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3. Internally Heated Convection Experiments and Simulations

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Abstract

Laboratory experiments and numerical simulations of internally heated convection are reviewed. The emphasis is on quantitative results, especially integral quantities important to heat transport and their dependence on the Rayleigh number, which is proportional to the heating rate. For all experiments and three-dimensional simulations, the various measures of mean temperature can be fit to powers of the rate of volumetric heating. The exponents of these fits range from 0. 75 to 0. 77 when the bottom is insulating, and they range from 0. 78 to 0. 82 when the top and bottom are fixed at equal temperatures. In the latter configuration, the fraction of internally produced heat flowing outward across the bottom boundary falls quite slowly as heating is strengthened. When this fraction is fit to a power of the heating rate, the fit exponents lie between − 0. 049 and − 0. 099.

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Literature
1.
go back to reference Ahlers, G., Grossmann, S., Lohse, D.: Heat transfer and large scale dynamics in turbulent Rayleigh-Bénard convection. Rev. Mod. Phys. 81(2), 503–537 (2009)CrossRef Ahlers, G., Grossmann, S., Lohse, D.: Heat transfer and large scale dynamics in turbulent Rayleigh-Bénard convection. Rev. Mod. Phys. 81(2), 503–537 (2009)CrossRef
2.
3.
go back to reference Arcidiacono, S., Ciofalo, M.: Low-Prandtl number natural convection in volumetrically heated rectangular enclosures III. Shallow cavity, AR=0.25. Int. J. Heat Mass Transf. 44, 3053–3065 (2001) Arcidiacono, S., Ciofalo, M.: Low-Prandtl number natural convection in volumetrically heated rectangular enclosures III. Shallow cavity, AR=0.25. Int. J. Heat Mass Transf. 44, 3053–3065 (2001)
4.
go back to reference Arcidiacono, S., Di Piazza, I., Ciofalo, M.: Low-Prandtl number natural convection in volumetrically heated rectangular enclosures II. Square cavity, AR=1. Int. J. Heat Mass Transf. 44, 537–550 (2001) Arcidiacono, S., Di Piazza, I., Ciofalo, M.: Low-Prandtl number natural convection in volumetrically heated rectangular enclosures II. Square cavity, AR=1. Int. J. Heat Mass Transf. 44, 537–550 (2001)
5.
go back to reference Asfia, F.J., Dhir, V.K.: An experimental study of natural convection in a volumetrically heated spherical pool bounded on top with a rigid wall. Nucl. Eng. Des. 163(3), 333–348 (1996)CrossRef Asfia, F.J., Dhir, V.K.: An experimental study of natural convection in a volumetrically heated spherical pool bounded on top with a rigid wall. Nucl. Eng. Des. 163(3), 333–348 (1996)CrossRef
6.
go back to reference Bergholz, R.F.: Natural convection of a heat generating fluid in a closed cavity. J. Heat Transfer 102, 242–247 (1980)CrossRef Bergholz, R.F.: Natural convection of a heat generating fluid in a closed cavity. J. Heat Transfer 102, 242–247 (1980)CrossRef
7.
go back to reference Berlengiero, M., Emanuel, K.A., von Hardenberg, J., Provenzale, A., Spiegel, E.A.: Internally cooled convection: A fillip for Philip. Commun. Nonlinear Sci. Numer. Simul. 17(5), 1998–2007 (2012)CrossRefMathSciNet Berlengiero, M., Emanuel, K.A., von Hardenberg, J., Provenzale, A., Spiegel, E.A.: Internally cooled convection: A fillip for Philip. Commun. Nonlinear Sci. Numer. Simul. 17(5), 1998–2007 (2012)CrossRefMathSciNet
8.
go back to reference Busse, F.H.: Patterns of convection in spherical shells. J. Fluid Mech. 72(1), 67–85 (1975)CrossRefMATH Busse, F.H.: Patterns of convection in spherical shells. J. Fluid Mech. 72(1), 67–85 (1975)CrossRefMATH
9.
