On the convective instability of a thermal boundary layer
Abstract When the surface temperature of a liquid is a harmonic function of time with a frequencyω, a temperature wave propagates into the liquid. The amplitude of this wave decreases exponentially with distance from the surface. The temperature oscillation is essentially concentrated in a layer of...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Gershuni, G. Z. [verfasserIn] |
|---|
| Format: |
Artikel |
|---|---|
| Sprache: |
Englisch |
| Erschienen: |
1965 |
|---|
| Schlagwörter: |
|---|
| Anmerkung: |
© The Faraday Press, Inc. 1967 |
|---|
| Übergeordnetes Werk: |
Enthalten in: Journal of applied mechanics and technical physics - Kluwer Academic Publishers-Plenum Publishers, 1966, 6(1965), 6 vom: Nov., Seite 34-36 |
|---|---|
| Übergeordnetes Werk: |
volume:6 ; year:1965 ; number:6 ; month:11 ; pages:34-36 |
| Links: |
|---|
| DOI / URN: |
10.1007/BF00919308 |
|---|
| Katalog-ID: |
OLC2034369017 |
|---|
| LEADER | 01000caa a22002652 4500 | ||
|---|---|---|---|
| 001 | OLC2034369017 | ||
| 003 | DE-627 | ||
| 005 | 20230503104438.0 | ||
| 007 | tu | ||
| 008 | 200819s1965 xx ||||| 00| ||eng c | ||
| 024 | 7 | |a 10.1007/BF00919308 |2 doi | |
| 035 | |a (DE-627)OLC2034369017 | ||
| 035 | |a (DE-He213)BF00919308-p | ||
| 040 | |a DE-627 |b ger |c DE-627 |e rakwb | ||
| 041 | |a eng | ||
| 082 | 0 | 4 | |a 530 |q VZ |
| 100 | 1 | |a Gershuni, G. Z. |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a On the convective instability of a thermal boundary layer |
| 264 | 1 | |c 1965 | |
| 336 | |a Text |b txt |2 rdacontent | ||
| 337 | |a ohne Hilfsmittel zu benutzen |b n |2 rdamedia | ||
| 338 | |a Band |b nc |2 rdacarrier | ||
| 500 | |a © The Faraday Press, Inc. 1967 | ||
| 520 | |a Abstract When the surface temperature of a liquid is a harmonic function of time with a frequencyω, a temperature wave propagates into the liquid. The amplitude of this wave decreases exponentially with distance from the surface. The temperature oscillation is essentially concentrated in a layer of the order of (2χ/ω)1/2, where x is the thermal conductivity of the liquid (thermal boundary layer). Depending on the phase, at certain positions below the surface the temperature gradient is directed downwards and if its magnitude is sufficiently large (the magnitude is a function of the amplitude and frequency of the surface oscillations) the liquid can become unstable with respect to the onset of convection. In that case the convective motion may spread beyond the initial unstable layer. For low frequencies the stability condition can be derived from the usual static Rayleigh criterion, on the basis of the Rayleigh number and the average temperature gradient of the unstable layer. This quasi-static approach, used by Sal'nikov [1], is appropriate to those cases in which the period of the temperature oscillations is much larger than the characteristic time of the perturbations. But when these times are of the same order, the problem must be analyzed in dynamic terms. The stability problem must then be formulated as a problem of parametricresonance excitation of velocity oscillations due to the action of a variable parameter-the temperature gradient. In an earlier work [2] we considered the problem of the stability of a horizontal layer of liquid with a periodically varying temperature gradient. It was assumed that the thickness of the layer was much smaller than the penetration depth of the thermal wave, so that the temperature gradient could be assumed to be independent of position. In the present work we consider the opposite case, in which the liquid layer is assumed to be much larger than the penetration depth, i. e., a thermal boundary layer can be defined. The temperature gradient at equilibrium, which is a parameter in the equations determining the onset of perturbations, is here a periodic function of time and a relatively complicated function of the depth coordinate z. The periodic oscillations are solved by the Fourier method; the equations for the amplitudes are solved by the approximate method of KarmanPohlhausen. | ||
| 650 | 4 | |a Temperature Gradient | |
| 650 | 4 | |a Penetration Depth | |
| 650 | 4 | |a Rayleigh Number | |
| 650 | 4 | |a Thermal Boundary Layer | |
| 650 | 4 | |a Thermal Wave | |
| 700 | 1 | |a Zhukhovitskii, E. M. |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Journal of applied mechanics and technical physics |d Kluwer Academic Publishers-Plenum Publishers, 1966 |g 6(1965), 6 vom: Nov., Seite 34-36 |w (DE-627)129600946 |w (DE-600)241350-4 |w (DE-576)015094545 |x 0021-8944 |7 nnns |
| 773 | 1 | 8 | |g volume:6 |g year:1965 |g number:6 |g month:11 |g pages:34-36 |
| 856 | 4 | 1 | |u https://doi.org/10.1007/BF00919308 |z lizenzpflichtig |3 Volltext |
| 912 | |a GBV_USEFLAG_A | ||
| 912 | |a SYSFLAG_A | ||
| 912 | |a GBV_OLC | ||
| 912 | |a SSG-OLC-TEC | ||
| 912 | |a SSG-OLC-PHY | ||
| 912 | |a GBV_ILN_11 | ||
| 912 | |a GBV_ILN_20 | ||
| 912 | |a GBV_ILN_70 | ||
| 951 | |a AR | ||
| 952 | |d 6 |j 1965 |e 6 |c 11 |h 34-36 | ||
| author_variant |
g z g gz gzg e m z em emz |
|---|---|
| matchkey_str |
article:00218944:1965----::nhcnetvisaiiyfteml |
| hierarchy_sort_str |
1965 |
