Joint European Summer School for Fuel Cell and

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Joint European Summer School for Fuel Cell and Hydrogen Technology Heat Exchangers Andreas Gubner

Joint European Summer School for Fuel Cell and Hydrogen Technology Heat Exchangers Andreas Gubner University of Applied Science Munich

Outline § Heat transfer fundamentals – Modes of Heat Transfer – Heat transfer by

Outline § Heat transfer fundamentals – Modes of Heat Transfer – Heat transfer by forced convection – Mean heat transfer coefficient in and around circular tubes and fuel cell gas channels, respectively – Fluid properties § Fundamentals of heat exchanger design – Co-, Counter- and Cross-Flow § Introduction to special heat exchangers: – Plate- and Compact Heat Exchangers § Outlook & Further Reading Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 2

Introduction: Scope § Introduction to an engineering approach to heat exchanger design and performance

Introduction: Scope § Introduction to an engineering approach to heat exchanger design and performance calculations § Introduction to common heat exchanger types § Introduction to compact heat exchangers § Literature used for most of the fundamentals and further reading tip: – F. P. Incropera, D. P. de Witt, Fundamentals of Heat and Mass Transfer, 4 th edition, John Wiley & Sons [In. Witt] Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 3

Introduction: What is Heat? § A temperature difference (always) causes an energy flux. §

Introduction: What is Heat? § A temperature difference (always) causes an energy flux. § That energy flux called Heat. It is directed toward decreasing temperature. § Alternative definition by M. Planck: Heat is the difference between the internal energy change and work. § § Since thermodynamics does not deliver information how the heat transfer rate is related to the driving temperature difference, additional transport laws must be established. That is the subject of Heat Transfer Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 4

Introduction: What is a Heat Exchanger? Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020

Introduction: What is a Heat Exchanger? Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 5

Tube and Shell Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 6

Tube and Shell Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 6

Modes Of Heat Transfer Heat Conduction in a resting (not moving, stationary) body Heat

Modes Of Heat Transfer Heat Conduction in a resting (not moving, stationary) body Heat Exchangers andreas. gubner@hm. edu Heat Conduction from a Heat Transfer due to surface into a flowing electromagnetic (moving): Convection radiation between two surfaces 31. 10. 2020 7

Forced Convection § Heat Transfer between a moving fluid and its containing wall §

Forced Convection § Heat Transfer between a moving fluid and its containing wall § A velocity boundary layer and a thermal boundary layer is formed next to the wall § There is a constant bulk temperature outside thermal boundary layer. Turbulent Flow = Bulk Flow Laminar Flow = Boundary Layer Wall Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 8

Forced Convection TF Turbulent Flow = Bulk Flow x Laminar Flow = Boundary Layer

Forced Convection TF Turbulent Flow = Bulk Flow x Laminar Flow = Boundary Layer Wall TW Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 9

Thermal Boundary Layer § Friction forces keep fluid at the wall stagnant so the

Thermal Boundary Layer § Friction forces keep fluid at the wall stagnant so the standard model is a steady velocity increase toward the pipe center called the velocity boundary layer. § This model also knows a velocity boundary layer that corresponds to the velocity boundary layer (not equal) Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 10

Heat Transfer Model Theory § Newton‘s law of cooling § Task: How to determine

Heat Transfer Model Theory § Newton‘s law of cooling § Task: How to determine the heat transfer coefficient h? § Modern CFD can be used, however experimental validation still needed. § Too complicated and expensive for everyday engineering jobs, a model für thermal boundary layer t is used Determining h is equivalent to the determination of thermal boundary layer thickness. Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 11

Heat transfer coefficients for inner flow § Typical Values für h in W/m²K: Transportmechanism

Heat transfer coefficients for inner flow § Typical Values für h in W/m²K: Transportmechanism Medium h in W/m²K free convection in gas: in liquids: 2 – 25 50 – 1000 forces convection in gas: in liquids: 10 – 250 100 – 15000 boiling (evaporation) 2000 – 25000 condensation 5000 – 100000 Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 12