go back to reference Busse, F.H., Riahi, N.: Patterns of convection in spherical shells. Part 2. J. Fluid Mech. 123, 282–301 (1975) Busse, F.H., Riahi, N.: Patterns of convection in spherical shells. Part 2. J. Fluid Mech. 123, 282–301 (1975)
10.
go back to reference Cartland Glover, G.M., Generalis, S.C.: Pattern competition in homogeneously heated fluid layers. Eng. Appl. Comput. Fluid Mech. 3(2), 164–174 (2009) Cartland Glover, G.M., Generalis, S.C.: Pattern competition in homogeneously heated fluid layers. Eng. Appl. Comput. Fluid Mech. 3(2), 164–174 (2009)
11.
go back to reference Cartland Glover, G., Fujimura, K., Generalis, S.: Pattern formation in volumetrically heated fluids. Chaotic Model. Simul. 1, 19–30 (2013) Cartland Glover, G., Fujimura, K., Generalis, S.: Pattern formation in volumetrically heated fluids. Chaotic Model. Simul. 1, 19–30 (2013)
12.
go back to reference Chapman, C.J., Childress, S., Proctor, M.R.E.: Long wavelength thermal convection between non-conducting boundaries. Earth Planet. Sci. Lett. 51, 362–369 (1980)CrossRef Chapman, C.J., Childress, S., Proctor, M.R.E.: Long wavelength thermal convection between non-conducting boundaries. Earth Planet. Sci. Lett. 51, 362–369 (1980)CrossRef
13.
go back to reference Chavanne, X., Chilla, F., Castaing, B., Hebral, B., Chabaud, B., Chaussy, J.: Observation of the ultimate regime in Rayleigh-Bénard convection. Phys. Rev. Lett. 79(19), 3648–3651 (1997)CrossRef Chavanne, X., Chilla, F., Castaing, B., Hebral, B., Chabaud, B., Chaussy, J.: Observation of the ultimate regime in Rayleigh-Bénard convection. Phys. Rev. Lett. 79(19), 3648–3651 (1997)CrossRef
14.
go back to reference Chen, S., Krafczyk, M.: Entropy generation in turbulent natural convection due to internal heat generation. Int. J. Therm. Sci. 48(10), 1978–1987 (2009)CrossRef Chen, S., Krafczyk, M.: Entropy generation in turbulent natural convection due to internal heat generation. Int. J. Therm. Sci. 48(10), 1978–1987 (2009)CrossRef
15.
go back to reference Cheung, F.B.: Natural convection in a volumetrically heated fluid layer at high Rayleigh numbers. Int. J. Heat Mass Transf. 20(5), 499–506 (1977)CrossRef Cheung, F.B.: Natural convection in a volumetrically heated fluid layer at high Rayleigh numbers. Int. J. Heat Mass Transf. 20(5), 499–506 (1977)CrossRef
16.
17.
go back to reference Cheung, F.B., Chawla, T.C.: Complex heat transfer processes in heat-generating horizontal fluid layers. In: Annual review of numerical fluid mechanics and heat transfer, vol. 1, pp. 403–448. Hemisphere, New York (1987) Cheung, F.B., Chawla, T.C.: Complex heat transfer processes in heat-generating horizontal fluid layers. In: Annual review of numerical fluid mechanics and heat transfer, vol. 1, pp. 403–448. Hemisphere, New York (1987)
18.
go back to reference Chillà, F., Schumacher, J.: New perspectives in turbulent Rayleigh-Bénard convection. Eur. Phys. J. E 35(7) (2012) Chillà, F., Schumacher, J.: New perspectives in turbulent Rayleigh-Bénard convection. Eur. Phys. J. E 35(7) (2012)
19.
go back to reference Clever, R.M.: Heat transfer and stability properties of convection rolls in an internally heated fluid layer. J. Appl. Math. Phys. 28, 585–597 (1977)CrossRefMathSciNetMATH Clever, R.M.: Heat transfer and stability properties of convection rolls in an internally heated fluid layer. J. Appl. Math. Phys. 28, 585–597 (1977)CrossRefMathSciNetMATH
20.
