Heat Transfer at Proximity

Transcription

1 Heat Transfer at Proximity Matthias Krüger Universität Stuttgart an MPI for Intelligent Systems, Stuttgart Group Members: Artem Aerov Roberta Incarone External Stuent: Vlayslav Golyk, MIT Collaborators: Mehran Karar, MIT Thorsten Emig, Paris Giuseppe Bimonte, Naples Joseph Braer, Fribourg T 2 T 1

2 Table of Contents 1 Scattering Approach 2 Graient expansion 3 Surface roughness/moulation

3 Table of Contents 1 Scattering Approach 2 Graient expansion 3 Surface roughness/moulation

4 Scattering approach for Non-eq. QED (Rytov 196) Phenomenology Single object: Heat raiation Immerse other objects Force Formula for N arbitrary objects (212) Generalizes equilibrium result Rahi, Emig, Graham, Jaffe, Karar (29) Heat transfer (212) H = 2 ω [ ω Tr Re[T π ω k e B Ts 2 ] + T ] 2 T 1 [ 2 U Re[T 1 ] + T 1 T ]U 1 1 UT 1 UT T 1 2 U T 1 U. T p T 2 n T s T 1 Krüger, Bimonte, Emig, Karar, Phys. Rev. B 86, (212) Krüger, Emig, Karar, Phys. Rev. Lett. 16, 2144 (211) Messina, Antezza (211) Roriguez, Rei, Johnson (212) Narayanaswamy, Zheng (213)

5 Table of Contents 1 Scattering Approach 2 Graient expansion 3 Surface roughness/moulation

6 Experiments Typical setups: Curve surfaces Sphere-plate Sheng, Narayanaswamy, Chen (29) Rousseau et. al. (29)

7 Heat transfer: Theory Asymptotic {R,λ T } : H 2πR +R {R,λ T } : lim {R λ T } H R M. Krüger, T. Emig an M. Karar, Phys. Rev. Lett. 16, 2144 (211) Otey an Fan (211) Transfer Rate H s [σ T 4 2πR 2 ].7.5 PTA Ratio full solution one reflection s H PP (s) 1 lim {R λ T } H R / R H s ( = ) / R Class. R R [µm] = 2 R

8 Graient expansion y x S(x, y) Graient expansion H[S(x)] = Σ 2 x H pp (S)+ 2 x β H pp (S) S S + Σ Sphere-plate near = H pp 1 S 2 H = 2πRλ [ 1+(2β 1) R log ] +O( ) R Proximity Golyk, Krüger, McCauley, Karar, Europhys. Lett. 11, 342 (213) Fosco, Lombaro, Mazzitelli (211) Bimonte, Emig, Jaffe, Karar (212) Graient expansion

9 Sphere-plate Sphere near = H = 2πRλ [ 1+(2β 1) R log ] +O( ) R Proximity Graient expansion H()-H(=.4R) [nw] -5-1 SiO 2 SiC PTA-HT [nw] (SiC).5241(SiO 2 ).1.1 /R nw (SiC).2558 nw (SiO 2 ) /R Golyk, Krüger, McCauley, Karar, Europhys. Lett. 11, 342 (213) 4 2 B con. [nw/k] - con. (1 µm) Self emission Heat transfer R = 5 µm 1 1 [µm] =

10 Different geometries Sphere an plate H() = 2πRλ [1 (2β 1) R ] log +O( ), β 1 2 for SiC, SiO 2 logarithm almost absent R Golyk, Krüger, McCauley, Karar, Europhys. Lett. 11, 342 (213)

11 Different geometries Sphere an plate H() = 2πRλ [1 (2β 1) R ] log +O( ), β 1 2 for SiC, SiO 2 logarithm almost absent Two spheres H() = 2πλ R 1 R 2 R 1 + R 2 ( (2β 1) + R 1 R 2 [ 1+ R 1 + R 2 log ) log ]+... R R 2 R 1 Golyk, Krüger, McCauley, Karar, Europhys. Lett. 11, 342 (213)

12 Different geometries Sphere an plate H() = 2πRλ [1 (2β 1) R ] log +O( ), β 1 2 for SiC, SiO 2 logarithm almost absent Two spheres H() = 2πλ R 1 R 2 R 1 + R 2 ( (2β 1) + R 1 R 2 Cyliner an plate H() L = π Rλ 2 3/2 [ 1+ R 1 + R 2 log ) log ]+... [ ( 1+ 2β 3 ) ] +O( ) 4 R R R 2 R 1 R Golyk, Krüger, McCauley, Karar, Europhys. Lett. 11, 342 (213)

13 Table of Contents 1 Scattering Approach 2 Graient expansion 3 Surface roughness/moulation

14 Maximal non-contact transfer? Proximity approximation Parallel surfaces H 1 2.

15 Maximal non-contact transfer? Proximity approximation Parallel surfaces H 1 2. H 1 C = 1 H() - H(3 nm) [α 1 3 ] 5 45 h=4 nm 4 σ =1 nm / [nm] Krüger, Golyk, Bimonte, Karar, arxiv:

16 Maximal non-contact transfer? Proximity approximation Parallel surfaces H 1 2. McCauley, Rei, Krüger, Johnson, Phys. Rev. B 85, (212) H 1 C = 1 H log C = 2 H() - H(3 nm) [α 1 3 ] 5 45 h=4 nm 4 σ =1 nm / [nm] Krüger, Golyk, Bimonte, Karar, arxiv:

17 Maximal non-contact transfer? Proximity approximation Parallel surfaces H 1 2. H 1 C = 1 H log C = 2 McCauley, Rei, Krüger, Johnson, Phys. Rev. B 85, (212) H log C = 2 H() - H(3 nm) [α 1 3 ] 5 45 h=4 nm 4 log σ =1 nm / [nm] Krüger, Golyk, Bimonte, Karar, arxiv:

18 Maximal non-contact transfer? Proximity approximation Parallel surfaces H 1 2. H 1 C = 1 H log C = 2 McCauley, Rei, Krüger, Johnson, Phys. Rev. B 85, (212) H log C = 2 H C = 3 H() - H(3 nm) [α 1 3 ] 5 45 h=4 nm 4 log σ =1 nm / [nm] Krüger, Golyk, Bimonte, Karar, arxiv:

19 Maximal non-contact transfer? Proximity approximation Parallel surfaces H 1 2. H 1 C = 1 H log C = 2 Roughness: C = McCauley, Rei, Krüger, Johnson, Phys. Rev. B 85, (212) H log C = 2 H C = 3 H() - H(3 nm) [α 1 3 ] 5 45 h=4 nm 4 log σ =1 nm Roughness / [nm] Krüger, Golyk, Bimonte, Karar, arxiv:

20 Maximal non-contact transfer? Proximity approximation Parallel surfaces H 1 2. H 1 C = 1 H log C = 2 Roughness: C = McCauley, Rei, Krüger, Johnson, Phys. Rev. B 85, (212) H log C = 2 H C = 3 H() - H(3 nm) [α 1 3 ] 5 45 h=4 nm 4 log σ =1 nm Roughness / [nm] Krüger, Golyk, Bimonte, Karar, arxiv: Geometry with C = 4: Force: F 1 3

21 Summary Graient expansion quantifies corrections to proximity transfer approximation Near fiel ajuste plot suitable to apply PTA Effects of roughness/moulation can be estimate in simple scheme