| publishDate |
1965 |
| allfields |
10.1007/BF00919308 doi (DE-627)OLC2034369017 (DE-He213)BF00919308-p DE-627 ger DE-627 rakwb eng 530 VZ Gershuni, G. Z. verfasserin aut On the convective instability of a thermal boundary layer 1965 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Faraday Press, Inc. 1967 Abstract When the surface temperature of a liquid is a harmonic function of time with a frequencyω, a temperature wave propagates into the liquid. The amplitude of this wave decreases exponentially with distance from the surface. The temperature oscillation is essentially concentrated in a layer of the order of (2χ/ω)1/2, where x is the thermal conductivity of the liquid (thermal boundary layer). Depending on the phase, at certain positions below the surface the temperature gradient is directed downwards and if its magnitude is sufficiently large (the magnitude is a function of the amplitude and frequency of the surface oscillations) the liquid can become unstable with respect to the onset of convection. In that case the convective motion may spread beyond the initial unstable layer. For low frequencies the stability condition can be derived from the usual static Rayleigh criterion, on the basis of the Rayleigh number and the average temperature gradient of the unstable layer. This quasi-static approach, used by Sal'nikov [1], is appropriate to those cases in which the period of the temperature oscillations is much larger than the characteristic time of the perturbations. But when these times are of the same order, the problem must be analyzed in dynamic terms. The stability problem must then be formulated as a problem of parametricresonance excitation of velocity oscillations due to the action of a variable parameter-the temperature gradient. In an earlier work [2] we considered the problem of the stability of a horizontal layer of liquid with a periodically varying temperature gradient. It was assumed that the thickness of the layer was much smaller than the penetration depth of the thermal wave, so that the temperature gradient could be assumed to be independent of position. In the present work we consider the opposite case, in which the liquid layer is assumed to be much larger than the penetration depth, i. e., a thermal boundary layer can be defined. The temperature gradient at equilibrium, which is a parameter in the equations determining the onset of perturbations, is here a periodic function of time and a relatively complicated function of the depth coordinate z. The periodic oscillations are solved by the Fourier method; the equations for the amplitudes are solved by the approximate method of KarmanPohlhausen. Temperature Gradient Penetration Depth Rayleigh Number Thermal Boundary Layer Thermal Wave Zhukhovitskii, E. M. aut Enthalten in Journal of applied mechanics and technical physics Kluwer Academic Publishers-Plenum Publishers, 1966 6(1965), 6 vom: Nov., Seite 34-36 (DE-627)129600946 (DE-600)241350-4 (DE-576)015094545 0021-8944 nnns volume:6 year:1965 number:6 month:11 pages:34-36 https://doi.org/10.1007/BF00919308 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_11 GBV_ILN_20 GBV_ILN_70 AR 6 1965 6 11 34-36 |
| spelling |
10.1007/BF00919308 doi (DE-627)OLC2034369017 (DE-He213)BF00919308-p DE-627 ger DE-627 rakwb eng 530 VZ Gershuni, G. Z. verfasserin aut On the convective instability of a thermal boundary layer 1965 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Faraday Press, Inc. 1967 Abstract When the surface temperature of a liquid is a harmonic function of time with a frequencyω, a temperature wave propagates into the liquid. The amplitude of this wave decreases exponentially with distance from the surface. The temperature oscillation is essentially concentrated in a layer of the order of (2χ/ω)1/2, where x is the thermal conductivity of the liquid (thermal boundary layer). Depending on the phase, at certain positions below the surface the temperature gradient is directed downwards and if its magnitude is sufficiently large (the magnitude is a function of the amplitude and frequency of the surface oscillations) the liquid can become unstable with respect to the onset of convection. In that case the convective motion may spread beyond the initial unstable layer. For low frequencies the stability condition can be derived from the usual static Rayleigh criterion, on the basis of the Rayleigh number and the average temperature gradient of the unstable layer. This quasi-static approach, used by Sal'nikov [1], is appropriate to those cases in which the period of the temperature oscillations is much larger than the characteristic time of the perturbations. But when these times are of the same order, the problem must be analyzed in dynamic terms. The stability problem must then be formulated as a problem of parametricresonance excitation of velocity oscillations due to the action of a variable parameter-the temperature gradient. In an earlier work [2] we considered the problem of the stability of a horizontal layer of liquid with a periodically varying temperature gradient. It was assumed that the thickness of the layer was much smaller than the penetration depth of the thermal wave, so that the temperature gradient could be assumed to