go back to reference De la Cruz Reyna, S.: Asymmetric convection in the upper mantle. Geofis. Int. 10, 49–56 (1970) De la Cruz Reyna, S.: Asymmetric convection in the upper mantle. Geofis. Int. 10, 49–56 (1970)
21.
go back to reference Di Piazza, I., Ciofalo, M.: Low-Prandtl number natural convection in volumetrically heated rectangular enclosures I. Slender cavity, AR=4. Int. J. Heat Mass Transf. 43, 3027–3051 (2000) Di Piazza, I., Ciofalo, M.: Low-Prandtl number natural convection in volumetrically heated rectangular enclosures I. Slender cavity, AR=4. Int. J. Heat Mass Transf. 43, 3027–3051 (2000)
22.
go back to reference Emara, A.A., Kulacki, F.A.: A numerical investigation of thermal convection in a heat-generating fluid layer. J. Heat Transf. 102, 531–537 (1980)CrossRef Emara, A.A., Kulacki, F.A.: A numerical investigation of thermal convection in a heat-generating fluid layer. J. Heat Transf. 102, 531–537 (1980)CrossRef
23.
go back to reference Farouk, B.: Turbulent thermal convection in an enclosure with internal heat generation. J. Heat Transf. 110(1), 126 (1988)CrossRef Farouk, B.: Turbulent thermal convection in an enclosure with internal heat generation. J. Heat Transf. 110(1), 126 (1988)CrossRef
24.
go back to reference Fiedler, H.E., Wille, R.: Turbulente freie konvektion in einer horizontalen flüssigkeitsschicht mit volumen-wärmequelle. In: Proceeding of 4th International Heat Transfer Conference (1970) Fiedler, H.E., Wille, R.: Turbulente freie konvektion in einer horizontalen flüssigkeitsschicht mit volumen-wärmequelle. In: Proceeding of 4th International Heat Transfer Conference (1970)
25.
go back to reference Filippov, A.S.: Numerical simulation of experiments on turbulent natural convection of heat generating liquid in cylindrical pool. J. Eng. Thermophys. 20(1), 64–76 (2011)CrossRef Filippov, A.S.: Numerical simulation of experiments on turbulent natural convection of heat generating liquid in cylindrical pool. J. Eng. Thermophys. 20(1), 64–76 (2011)CrossRef
26.
go back to reference Getling, A.V.: Rayleigh-Bénard convection: structures and dynamics. World Scientific Publishing Co (1998) Getling, A.V.: Rayleigh-Bénard convection: structures and dynamics. World Scientific Publishing Co (1998)
27.
go back to reference Goluskin, D., Spiegel, E.A.: Convection driven by internal heating. Phys. Lett. A 377(1-2), 83–92 (2012)CrossRef Goluskin, D., Spiegel, E.A.: Convection driven by internal heating. Phys. Lett. A 377(1-2), 83–92 (2012)CrossRef
28.
go back to reference Goluskin, D., van der Poel, E.P.: Penetrative internally heated convection and the importance of dimensionality (2015) Goluskin, D., van der Poel, E.P.: Penetrative internally heated convection and the importance of dimensionality (2015)
30.
go back to reference Grötzbach, G.: Turbulent heat transfer in an internally heated fluid layer. In: The Third International Symposium on Refined Flow Modelling and Turbulence Measurements, vol. 2, p. 8. Tokyo (1988) Grötzbach, G.: Turbulent heat transfer in an internally heated fluid layer. In: The Third International Symposium on Refined Flow Modelling and Turbulence Measurements, vol. 2, p. 8. Tokyo (1988)
31.
go back to reference Hartlep, T., Busse, F.H.: Convection in an internally cooled fluid layer heated from below. Technical Representation, Center for Turnulence Research (2006) Hartlep, T., Busse, F.H.: Convection in an internally cooled fluid layer heated from below. Technical Representation, Center for Turnulence Research (2006)
32.
go back to reference He, X., Funfschilling, D., Nobach, H., Bodenschatz, E., Ahlers, G.: Transition to the ultimate state of turbulent Rayleigh-Bénard convection. Phys. Rev. Lett. 108, 024,502 (2012) He, X., Funfschilling, D., Nobach, H., Bodenschatz, E., Ahlers, G.: Transition to the ultimate state of turbulent Rayleigh-Bénard convection. Phys. Rev. Lett. 108, 024,502 (2012)
33.
