat exchangers 0, 67 Pr 300 1 Re 105. Cross flow around a plate (Sparrow 2004) Rear side (wake)

HP 6 HEAT TRANSFER EXTERNAL FLOWS Cross flow around a cylinder according to VDI Wärmeatlas is based upon modified definition of characteristic length D Laminar flow (theoretical correlation for parallel flow at plate) Turbulent flow Blended correlation

HP 6 HEAT TRANSFER tutorial 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

HP 6 HEAT TRANSFER EXTERNAL FLOWS Heat transfer from a sphere. Limiting case for Re=0 Tw T D r Heat transfer from a cylinder. Limiting case for Re=0 Tw D T =Tw r 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).

Example EXTERNAL FLOWS HP 6 How to determine heat transfer coefficient experimentally Procedure: D T T 1. Record temperature T(t) 2. Evaluate time constant 3. Evaluate 35. 1 0 C Thermal resistance of body has to be much less than thermal resistance of thermal boundary layer s is thermal conductivity of solid (not fluid)

HP 6 HEAT PROCESSES tutorial Identify heat transfer coefficient (cross flow around cylinder) Pt 100 Cylinder H=0. 075, D=0. 07 [m] Aluminium cp=910, rho=2800 kg/m 3 Df=0. 05 m Air cp=1000, =1 kg/m 3, =0. 03 W/m/K OMEGA data logger (thermocouples) T 1, T 2 , T 3 T [C] 1400 C FAN (hot air) 190 C Watt meter Measured 1. 3. 2011 1200 W

HP 6 HEAT PROCESSES tutorial Example: velocity of air calculated from the enthalpy balance is 5 m/s (Tnozzle=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 This is result from the heat transfer correlation More than 2 times less is predicted from the time constant Experiment 1. 3. 2011 =585 s Probable explanation of this discrepancy: T 0=19. 2, T =81 C Velocity of air (5 m/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)

HP 6 HEAT TRANSFER EXTERNAL FLOWS 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 Dh is replaced by width l in Nu and Re definition

HP 6 HEAT TRANSFER EXTERNAL FLOWS 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 Vortex shedding behind circular pipe increases pressure drop Flow behind an oval tube is almost steady and symmetric Air flow in narrow gap of fin-tube heat exchanger is usually laminar Nu enhancement by winglets

HP 6 HEAT TRANSFER Bundle of tubes cross flow Delvaux

HP 6 HEAT TRANSFER Bundle of tubes cross flow Zhukauskas (1972) 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.

HP 6 HEAT TRANSFER Bundle of tubes Procedure recommended by VDI Warmeatlas 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) Nussels number for 1 row of tubes calculated from correlation (e. g. Sparrow) for single tube using modified velocity in Re

HP 6 HEAT TRANSFER Film flow Wyeth

HP 6 HEAT TRANSFER Film flow 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 y Parabolic velocity profile gravity Viscous force at wall Correlation for laminar film Re= / < 400 Turbulent film

HP 6 HEAT TRANSFER Film flow Falling film evaporators – liquid film flows down on inner surface of vertical tubes, heated from outside. Heat transfer coefficient is usually calculated as = /. Nii S. et al: Membrane evaporators. Journal of membrane science, 201 (2002), 149 -159 Flow Distribution into tubes of evaporator calandria 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) Consequence: the heat transfer coefficient cannot be greater than Very restrictive!!

HP 6 HEAT TRANSFER wiped film Scraped surface heat exchangers are applied for processing of highly viscous and fouling sensitive materials. Thickness of boundary layer 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 -1404

HP 6

HP 6 EXAM Heat transfer external flows

HP 6 What is important (at least for exam) sphere derive Nu=2 for Re=0 from equation cylinder cross flow on bundle of tubes (N-rows) heat transfer at falling film