be independent of position. In the present work we consider the opposite case, in which the liquid layer is assumed to be much larger than the penetration depth, i. e., a thermal boundary layer can be defined. The temperature gradient at equilibrium, which is a parameter in the equations determining the onset of perturbations, is here a periodic function of time and a relatively complicated function of the depth coordinate z. The periodic oscillations are solved by the Fourier method; the equations for the amplitudes are solved by the approximate method of KarmanPohlhausen. Temperature Gradient Penetration Depth Rayleigh Number Thermal Boundary Layer Thermal Wave Zhukhovitskii, E. M. aut Enthalten in Journal of applied mechanics and technical physics Kluwer Academic Publishers-Plenum Publishers, 1966 6(1965), 6 vom: Nov., Seite 34-36 (DE-627)129600946 (DE-600)241350-4 (DE-576)015094545 0021-8944 nnns volume:6 year:1965 number:6 month:11 pages:34-36 https://doi.org/10.1007/BF00919308 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_11 GBV_ILN_20 GBV_ILN_70 AR 6 1965 6 11 34-36 |
| allfields_unstemmed |
10.1007/BF00919308 doi (DE-627)OLC2034369017 (DE-He213)BF00919308-p DE-627 ger DE-627 rakwb eng 530 VZ Gershuni, G. Z. verfasserin aut On the convective instability of a thermal boundary layer 1965 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Faraday Press, Inc. 1967 Abstract When the surface temperature of a liquid is a harmonic function of time with a frequencyω, a temperature wave propagates into the liquid. The amplitude of this wave decreases exponentially with distance from the surface. The temperature oscillation is essentially concentrated in a layer of the order of (2χ/ω)1/2, where x is the thermal conductivity of the liquid (thermal boundary layer). Depending on the phase, at certain positions below the surface the temperature gradient is directed downwards and if its magnitude is sufficiently large (the magnitude is a function of the amplitude and frequency of the surface oscillations) the liquid can become unstable with respect to the onset of convection. In that case the convective motion may spread beyond the initial unstable layer. For low frequencies the stability condition can be derived from the usual static Rayleigh criterion, on the basis of the Rayleigh number and the average temperature gradient of the unstable layer. This quasi-static approach, used by Sal'nikov [1], is appropriate to those cases in which the period of the temperature oscillations is much larger than the characteristic time of the perturbations. But when these times are of the same order, the problem must be analyzed in dynamic terms. The stability problem must then be formulated as a problem of parametricresonance excitation of velocity oscillations due to the action of a variable parameter-the temperature gradient. In an earlier work [2] we considered the problem of the stability of a horizontal layer of liquid with a periodically varying temperature gradient. It was assumed that the thickness of the layer was much smaller than the penetration depth of the thermal wave, so that the temperature gradient could be assumed to be independent of position. In the present work we consider the opposite case, in which the liquid layer is assumed to be much larger than the penetration depth, i. e., a thermal boundary layer can be defined. The temperature gradient at equilibrium, which is a parameter in the equations determining the onset of perturbations, is here a periodic function of time and a relatively complicated function of the depth coordinate z. The periodic oscillations are solved by the Fourier method; the equations for the amplitudes are solved by the approximate method of KarmanPohlhausen. Temperature Gradient Penetration Depth Rayleigh Number Thermal Boundary Layer Thermal Wave Zhukhovitskii, E. M. aut Enthalten in Journal of applied mechanics and technical physics Kluwer Academic Publishers-Plenum Publishers, 1966 6(1965), 6 vom: Nov., Seite 34-36 (DE-627)129600946 (DE-600)241350-4 (DE-576)015094545 0021-8944 nnns volume:6 year:1965 number:6 month:11 pages:34-36 https://doi.org/10.1007/BF00919308 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_11 GBV_ILN_20 GBV_ILN_70 AR 6 1965 6 11 34-36 |
| allfieldsGer |
10.1007/BF00919308 doi (DE-627)OLC2034369017 (DE-He213)BF00919308-p DE-627 ger DE-627 rakwb eng 530 VZ Gershuni, G. Z. verfasserin aut On the convective instability of a thermal boundary layer 1965 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Faraday Press, Inc. 1967 Abstract When the surface temperature of a liquid is a harmonic function of time with a frequencyω, a temperature wave propagates into the liquid. The amplitude of this wave decreases exponentially with distance from the surface. The temperature oscillation is essentially concentrated in a layer of the order of (2χ/ω)1/2, where x is the thermal conductivity of the liquid (thermal boundary layer). Depending on the phase, at certain positions below the surface the temperature gradient is directed downwards and if its magnitude is sufficiently large (the magnitude is a function of the amplitude and frequency of the surface oscillations) the liquid can become unstable with respect