go back to reference Hewitt, J.M., McKenzie, D.P., Weiss, N.O.: Large aspect ratio cells in two-dimensional thermal convection. Earth Planet. Sci. Lett. 51, 370–380 (1980)CrossRef Hewitt, J.M., McKenzie, D.P., Weiss, N.O.: Large aspect ratio cells in two-dimensional thermal convection. Earth Planet. Sci. Lett. 51, 370–380 (1980)CrossRef
34.
go back to reference Horvat, A., Kljenak, I., Marn, J.: Two-dimensional large-eddy simulation of turbulent natural convection due to internal heat generation. Int. J. Heat Mass Transf. 44(21), 3985–3995 (2001)CrossRefMATH Horvat, A., Kljenak, I., Marn, J.: Two-dimensional large-eddy simulation of turbulent natural convection due to internal heat generation. Int. J. Heat Mass Transf. 44(21), 3985–3995 (2001)CrossRefMATH
35.
go back to reference Houseman, G.: The dependence of convection planform on mode of heating. Nature 332, 346–349 (1988)CrossRef Houseman, G.: The dependence of convection planform on mode of heating. Nature 332, 346–349 (1988)CrossRef
36.
go back to reference Ichikawa, H., Kurita, K., Yamagishi, Y., Yanagisawa, T.: Cell pattern of thermal convection induced by internal heating. Phys. Fluids 18(3), 038,101 (2006) Ichikawa, H., Kurita, K., Yamagishi, Y., Yanagisawa, T.: Cell pattern of thermal convection induced by internal heating. Phys. Fluids 18(3), 038,101 (2006)
37.
go back to reference Ingersoll, A.P., Porco, C.C.: Solar heating and internal heat flow on Jupiter. Icarus 35, 27–43 (1978)CrossRef Ingersoll, A.P., Porco, C.C.: Solar heating and internal heat flow on Jupiter. Icarus 35, 27–43 (1978)CrossRef
38.
go back to reference Ishiwatari, M., Takehiro, S.I., Hayashi, Y.Y.: The effects of thermal conditions on the cell sizes of two-dimensional convection. J. Fluid Mech. 281, 33–50 (1994)CrossRefMATH Ishiwatari, M., Takehiro, S.I., Hayashi, Y.Y.: The effects of thermal conditions on the cell sizes of two-dimensional convection. J. Fluid Mech. 281, 33–50 (1994)CrossRefMATH
39.
go back to reference Jahn, M., Reineke, H.H.: Free convection heat transfer with internal heat sources, calculations and measurements. In: Proceedings of 5th International Heat Transfer Conference, pp. 74–78. Tokyo (1974) Jahn, M., Reineke, H.H.: Free convection heat transfer with internal heat sources, calculations and measurements. In: Proceedings of 5th International Heat Transfer Conference, pp. 74–78. Tokyo (1974)
40.
go back to reference Jaupart, C., Brandeis, G.: The stagnant bottom layer of convecting magma chambers. Earth Planet. Sci. Lett. 80, 183–199 (1986)CrossRef Jaupart, C., Brandeis, G.: The stagnant bottom layer of convecting magma chambers. Earth Planet. Sci. Lett. 80, 183–199 (1986)CrossRef
41.
go back to reference Jaupart, C., Brandeis, G., Allègre, C.J.: Stagnant layers at the bottom of convecting magma chambers. Nature 308, 535–538 (1984)CrossRef Jaupart, C., Brandeis, G., Allègre, C.J.: Stagnant layers at the bottom of convecting magma chambers. Nature 308, 535–538 (1984)CrossRef
42.
go back to reference Joseph, D.D.: Subcritical Instability and Exchange of Stability in a Horizontal Fluid Layer. Phys. Fluids 11(1968), 903 (1968)CrossRefMATH Joseph, D.D.: Subcritical Instability and Exchange of Stability in a Horizontal Fluid Layer. Phys. Fluids 11(1968), 903 (1968)CrossRefMATH
43.
