1. winter/20011-12IntroductionM. Shapiro 1 Can calculate Q 12 [J] from the first law of thermo. קצב מעבר חום heat transfer rate can’t calculate from thermo שטף חום Heat flux Heat Interaction Temperature difference  T=T 1 -T 2 between bodies causes heat interaction Q 12 חםT1T1 גוף 1 קרT2T2 גוף 2 Heat Q 12 T 1, T 2 :t=0 התחלה זהה T :t=t סוף :

2. winter/20011-12IntroductionM. Shapiro 2 Heat Transfer Mechanisms הולכהConduction (no flow) T1T1 T 2 <T 1 Moving fluid T1T1 T2T2 Convection הסעה T1T1 T2T2 קרינהRadiation solid Solid or fluid Also exist Boiling, condensation עבוי אידוי חום

3. winter/20011-12IntroductionM. Shapiro 3 שטף חוםHeat flux Heat flux normal to the surface area Heat transfer within a body heated nonuniformly Heat flux vector: Hot Cold Hot

4. winter/20011-12IntroductionM. Shapiro 4 Field of Temperature within a body flux T1T1 T=const (איזותרמות) T2T2 T1T1 T2T2 q”-lines T=const (Isotherms) flux Plane wall Cylindrical/spherical wall Isotherms and q”-lines are orthogonal קווי זרם החום

5. winter/20011-12IntroductionM. Shapiro 5 מקורות חוםVolume heat generation Heat generation intensity Not a vector! Heat generation Electric current Volume Total heat generation rate Electrode

6. winter/20011-12IntroductionM. Shapiro 6 Fourier Law Conduction T1T1 T2T2 T 1 >T 2 k – thermal conductivity, [W/mK] For linear temperature distribution: k =k(T,p) –material’s thermodynamic property T(x) T1T1 T2T2 1D General

7. winter/20011-12IntroductionM. Shapiro 7 Conduction in gases/liquids Temperature: Kinetic energy of molecules’ motion Gas molecules Energy transfer or Heat transfer T1T1 T2T2 x T(x) Internal (thermal) Energy: Hot Cold

8. winter/20011-12IntroductionM. Shapiro 8 Conduction in solids Temperature: Kinetic energy of atoms’ vibrations Model of solid crystal Vibrations T1T1 T2T2 x T(x) Internal (thermal) Energy: Energy transfer or Heat transfer T2T2 T2T2

9. winter/20011-12IntroductionM. Shapiro 9 Thermal conductivity k, W/mK Material (room conditions) 0.01-0.05 Gases 150 Oil 0.55water 240Al 15-60Steel 20-50Al 2 O 3 ~2000Graphite 0.1-0.2Wood

10. winter/20011-12IntroductionM. Shapiro 10 מקדם מעבר חום בהסעה זורם (קר) Boundary layer h - heat transfer coefficient, [W/m 2 K] solid From the wall Towards the wall Heat flux לא תכונה! Newton’s Law: Heat flux on the solid-fluid interface: מוצק (חם)

11. winter/20011-12IntroductionM. Shapiro 11 Convection processes Forced convection (fan) Free convection (due to buoyancy) Boiling (phase transition + buoyancy) Condensation

12. winter/20011-12IntroductionM. Shapiro 12 Black-body radiation Energy emitted by surfaces and transferred by electromagnetic waves or moving photons Rate of energy transfer from surface – emissive power TsTs Black body Irradiation Emissive power Stefan-Boltzmann constant A

13. winter/20011-12IntroductionM. Shapiro 13 Real surface radiation TsTs Surface with emissivity  T sur Large surroundings at A Net radiation heat transfer rate from surface emissivity 

14. winter/20011-12IntroductionM. Shapiro 14 Climate System Energy Balance

15. winter/20011-12IntroductionM. Shapiro 15 Microchannel heat collector