to the onset of convection. In that case the convective motion may spread beyond the initial unstable layer. For low frequencies the stability condition can be derived from the usual static Rayleigh criterion, on the basis of the Rayleigh number and the average temperature gradient of the unstable layer. This quasi-static approach, used by Sal'nikov [1], is appropriate to those cases in which the period of the temperature oscillations is much larger than the characteristic time of the perturbations. But when these times are of the same order, the problem must be analyzed in dynamic terms. The stability problem must then be formulated as a problem of parametricresonance excitation of velocity oscillations due to the action of a variable parameter-the temperature gradient. In an earlier work [2] we considered the problem of the stability of a horizontal layer of liquid with a periodically varying temperature gradient. It was assumed that the thickness of the layer was much smaller than the penetration depth of the thermal wave, so that the temperature gradient could be assumed to be independent of position. In the present work we consider the opposite case, in which the liquid layer is assumed to be much larger than the penetration depth, i. e., a thermal boundary layer can be defined. The temperature gradient at equilibrium, which is a parameter in the equations determining the onset of perturbations, is here a periodic function of time and a relatively complicated function of the depth coordinate z. The periodic oscillations are solved by the Fourier method; the equations for the amplitudes are solved by the approximate method of KarmanPohlhausen. Temperature Gradient Penetration Depth Rayleigh Number Thermal Boundary Layer Thermal Wave Zhukhovitskii, E. M. aut Enthalten in Journal of applied mechanics and technical physics Kluwer Academic Publishers-Plenum Publishers, 1966 6(1965), 6 vom: Nov., Seite 34-36 (DE-627)129600946 (DE-600)241350-4 (DE-576)015094545 0021-8944 nnns volume:6 year:1965 number:6 month:11 pages:34-36 https://doi.org/10.1007/BF00919308 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_11 GBV_ILN_20 GBV_ILN_70 AR 6 1965 6 11 34-36 |
| allfieldsSound |
10.1007/BF00919308 doi (DE-627)OLC2034369017 (DE-He213)BF00919308-p DE-627 ger DE-627 rakwb eng 530 VZ Gershuni, G. Z. verfasserin aut On the convective instability of a thermal boundary layer 1965 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Faraday Press, Inc. 1967 Abstract When the surface temperature of a liquid is a harmonic function of time with a frequencyω, a temperature wave propagates into the liquid. The amplitude of this wave decreases exponentially with distance from the surface. The temperature oscillation is essentially concentrated in a layer of the order of (2χ/ω)1/2, where x is the thermal conductivity of the liquid (thermal boundary layer). Depending on the phase, at certain positions below the surface the temperature gradient is directed downwards and if its magnitude is sufficiently large (the magnitude is a function of the amplitude and frequency of the surface oscillations) the liquid can become unstable with respect to the onset of convection. In that case the convective motion may spread beyond the initial unstable layer. For low frequencies the stability condition can be derived from the usual static Rayleigh criterion, on the basis of the Rayleigh number and the average temperature gradient of the unstable layer. This quasi-static approach, used by Sal'nikov [1], is appropriate to those cases in which the period of the temperature oscillations is much larger than the characteristic time of the perturbations. But when these times are of the same order, the problem must be analyzed in dynamic terms. The stability problem must then be formulated as a problem of parametricresonance excitation of velocity oscillations due to the action of a variable parameter-the temperature gradient. In an earlier work [2] we considered the problem of the stability of a horizontal layer of liquid with a periodically varying temperature gradient. It was assumed that the thickness of the layer was much smaller than the penetration depth of the thermal wave, so that the temperature gradient could be assumed to be independent of position. In the present work we consider the opposite case, in which the liquid layer is assumed to be much larger than the penetration depth, i. e., a thermal boundary layer can be defined. The temperature gradient at equilibrium, which is a parameter in the equations determining the onset of perturbations, is here a periodic function of time and a relatively complicated function of the depth coordinate z. The periodic oscillations are solved by the Fourier method; the equations for the amplitudes are solved by the approximate method of KarmanPohlhausen. Temperature Gradient Penetration Depth Rayleigh Number Thermal Boundary Layer Thermal Wave Zhukhovitskii, E. M. aut Enthalten in Journal of applied mechanics and technical physics Kluwer Academic Publishers-Plenum Publishers, 1966 6(1965), 6 vom: Nov., Seite 34-36 (DE-627)129600946 (DE-600)241350-4 (DE-576)015094545 0021-8944 nnns volume:6 year:1965 number:6 month:11 pages:34-36 https://doi.org/10.1007/BF00919308 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_11 GBV_ILN_20 GBV_ILN_70 AR 6 1965 6 11 34-36 |