go back to reference Joseph, D.D., Shir, C.C.: Subcritical convective instability: Part 1. Fluid layers. J. Fluid Mech. 26(4), 753–768 (1966)CrossRefMATH Joseph, D.D., Shir, C.C.: Subcritical convective instability: Part 1. Fluid layers. J. Fluid Mech. 26(4), 753–768 (1966)CrossRefMATH
44.
go back to reference Kolmychkov, V.V., Mazhorova, O.S., Shcheritsa, O.V.: Numerical study of convection near the stability threshold in a square box with internal heat generation. Phys. Lett. A 377, 2111–2117 (2013)CrossRefMathSciNet Kolmychkov, V.V., Mazhorova, O.S., Shcheritsa, O.V.: Numerical study of convection near the stability threshold in a square box with internal heat generation. Phys. Lett. A 377, 2111–2117 (2013)CrossRefMathSciNet
45.
go back to reference Kondratenko, P.S., Nikolski, D.V., Strizhov, V.F.: Free-convective heat transfer in fluids with non-uniform volumetric heat generation. Int. J. Heat Mass Transf. 51(7-8), 1590–1595 (2008)CrossRefMATH Kondratenko, P.S., Nikolski, D.V., Strizhov, V.F.: Free-convective heat transfer in fluids with non-uniform volumetric heat generation. Int. J. Heat Mass Transf. 51(7-8), 1590–1595 (2008)CrossRefMATH
46.
go back to reference Kulacki, F.A., Emara, A.A.: Steady and transient thermal convection in a fluid layer with uniform volumetric energy sources. J. Fluid Mech. 83(2), 375–395 (1977)CrossRef Kulacki, F.A., Emara, A.A.: Steady and transient thermal convection in a fluid layer with uniform volumetric energy sources. J. Fluid Mech. 83(2), 375–395 (1977)CrossRef
47.
go back to reference Kulacki, F.A., Goldstein, R.J.: Thermal convection in a horizontal fluid layer with uniform volumetric energy sources. J. Fluid Mech. 55(02), 271–287 (1972)CrossRef Kulacki, F.A., Goldstein, R.J.: Thermal convection in a horizontal fluid layer with uniform volumetric energy sources. J. Fluid Mech. 55(02), 271–287 (1972)CrossRef
48.
go back to reference Kulacki, F.A., Nagle, M.E.: Natural convection in a horizontal fluid layer with volumetric energy sources. J. Heat Transf. 97, 204–211 (1975)CrossRef Kulacki, F.A., Nagle, M.E.: Natural convection in a horizontal fluid layer with volumetric energy sources. J. Heat Transf. 97, 204–211 (1975)CrossRef
49.
go back to reference Kulacki, F.A., Richards, D.E.: Natural convection in plane layers and cavities with volumetric energy sources. In: Natural Convection: Fundamentals and Applications, pp. 179–254. Hemisphere, New York (1985) Kulacki, F.A., Richards, D.E.: Natural convection in plane layers and cavities with volumetric energy sources. In: Natural Convection: Fundamentals and Applications, pp. 179–254. Hemisphere, New York (1985)
50.
go back to reference Lee, S.D., Lee, J.K., Suh, K.Y.: Boundary condition dependent natural convection in a rectangular pool with internal heat sources. J. Heat Transf. 129(5), 679–682 (2007)CrossRef Lee, S.D., Lee, J.K., Suh, K.Y.: Boundary condition dependent natural convection in a rectangular pool with internal heat sources. J. Heat Transf. 129(5), 679–682 (2007)CrossRef
51.
go back to reference Liu, H., Zou, C., Shi, B., Tian, Z., Zhang, L., Zheng, C.: Thermal lattice-BGK model based on large-eddy simulation of turbulent natural convection due to internal heat generation. Int. J. Heat Mass Transf. 49, 4672–4680 (2006)CrossRefMATH Liu, H., Zou, C., Shi, B., Tian, Z., Zhang, L., Zheng, C.: Thermal lattice-BGK model based on large-eddy simulation of turbulent natural convection due to internal heat generation. Int. J. Heat Mass Transf. 49, 4672–4680 (2006)CrossRefMATH
52.