The average (mean) heat transfer coefficient Newton‘s Law of Cooling: Local hear transfer coefficient:

The average (mean) heat transfer coefficient Newton‘s Law of Cooling: Local hear transfer coefficient: Local heat transfer rate (per unit area): The total heat transfer rate (by the heat exchanger) must be „added up“: This leads to the concept of averaged heat transfer coefficients with: Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 13

The normalized convection transfer equations § A mathematical analysis of the fluid mechanical phenomena

The normalized convection transfer equations § A mathematical analysis of the fluid mechanical phenomena delivers a set of normalized equations how the heat transfer rate depends on the flow conditions. § Physical phenomena are assigned to dimensionless groups that allow its characterization. § Most important examples: § Reynolds Number Re § Prandtl Number Pr § Re and Pr are used to calculate another dimensionless number quantity called the Nusselt Number Nu. § The heat transfer coefficient is then calculated using the Nusselt Number. Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 14

Formal structure and Fluid Properties The most important dimensionless groups (numbers) for heat transfer

Formal structure and Fluid Properties The most important dimensionless groups (numbers) for heat transfer due to forced convection are displayed in the box on the left. § There are many others. They are used forced convection in pipes, ducts (channels), across cylinders (tubes) or tube banks etc. § Each geometry has its own equation which must be determined experimentally. § The Fluid Properties must be taken from the literature or calculated by using suitable databanks/software. § [In. Witt] § http: //www. nist. gov/srd/nist 23. cfm § Unfortunately all fluid properties are temperature dependent. Finding suitable simplifications / average temperatures or taking the temperature dependance into account fully can be challenging. Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 15

External Flow • Spatially and temporally constant surface temperature • Semi empirical models by

External Flow • Spatially and temporally constant surface temperature • Semi empirical models by curve fitting to free parameters • Measurements can be reproduced well by relationships of the form: Fluid properties for calculating Re and Pr have to be evaluated using an average temperature given by Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 16

The cylinder in cross flow • laminar boundary layer facing upstream • flow separation

The cylinder in cross flow • laminar boundary layer facing upstream • flow separation and turbulences downstream • Hilpert Equation: Re and Nu are calulated using the cylinder diameter D. The constants depend on the Reynolds Number Re. D C m 0, 4 to 4 0, 989 0, 330 4 to 40 0, 911 0, 385 40 to 4000 0, 683 0, 466 4000 to 40000 0, 193 0, 618 40000 bis 106 0, 027 0, 805 Heat Exchangers andreas. gubner@hm. edu The equation is experimentally verified for: 31. 10. 2020 17

Flow across tube banks http: //www. thermopedia. com/content/1211/? tid=104&s n=1410 In-line (aligned): Staggered: If

Flow across tube banks http: //www. thermopedia. com/content/1211/? tid=104&s n=1410 In-line (aligned): Staggered: If Amin same as aligned: Heat Exchangers andreas. gubner@hm. edu If Amin found in alternate location: 31. 10. 2020 18

Calculation of the Nusselt Number Equation proposed by Zhukauskas [In. Witt] Fluid Properties evaluated

Calculation of the Nusselt Number Equation proposed by Zhukauskas [In. Witt] Fluid Properties evaluated at Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 19

Correction Factor for Few Tubes § If NL < 20 a correction factor should

Correction Factor for Few Tubes § If NL < 20 a correction factor should be applied [In. Witt] Heat Exchangers andreas. gubner@hm. edu 13 16 0. 98 0. 99 31. 10. 2020 20

Flow Through Tubes and Ducts Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 21

Flow Through Tubes and Ducts Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 21

Thermal Entry Length Development of thermal boundary layer Flow in circular tubes Corresponding local

Thermal Entry Length Development of thermal boundary layer Flow in circular tubes Corresponding local heat transfer coefficient hx Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 22

Combined Entry Length, FLow regimes Transition from laminar to turbulent at Entry region Fluid