| language |
English |
| source |
Enthalten in Journal of applied mechanics and technical physics 6(1965), 6 vom: Nov., Seite 34-36 volume:6 year:1965 number:6 month:11 pages:34-36 |
| sourceStr |
Enthalten in Journal of applied mechanics and technical physics 6(1965), 6 vom: Nov., Seite 34-36 volume:6 year:1965 number:6 month:11 pages:34-36 |
| format_phy_str_mv |
Article |
| institution |
findex.gbv.de |
| topic_facet |
Temperature Gradient Penetration Depth Rayleigh Number Thermal Boundary Layer Thermal Wave |
| dewey-raw |
530 |
| isfreeaccess_bool |
false |
| container_title |
Journal of applied mechanics and technical physics |
| authorswithroles_txt_mv |
Gershuni, G. Z. @@aut@@ Zhukhovitskii, E. M. @@aut@@ |
| publishDateDaySort_date |
1965-11-01T00:00:00Z |
| hierarchy_top_id |
129600946 |
| dewey-sort |
3530 |
| id |
OLC2034369017 |
| language_de |
englisch |
| fullrecord |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">OLC2034369017</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230503104438.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">200819s1965 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/BF00919308</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2034369017</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)BF00919308-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">530</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Gershuni, G. Z.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">On the convective instability of a thermal boundary layer</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">1965</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© The Faraday Press, Inc. 1967</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract When the surface temperature of a liquid is a harmonic function of time with a frequencyω, a temperature wave propagates into the liquid. The amplitude of this wave decreases exponentially with distance from the surface. The temperature oscillation is essentially concentrated in a layer of the order of (2χ/ω)1/2, where x is the thermal conductivity of the liquid (thermal boundary layer). Depending on the phase, at certain positions below the surface the temperature gradient is directed downwards and if its magnitude is sufficiently large (the magnitude is a function of the amplitude and frequency of the surface oscillations) the liquid can become unstable with respect to the onset of convection. In that case the convective motion may spread beyond the initial unstable layer. For low frequencies the stability condition can be derived from the usual static Rayleigh criterion, on the basis of the Rayleigh number and the average temperature gradient of the unstable layer. This quasi-static approach, used by Sal'nikov [1], is appropriate to those cases in which the period of the temperature oscillations is much larger than the characteristic time of the perturbations. But when these times are of the same order, the problem must be analyzed in dynamic terms. The stability problem must then be formulated as a problem of parametricresonance excitation of velocity oscillations due to the action of a variable parameter-the temperature gradient. In an earlier work [2] we considered the problem of the stability of a horizontal layer of liquid with a periodically varying temperature gradient. It was assumed that the thickness of the layer was much smaller than the penetration depth of the thermal wave, so that the temperature gradient could be assumed to be independent of position. In the present work we consider the opposite case, in which the liquid layer is assumed to be much larger than the penetration depth, i. e., a thermal boundary layer can be defined. The temperature gradient at equilibrium, which is a parameter in the equations determining the onset of perturbations, is here a periodic function of time and a relatively complicated function of the depth coordinate z. The periodic oscillations are solved by the Fourier method; the equations for the amplitudes are solved by the approximate method of KarmanPohlhausen.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Temperature Gradient</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Penetration Depth</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Rayleigh Number</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Thermal Boundary Layer</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Thermal Wave</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Zhukhovitskii, E. M.</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Journal of applied mechanics and technical physics</subfield><subfield code="d">Kluwer Academic Publishers-Plenum Publishers, 1966</subfield><subfield code="g">6(1965), 6 vom: Nov., Seite 34-36</subfield><subfield code="w">(DE-627)129600946</subfield><subfield code="w">(DE-600)241350-4</subfield><subfield code="w">(DE-576)015094545</subfield><subfield code="x">0021-8944</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:6</subfield><subfield code="g">year:1965</subfield><subfield code="g">number:6</subfield><subfield code="g">month:11</subfield><subfield code="g">pages:34-36</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">https://doi.org/10.1007/BF00919308</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-TEC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-PHY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_11</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_20</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">6</subfield><subfield code="j">1965</subfield><subfield code="e">6</subfield><subfield code="c">11</subfield><subfield code="h">34-36</subfield></datafield></record></collection>