go back to reference Lohse, D., Xia, K.Q.: Small-scale properties of turbulent Rayleigh-Bénard convection. Annu. Rev. Fluid Mech. 42(1), 335–364 (2010)CrossRef Lohse, D., Xia, K.Q.: Small-scale properties of turbulent Rayleigh-Bénard convection. Annu. Rev. Fluid Mech. 42(1), 335–364 (2010)CrossRef
53.
go back to reference Mayinger, F., Jahn, M., Reineke, H.H., Steinberner, U.: Examination of thermohydraulic processes and heat transfer in a core melt. Technical Representation, Hannover Technical University, Hannover, Germany (1975) Mayinger, F., Jahn, M., Reineke, H.H., Steinberner, U.: Examination of thermohydraulic processes and heat transfer in a core melt. Technical Representation, Hannover Technical University, Hannover, Germany (1975)
54.
go back to reference McKenzie, D.P., Roberts, J.M., Weiss, N.O.: Convection in the earth’s mantle: towards a numerical simulation. J. Fluid Mech. 62(3), 465–538 (1974)CrossRefMATH McKenzie, D.P., Roberts, J.M., Weiss, N.O.: Convection in the earth’s mantle: towards a numerical simulation. J. Fluid Mech. 62(3), 465–538 (1974)CrossRefMATH
55.
go back to reference Nourgaliev, R.R., Dinh, T.N., Sehgal, B.R.: Effect of fluid Prandtl number on heat transfer characteristics in internally heated liquid pools with Rayleigh numbers up to 1012. Nucl. Eng. Des. 169, 165–184 (1997)CrossRef Nourgaliev, R.R., Dinh, T.N., Sehgal, B.R.: Effect of fluid Prandtl number on heat transfer characteristics in internally heated liquid pools with Rayleigh numbers up to 1012. Nucl. Eng. Des. 169, 165–184 (1997)CrossRef
56.
go back to reference Olwi, I.A., Kulacki, F.A.: Numerical simulation of the transient convection process in a volumetrically heated fluid layer. In: Proceeding of ASME, p. 185 (1995) Olwi, I.A., Kulacki, F.A.: Numerical simulation of the transient convection process in a volumetrically heated fluid layer. In: Proceeding of ASME, p. 185 (1995)
57.
go back to reference Peckover, R.S., Hutchinson, I.H.: Convective rolls driven by internal heat sources. Phys. Fluids 17(7), 1369 (1974)CrossRef Peckover, R.S., Hutchinson, I.H.: Convective rolls driven by internal heat sources. Phys. Fluids 17(7), 1369 (1974)CrossRef
58.
go back to reference Ralph, J.C., Roberts, D.N.: Free convection heat transfer measurements in horizontal liquid layers with internal heat generation. Technical Representation, UKAEA (1974) Ralph, J.C., Roberts, D.N.: Free convection heat transfer measurements in horizontal liquid layers with internal heat generation. Technical Representation, UKAEA (1974)
59.
go back to reference Ralph, J.C., McGreevy, R., Peckover, R.S.: Experiments in tubulent thermal convection driven by internal heat sources. In: Spalding, D.B., Afgan, N. (eds.) Heat Transfer and Turbulent Buoyant Convection: Studies and Applications for Natural Environment, Buildings, Engineering Systems, pp. 587–599. Hemisphere, New York (1977) Ralph, J.C., McGreevy, R., Peckover, R.S.: Experiments in tubulent thermal convection driven by internal heat sources. In: Spalding, D.B., Afgan, N. (eds.) Heat Transfer and Turbulent Buoyant Convection: Studies and Applications for Natural Environment, Buildings, Engineering Systems, pp. 587–599. Hemisphere, New York (1977)
60.
go back to reference Riahi, N.: Nonlinear convection in a horizontal layer with an internal heat source. J. Phys. Soc. Japan 53(12), 4169–4178 (1984)CrossRefMathSciNet Riahi, N.: Nonlinear convection in a horizontal layer with an internal heat source. J. Phys. Soc. Japan 53(12), 4169–4178 (1984)CrossRefMathSciNet
61.