Combined Entry Length, FLow regimes Transition from laminar to turbulent at Entry region Fluid dynamical entry length: Heat Exchangers andreas. gubner@hm. edu Fully developed region Def. of the mean flow velocity laminar turbulent 31. 10. 2020 23

Thermal Entry Length, Mean Fluid Temperature boundary condition at tube wall to be applied

Thermal Entry Length, Mean Fluid Temperature boundary condition at tube wall to be applied Thermal entry length Mass flux and Enthalpy flux: laminar turbulent Heat Exchangers Def. of mean fluid temperature TF at x:

Correlation for Laminar Flow, Combined Entry Length § Constant surface temperature and combined (thermal

Correlation for Laminar Flow, Combined Entry Length § Constant surface temperature and combined (thermal and velocity) entry length: Sieder and Tate Heat Exchangers

Correlations for Turbulent Flow Regime § § Fairly complicated equation by Gnielinski is today‘s

Correlations for Turbulent Flow Regime § § Fairly complicated equation by Gnielinski is today‘s industrial standard. However for quick estimations much simpler equations may be used at a max. error of approx 25 % – Use Dittus-Boelter if property variations are small – Use Sieder and Tate if property variations are large Dittus-Boelter: Sieder and Tate: Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 26

Mean Fluid Temperature is a Function of Position Differential energy balance at circumferential area

Mean Fluid Temperature is a Function of Position Differential energy balance at circumferential area element d. A 1. Constant heat flux: 2. Constant wall temperature: 1. Solution/temperature profile for constant heat flux: 2. Solution/temperature profile for constant wall temperature: Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 27

Calculation of the overall heat transfer rate Since the temperature difference TW-T(x) changes with

Calculation of the overall heat transfer rate Since the temperature difference TW-T(x) changes with position, it is defined: with the mean logarithmic temperature difference Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 28

Non-circular channels and ducts Usage of the hydraulic diameter: Example: Rectangular Channel with width

Non-circular channels and ducts Usage of the hydraulic diameter: Example: Rectangular Channel with width B and height H: Fluid properties at: Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 29

Heat Exchanger Classification § Basic flow types: used to model most design types –

Heat Exchanger Classification § Basic flow types: used to model most design types – Parallel-Flow – Counterflow – Crossflow § Design types – Shell and tubes – Plates – Compact heat exchangers • Hybrid of shell-tubes/plate: Channel structure instead of inner tubes connected by a single fin per plane • Prominent example: car engine radiator Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 30

Another Shell and Tube Example Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 31

Another Shell and Tube Example Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 31

Plate Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 32

Plate Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 32

Plate Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 33

Plate Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 33

Plate Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 34

Plate Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 34

The Overall Heat Transfer Coefficient § Determines the heat transfer rate from one fluid

The Overall Heat Transfer Coefficient § Determines the heat transfer rate from one fluid to another in heat exchangers. § Applicable to all heat exchanger types U: Overall heat transfer coefficient in W/(m²K) Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 35

Typical Model for Heat Exchangers § 1 d heat conduction through a composite cylinder

Typical Model for Heat Exchangers § 1 d heat conduction through a composite cylinder wall Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 36

Parallel Flow [In. Witt] Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 37

Parallel Flow [In. Witt] Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 37

Counterflow [In. Witt] Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 38

Counterflow [In. Witt] Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 38

Design Equations a) Parallel-Flow Logarithmic mean temp. b) Counterflow Fundamental HEX design equation Heat

Design Equations a) Parallel-Flow Logarithmic mean temp. b) Counterflow Fundamental HEX design equation Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 39

Special Operating Conditions [In. Witt] Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 40

Special Operating Conditions [In. Witt] Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 40

Cross-Flow and Multipass Heat Exchangers See next slide for usage of the correction factor

Cross-Flow and Multipass Heat Exchangers See next slide for usage of the correction factor F [In. Witt] Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 41

Design Equations Fundamental HEX design equation by introducing the modification And using the logarithmic