|
| author |
Gershuni, G. Z. |
| spellingShingle |
Gershuni, G. Z. ddc 530 misc Temperature Gradient misc Penetration Depth misc Rayleigh Number misc Thermal Boundary Layer misc Thermal Wave On the convective instability of a thermal boundary layer |
| authorStr |
Gershuni, G. Z. |
| ppnlink_with_tag_str_mv |
@@773@@(DE-627)129600946 |
| format |
Article |
| dewey-ones |
530 - Physics |
| delete_txt_mv |
keep |
| author_role |
aut aut |
| collection |
OLC |
| remote_str |
false |
| illustrated |
Not Illustrated |
| issn |
0021-8944 |
| topic_title |
530 VZ On the convective instability of a thermal boundary layer Temperature Gradient Penetration Depth Rayleigh Number Thermal Boundary Layer Thermal Wave |
| topic |
ddc 530 misc Temperature Gradient misc Penetration Depth misc Rayleigh Number misc Thermal Boundary Layer misc Thermal Wave |
| topic_unstemmed |
ddc 530 misc Temperature Gradient misc Penetration Depth misc Rayleigh Number misc Thermal Boundary Layer misc Thermal Wave |
| topic_browse |
ddc 530 misc Temperature Gradient misc Penetration Depth misc Rayleigh Number misc Thermal Boundary Layer misc Thermal Wave |
| format_facet |
Aufsätze Gedruckte Aufsätze |
| format_main_str_mv |
Text Zeitschrift/Artikel |
| carriertype_str_mv |
nc |
| hierarchy_parent_title |
Journal of applied mechanics and technical physics |
| hierarchy_parent_id |
129600946 |
| dewey-tens |
530 - Physics |
| hierarchy_top_title |
Journal of applied mechanics and technical physics |
| isfreeaccess_txt |
false |
| familylinks_str_mv |
(DE-627)129600946 (DE-600)241350-4 (DE-576)015094545 |
| title |
On the convective instability of a thermal boundary layer |
| ctrlnum |
(DE-627)OLC2034369017 (DE-He213)BF00919308-p |
| title_full |
On the convective instability of a thermal boundary layer |
| author_sort |
Gershuni, G. Z. |
| journal |
Journal of applied mechanics and technical physics |
| journalStr |
Journal of applied mechanics and technical physics |
| lang_code |
eng |
| isOA_bool |
false |
| dewey-hundreds |
500 - Science |
| recordtype |
marc |
| publishDateSort |
1965 |
| contenttype_str_mv |
txt |
| container_start_page |
34 |
| author_browse |
Gershuni, G. Z. Zhukhovitskii, E. M. |
| container_volume |
6 |
| class |
530 VZ |
| format_se |
Aufsätze |
| author-letter |
Gershuni, G. Z. |
| doi_str_mv |
10.1007/BF00919308 |
| dewey-full |
530 |
| title_sort |
on the convective instability of a thermal boundary layer |
| title_auth |
On the convective instability of a thermal boundary layer |
| abstract |
Abstract When the surface temperature of a liquid is a harmonic function of time with a frequencyω, a temperature wave propagates into the liquid. The amplitude of this wave decreases exponentially with distance from the surface. The temperature oscillation is essentially concentrated in a layer of the order of (2χ/ω)1/2, where x is the thermal conductivity of the liquid (thermal boundary layer). Depending on the phase, at certain positions below the surface the temperature gradient is directed downwards and if its magnitude is sufficiently large (the magnitude is a function of the amplitude and frequency of the surface oscillations) the liquid can become unstable with respect to the onset of convection. In that case the convective motion may spread beyond the initial unstable layer. For low frequencies the stability condition can be derived from the usual static Rayleigh criterion, on the basis of the Rayleigh number and the average temperature gradient of the unstable layer. This quasi-static approach, used by Sal'nikov [1], is appropriate to those cases in which the period of the temperature oscillations is much larger than the characteristic time of the perturbations. But when these times are of the same order, the problem must be analyzed in dynamic terms. The stability problem must then be formulated as a problem of parametricresonance excitation of velocity oscillations due to the action of a variable parameter-the temperature gradient. In an earlier work [2] we considered the problem of the stability of a horizontal layer of liquid with a periodically varying temperature gradient. It was assumed that the thickness of the layer was much smaller than the penetration depth of the thermal wave, so that the temperature gradient could be assumed to be independent of position. In the present work we consider the opposite case, in which the liquid layer is assumed to be much larger than the penetration depth, i. e., a thermal boundary layer can be defined. The temperature gradient at equilibrium, which is a parameter in the equations determining the onset of perturbations, is here a periodic function of time and a relatively complicated function of the depth coordinate z. The periodic oscillations are solved by the Fourier method; the equations for the amplitudes are solved by the approximate method of KarmanPohlhausen. © The Faraday Press, Inc. 1967 |