go back to reference Riahi, D.N., Busse, F.H.: Pattern generation by convection in spherical-shells. J. Appl. Math. Phys. 39, 699–712 (1988)CrossRefMATH Riahi, D.N., Busse, F.H.: Pattern generation by convection in spherical-shells. J. Appl. Math. Phys. 39, 699–712 (1988)CrossRefMATH
63.
go back to reference Roberts, P.H.: On the thermal instability of a rotating-fluid sphere containing heat sources. Philos. Trans. R. Soc. A 263, 93–117 (1968)CrossRefMATH Roberts, P.H.: On the thermal instability of a rotating-fluid sphere containing heat sources. Philos. Trans. R. Soc. A 263, 93–117 (1968)CrossRefMATH
64.
go back to reference Schmalzl, J., Breuer, M., Hansen, U.: On the validity of two-dimensional numerical approaches to time-dependent thermal convection. Europhys. Lett. 67(3), 390–396 (2004)CrossRef Schmalzl, J., Breuer, M., Hansen, U.: On the validity of two-dimensional numerical approaches to time-dependent thermal convection. Europhys. Lett. 67(3), 390–396 (2004)CrossRef
65.
go back to reference Schubert, G., Glatzmaier, G.A., Travis, B.: Steady, three-dimensional, internally heated convection. Phys. Fluids A 5(8), 1928–1932 (1993)CrossRef Schubert, G., Glatzmaier, G.A., Travis, B.: Steady, three-dimensional, internally heated convection. Phys. Fluids A 5(8), 1928–1932 (1993)CrossRef
66.
go back to reference Schwiderski, E.W., Schwab, H.J.A.: Convection experiments with electrolytically heated fluid layers. J. Fluid Mech. 48(4), 703–719 (1971)CrossRef Schwiderski, E.W., Schwab, H.J.A.: Convection experiments with electrolytically heated fluid layers. J. Fluid Mech. 48(4), 703–719 (1971)CrossRef
67.
go back to reference Shi, B.C., Guo, Z.L.: Thermal lattice BGK simulation of turbulent natural convection due to internal heat generation. Int. J. Mod. Phys. B 17(2), 173–177 (2003)CrossRefMathSciNet Shi, B.C., Guo, Z.L.: Thermal lattice BGK simulation of turbulent natural convection due to internal heat generation. Int. J. Mod. Phys. B 17(2), 173–177 (2003)CrossRefMathSciNet
69.
go back to reference Sotin, C., Labrosse, S.: Three-dimensional thermal convection in an iso-viscous, infinite Prandtl number fluid heated from within and from below: applications to the transfer of heat through planetary mantles. Phys. Earth Planet. Inter. 112, 171–190 (1999)CrossRef Sotin, C., Labrosse, S.: Three-dimensional thermal convection in an iso-viscous, infinite Prandtl number fluid heated from within and from below: applications to the transfer of heat through planetary mantles. Phys. Earth Planet. Inter. 112, 171–190 (1999)CrossRef
70.
go back to reference Sparrow, E.M., Goldstein, R.J., Jonsson, V.K.: Thermal instability in a horizontal fluid layer: effect of boundary conditions and non-linear temperature profile. J. Fluid Mech. 18(04), 513–528 (1963)CrossRefMathSciNet Sparrow, E.M., Goldstein, R.J., Jonsson, V.K.: Thermal instability in a horizontal fluid layer: effect of boundary conditions and non-linear temperature profile. J. Fluid Mech. 18(04), 513–528 (1963)CrossRefMathSciNet
71.
go back to reference Steinberner, U., Reineke, H.H.: Turbulent buoyancy convection heat transfer with internal heat sources. In: Proceeding of 6th International Heat Transfer Conference, vol. 2, pp. 305–310 (1978) Steinberner, U., Reineke, H.H.: Turbulent buoyancy convection heat transfer with internal heat sources. In: Proceeding of 6th International Heat Transfer Conference, vol. 2, pp. 305–310 (1978)
72.