Design Equations Fundamental HEX design equation by introducing the modification And using the logarithmic mean temp. for counterflow Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 42

Heat Exchanger Analysis § Log mean temperature difference (LMTD) method is fairly easy to

Heat Exchanger Analysis § Log mean temperature difference (LMTD) method is fairly easy to use if all temperatures are specified or can be calculated by the overall energy balances. – This is a typical design case for which the overall heat transfer area A is the remaining unknown to be calculated. § However, if the inlet temperatures and the overall heat transfer area are known but no overall heat transfer rate and outlet temperatures, then an iterative procedure is needed. – This is a typical performance calculation of a given heat exchanger as it occurs in system simulations. § There is an alternative that is called “NTU-effectiveness method”. It does not require iterations. Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 43

The Effectiveness-NTU Method Definitions: Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 44

The Effectiveness-NTU Method Definitions: Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 44

Definition of Heat Exchanger Effectiveness Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 45

Definition of Heat Exchanger Effectiveness Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 45

Definition of the Number of Transfer Units - NTU Performance Calculation Heat Exchangers andreas.

Definition of the Number of Transfer Units - NTU Performance Calculation Heat Exchangers andreas. gubner@hm. edu Design Calculation 31. 10. 2020 46

Effectiveness. NTU Relations Performance Calculation [In. Witt] Heat Exchangers andreas. gubner@hm. edu 31. 10.

Effectiveness. NTU Relations Performance Calculation [In. Witt] Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 47

Effectiveness. NTU Relations Design Calculation 11. 31 b 11. 31 c [In. Witt] Heat

Effectiveness. NTU Relations Design Calculation 11. 31 b 11. 31 c [In. Witt] Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 48

Compact Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 49

Compact Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 49

Compact Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 50

Compact Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 50

Finned Tubes Left boundary condition: For each fin: Repeat Element a. Adibatic tip: Two

Finned Tubes Left boundary condition: For each fin: Repeat Element a. Adibatic tip: Two simple solutions are sufficient in many cases: b. Very long fin: [In. Witt] Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 51

Fin Effectiveness As a rule of thumb, fins make sense if For fins of

Fin Effectiveness As a rule of thumb, fins make sense if For fins of infinite length: Thermal Resistances: Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 52

Fin Efficiency It is quite straightforward to define a fin efficiency: For fins with

Fin Efficiency It is quite straightforward to define a fin efficiency: For fins with adiabatic tips: Thermal Resistances: Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 53

Overall Finned Surface Efficiency Total heat transfer rate of finned surface (per tube): Number

Overall Finned Surface Efficiency Total heat transfer rate of finned surface (per tube): Number of Fins: N with it follows: Definition of overall finned surface efficiency: Thermal Resistance of finned surface: Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 54

Caution: Contact Resistances may occur § If the finned surface is manufactured be pressfitting

Caution: Contact Resistances may occur § If the finned surface is manufactured be pressfitting sheets of metal to a bunch of tubes, additional contact resistances may apply that diminish fin performance. § Hence care must be taken that Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 55

UA – Value of a Finned Tube § Tube composed of N-1 layers including

UA – Value of a Finned Tube § Tube composed of N-1 layers including contact resistances and fouling resistances Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 56

Overall Finned Surface Efficiency Alternative Formulation Thermal Resistance of finned surface including contact resistance:

Overall Finned Surface Efficiency Alternative Formulation Thermal Resistance of finned surface including contact resistance: [In. Witt] Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 57

Outlook / Further Reading § Include pressure drop calculations § Design conflict – Low

Outlook / Further Reading § Include pressure drop calculations § Design conflict – Low pressure drop -> large surface area -> big Investment Costs – small surface area -> great pressure drop -> big operating costs § Design is a trade of between cost and space requirements § R&D in heat transfer rates especially for compact heat exchangers with complex geometry still needed – maybe aided by CFD for heat transfer and pressure drop Heat Exchangers andreas. gubner@hm. edu 31. 10. 2020 58