| abstractGer |
Abstract When the surface temperature of a liquid is a harmonic function of time with a frequencyω, a temperature wave propagates into the liquid. The amplitude of this wave decreases exponentially with distance from the surface. The temperature oscillation is essentially concentrated in a layer of the order of (2χ/ω)1/2, where x is the thermal conductivity of the liquid (thermal boundary layer). Depending on the phase, at certain positions below the surface the temperature gradient is directed downwards and if its magnitude is sufficiently large (the magnitude is a function of the amplitude and frequency of the surface oscillations) the liquid can become unstable with respect to the onset of convection. In that case the convective motion may spread beyond the initial unstable layer. For low frequencies the stability condition can be derived from the usual static Rayleigh criterion, on the basis of the Rayleigh number and the average temperature gradient of the unstable layer. This quasi-static approach, used by Sal'nikov [1], is appropriate to those cases in which the period of the temperature oscillations is much larger than the characteristic time of the perturbations. But when these times are of the same order, the problem must be analyzed in dynamic terms. The stability problem must then be formulated as a problem of parametricresonance excitation of velocity oscillations due to the action of a variable parameter-the temperature gradient. In an earlier work [2] we considered the problem of the stability of a horizontal layer of liquid with a periodically varying temperature gradient. It was assumed that the thickness of the layer was much smaller than the penetration depth of the thermal wave, so that the temperature gradient could be assumed to be independent of position. In the present work we consider the opposite case, in which the liquid layer is assumed to be much larger than the penetration depth, i. e., a thermal boundary layer can be defined. The temperature gradient at equilibrium, which is a parameter in the equations determining the onset of perturbations, is here a periodic function of time and a relatively complicated function of the depth coordinate z. The periodic oscillations are solved by the Fourier method; the equations for the amplitudes are solved by the approximate method of KarmanPohlhausen. © The Faraday Press, Inc. 1967 |
| abstract_unstemmed |
Abstract When the surface temperature of a liquid is a harmonic function of time with a frequencyω, a temperature wave propagates into the liquid. The amplitude of this wave decreases exponentially with distance from the surface. The temperature oscillation is essentially concentrated in a layer of the order of (2χ/ω)1/2, where x is the thermal conductivity of the liquid (thermal boundary layer). Depending on the phase, at certain positions below the surface the temperature gradient is directed downwards and if its magnitude is sufficiently large (the magnitude is a function of the amplitude and frequency of the surface oscillations) the liquid can become unstable with respect to the onset of convection. In that case the convective motion may spread beyond the initial unstable layer. For low frequencies the stability condition can be derived from the usual static Rayleigh criterion, on the basis of the Rayleigh number and the average temperature gradient of the unstable layer. This quasi-static approach, used by Sal'nikov [1], is appropriate to those cases in which the period of the temperature oscillations is much larger than the characteristic time of the perturbations. But when these times are of the same order, the problem must be analyzed in dynamic terms. The stability problem must then be formulated as a problem of parametricresonance excitation of velocity oscillations due to the action of a variable parameter-the temperature gradient. In an earlier work [2] we considered the problem of the stability of a horizontal layer of liquid with a periodically varying temperature gradient. It was assumed that the thickness of the layer was much smaller than the penetration depth of the thermal wave, so that the temperature gradient could be assumed to be independent of position. In the present work we consider the opposite case, in which the liquid layer is assumed to be much larger than the penetration depth, i. e., a thermal boundary layer can be defined. The temperature gradient at equilibrium, which is a parameter in the equations determining the onset of perturbations, is here a periodic function of time and a relatively complicated function of the depth coordinate z. The periodic oscillations are solved by the Fourier method; the equations for the amplitudes are solved by the approximate method of KarmanPohlhausen. © The Faraday Press, Inc. 1967 |
| collection_details |
GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_11 GBV_ILN_20 GBV_ILN_70 |
| container_issue |
6 |
| title_short |
