Transport processes. 7. Semester Chemical Engineering Civil Engineering

Transcription

1 Transport processes 7. Semester Chemical Engineering Civil Engineering

2 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite Control Volume Analysis 4. Differential Analysis of Fluid Flow 5. Viscous Flow and Turbulence 6. Turbulent Boundary Layer Flow 7. Principles of Heat Transfer 8. Internal Forces Convection 9. Unsteady Heat Transfer 10. Boiling and Condensation 11. Mass Transfer 12. Porous Media Flow 13. Non-Newtonian Flow Course plan

3 Today's lecture Principles of Heat Transfer Heat transfer mechanisms Conduction Heat transfer Thermal resistance concept Contact resistance Thermal networks

4 Heat transfer Heat is transferred whenever there is a temperature difference

5 Heat conduction Heat is the kinetic energy of molecules When a molecule with high kinetic energy hit one with low kinetic energy momentum is transferred Heat transfer

6 Heat convection Besides heat conduction, heat I s also transferred due to the motion of the fluid Convection = Conduction + Advection (fluid motion) Forced convection Due to flow Natural convection Difference in temperature = difference in density

7 Radiation Heat energy is transferred by photons Everything emits radiation, i.e. inferred radiation

8 Thermal conductivity The thermal conductivity: k [ W / m C] How much heat (energy) per second, per meter, per degree Celsius there can be transferred I a given material Metals is good heat conductors Gasses are poor heat conductors

9 intermezzo Use the next two minutes to discuss with the person next to you how a double plated window works?

10 Thermal diffusivity The ratio between heat conduction and heat capacity How fast heat is conducted through the material α = = How much heat there can be stored in the material k ρc P One does not burn the fingers by putting them in an oven momentarily, but one does them if you touch the pot burn Iron: α=22.8m 2 /s ceramic: α=0.75m 2 /s wood: α=0.13m 2 /s Air: α= m 2 /s

11 Fouriers law Fouriers law of heat conduction dt dx T T x [ ] 1 2 Qcond = ka = ka W Heat always flows from warm to cold! A is the area normal to the flow direction

12 Newtons law of cooling Newton s law of cooling conv s s ( ) [ ] Q = ha T T W h is the convective heat transfer coefficient A s is the surface area T s is the surface temperature T is the temperature of the surroundings h [W/m 2 C] depends on the flow! And is not a property of the fluid.

13 Some empirical h relations For fully developed flows with constant surface temperature Flow over a flat plate hl Laminar: Nu = = Re k Pr hl Turbulent: Nu = = Re k Pr L L Pipe flow hd Laminar: Nu = = 3.66 k hl Turbulent: Nu = = 0.023Re Pr k L T in T out T S

14 Even more nondimensional numbers Nusselt number hl Nu = = k convection conduction Dimensionless convective heat transfer coefficient States how much more heat is transferred from convection (movement) compared to pure heat conduction (standstill) Prandtl number µ c momentum Pr = p = k heat Non-dimensional grouping of fluid properties Is temperature dependent! can be found in tables in the back of the book

15 Comparison of mechanisms

16 Stafan-boltzmann s law Stafan-boltzmann s law rad 4 4 ( s ) [ ] Q = εσ T T W ε is the emissivity (0<ε<1) σ is Boltzmanns constant ( W/m 2 K 4 ) Depends on T 4

17

18 Thermal resistance concept Ohms-law: Flow of electrons V = I = V R 1 2 e Fouriers law: Flow of heat Newtons law: T T T T = Q cond = ka = x R Q cond T T = R conv Wall

19 Chuck Norris law

20 Resistances in series

21 Resistances in series The heat flow is the same through the entire wall: T = T R 1 2 total 1 L 1 Rtotal = Rconv,1 + Rwall + Rconv,2 = + + h A ka h A 1 2

22 Parallel resistances

23 Kombinationer

24 Intermezzo Use the next 5 min to discuss how to calculate how much energy you need to heat up this architectural marvel on a winters day. What assumptions do I need to take? What information do I need to find? How should the thermal network look like?

25 Overall heat transfer coefficient Often we are only interested in one number for the heat transfer resistance. For example a heat exchanger can have a very complex geometry. Only the total resistance can be measured and is given by a U value. Overall heat transfer coefficient: U [W/m 2 C] the heat transfer is found from: [ ] Q = UA T W and it can be seen that: 1 = UA Rtotal

26

27 Heat transfer through a hollow cylinder Newtons law of cooling in cylindrical coordinates Q cond cyl dt, = ka (W) dr This can be integrated to give: Q cond, cyl T T T T = 2π Lk = ln r / r R ( ) 2 1 cyl

28 Heat transfer through a hollow cylinder Thermal Resistance with Convection Q = T T,1,2 R total R = R + R + R = total conv,1 cyl conv,2 ( ) ( r r ) 1 ln / 1 2πrL h 2πLk 2πr L h 2 1 = + + ( )

29 Heat transfer through a hollow cylinder Multi-layered Cylinders R = R + R + R + R + R = total conv,1 cyl,1 cyl,3 cyl,3 conv,2 ( ) ( r r ) ( r r ) ( r r ) 1 ln / ln / ln / 1 2πr L h 2πLk 2πLk 2πLk 2πr L h = ( )

30 Heat transfer through a hollow cylinder Critical radius of insulation Adding more insulation to a wall always decreases heat transfer. Adding insulation to a cylindrical pipe or a spherical shell, however, is a different matter. Adding insulation increases the conduction resistance of the insulation layer but decreases the convection resistance of the surface because of the increase in the outer surface area for convection. The heat transfer from the pipe may increase or decrease, depending on which effect dominates.

31 Heat transfer through a hollow cylinder The rate of heat transfer from the insulated pipe to the surrounding air can be expressed as: Q T1 T T1 T = = R ln ( r2 / r ins + Rconv 1) 1 + 2πLk h 2 r L increases with r 2 ( π ) 2 decreases with r 2

32 Heat transfer through a hollow cylinder The radius of critical insulation is found when: dq dr = Performing the differentiation gives: r 0 k, = (m) h cr cylinder

33 Example

34 Thermal contact resistance When two surfaces are pressed against each other, the peaks form good material contact but the valleys form voids filled with air Unfortunately, no empirical formulae exists to properly to predict contact resistances correctly! (material, pressure, surface roughness ) Thermal grease can significant reduce the contact resistance.

35 Thermal contact resistance

36 Excercises