On the convective instability of a thermal boundary layer |
| url |
https://doi.org/10.1007/BF00919308 |
| remote_bool |
false |
| author2 |
Zhukhovitskii, E. M. |
| author2Str |
Zhukhovitskii, E. M. |
| ppnlink |
129600946 |
| mediatype_str_mv |
n |
| isOA_txt |
false |
| hochschulschrift_bool |
false |
| doi_str |
10.1007/BF00919308 |
| up_date |
2024-07-03T20:46:45.221Z |
| _version_ |
1803592249086312448 |
| fullrecord_marcxml |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">OLC2034369017</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230503104438.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">200819s1965 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/BF00919308</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2034369017</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)BF00919308-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">530</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Gershuni, G. Z.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">On the convective instability of a thermal boundary layer</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">1965</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© The Faraday Press, Inc. 1967</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract When the surface temperature of a liquid is a harmonic function of time with a frequencyω, a temperature wave propagates into the liquid. The amplitude of this wave decreases exponentially with distance from the surface. The temperature oscillation is essentially concentrated in a layer of the order of (2χ/ω)1/2, where x is the thermal conductivity of the liquid (thermal boundary layer). Depending on the phase, at certain positions below the surface the temperature gradient is directed downwards and if its magnitude is sufficiently large (the magnitude is a function of the amplitude and frequency of the surface oscillations) the liquid can become unstable with respect to the onset of convection. In that case the convective motion may spread beyond the initial unstable layer. For low frequencies the stability condition can be derived from the usual static Rayleigh criterion, on the basis of the Rayleigh number and the average temperature gradient of the unstable layer. This quasi-static approach, used by Sal'nikov [1], is appropriate to those cases in which the period of the temperature oscillations is much larger than the characteristic time of the perturbations. But when these times are of the same order, the problem must be analyzed in dynamic terms. The stability problem must then be formulated as a problem of parametricresonance excitation of velocity oscillations due to the action of a variable parameter-the temperature gradient. In an earlier work [2] we considered the problem of the stability of a horizontal layer of liquid with a periodically varying temperature gradient. It was assumed that the thickness of the layer was much smaller than the penetration depth of the thermal wave, so that the temperature gradient could be assumed to be independent of position. In the present work we consider the opposite case, in which the liquid layer is assumed to be much larger than the penetration depth, i. e., a thermal boundary layer can be defined. The temperature gradient at equilibrium, which is a parameter in the equations determining the onset of perturbations, is here a periodic function of time and a relatively complicated function of the depth coordinate z. The periodic oscillations are solved by the Fourier method; the equations for the amplitudes are solved by the approximate method of KarmanPohlhausen.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Temperature Gradient</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Penetration Depth</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Rayleigh Number</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Thermal Boundary Layer</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Thermal Wave</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Zhukhovitskii, E. M.</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Journal of applied mechanics and technical physics</subfield><subfield code="d">Kluwer Academic Publishers-Plenum Publishers, 1966</subfield><subfield code="g">6(1965), 6 vom: Nov., Seite 34-36</subfield><subfield code="w">(DE-627)129600946</subfield><subfield code="w">(DE-600)241350-4</subfield><subfield code="w">(DE-576)015094545</subfield><subfield code="x">0021-8944</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:6</subfield><subfield code="g">year:1965</subfield><subfield code="g">number:6</subfield><subfield code="g">month:11</subfield><subfield code="g">pages:34-36</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">https://doi.org/10.1007/BF00919308</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-TEC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-PHY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_11</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_20</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">6</subfield><subfield code="j">1965</subfield><subfield code="e">6</subfield><subfield code="c">11</subfield><subfield code="h">34-36</subfield></datafield></record></collection>
|
| score |
7.399123 |