go back to reference Stevens, R.J.A.M., van der Poel, E.P., Grossmann, S., Lohse, D.: The unifying theory of scaling in thermal convection: the updated prefactors. J. Fluid Mech. 730, 295–308 (2013)CrossRefMATH Stevens, R.J.A.M., van der Poel, E.P., Grossmann, S., Lohse, D.: The unifying theory of scaling in thermal convection: the updated prefactors. J. Fluid Mech. 730, 295–308 (2013)CrossRefMATH
73.
go back to reference Straughan, B.: Continuous dependence on the heat source and non-linear stability for convection with internal heat generation. Math. Methods Appl. Sci. 13, 373–383 (1990)CrossRefMathSciNetMATH Straughan, B.: Continuous dependence on the heat source and non-linear stability for convection with internal heat generation. Math. Methods Appl. Sci. 13, 373–383 (1990)CrossRefMathSciNetMATH
74.
go back to reference Straus, J.M.: Penetrative convection in a layer of fluid heated from within. Astrophys. J. 209, 179–189 (1976)CrossRef Straus, J.M.: Penetrative convection in a layer of fluid heated from within. Astrophys. J. 209, 179–189 (1976)CrossRef
75.
go back to reference Takahashi, J., Tasaka, Y., Murai, Y., Takeda, Y., Yanagisawa, T.: Experimental study of cell pattern formation induced by internal heat sources in a horizontal fluid layer. Int. J. Heat Mass Transf. 53(7-8), 1483–1490 (2010)CrossRefMATH Takahashi, J., Tasaka, Y., Murai, Y., Takeda, Y., Yanagisawa, T.: Experimental study of cell pattern formation induced by internal heat sources in a horizontal fluid layer. Int. J. Heat Mass Transf. 53(7-8), 1483–1490 (2010)CrossRefMATH
76.
go back to reference Tasaka, Y., Takeda, Y.: Effects of heat source distribution on natural convection induced by internal heating. Int. J. Heat Mass Transf. 48(6), 1164–1174 (2005)CrossRefMATH Tasaka, Y., Takeda, Y.: Effects of heat source distribution on natural convection induced by internal heating. Int. J. Heat Mass Transf. 48(6), 1164–1174 (2005)CrossRefMATH
77.
go back to reference Tasaka, Y., Kudoh, Y., Takeda, Y., Yanagisawa, T.: Experimental investigation of natural convection induced by internal heat generation. J. Phys. Conf. Ser. 14, 168–179 (2005)CrossRef Tasaka, Y., Kudoh, Y., Takeda, Y., Yanagisawa, T.: Experimental investigation of natural convection induced by internal heat generation. J. Phys. Conf. Ser. 14, 168–179 (2005)CrossRef
78.
go back to reference Thirlby, R.: Convection in an internally heated layer. J. Fluid Mech. 44(04), 673–693 (1970)CrossRefMATH Thirlby, R.: Convection in an internally heated layer. J. Fluid Mech. 44(04), 673–693 (1970)CrossRefMATH
79.
go back to reference Tritton, D.J., Zarraga, M.N.: Convection in horizontal layers with internal heat generation. Experiments. J. Fluid Mech. 30(01), 21–31 (1967)CrossRef Tritton, D.J., Zarraga, M.N.: Convection in horizontal layers with internal heat generation. Experiments. J. Fluid Mech. 30(01), 21–31 (1967)CrossRef
80.
go back to reference Tveitereid, M.: Thermal convection in a horizontal fluid layer with internal heat sources. Int. J. Heat Mass Transf. 21, 335–339 (1978)CrossRefMATH Tveitereid, M.: Thermal convection in a horizontal fluid layer with internal heat sources. Int. J. Heat Mass Transf. 21, 335–339 (1978)CrossRefMATH
81.
go back to reference Tveitereid, M., Palm, E.: Convection due to internal heat sources. J. Fluid Mech. 76(03), 481 (1976)CrossRef Tveitereid, M., Palm, E.: Convection due to internal heat sources. J. Fluid Mech. 76(03), 481 (1976)CrossRef
82.
go back to reference van der Poel, E.P., Stevens, R.J.A.M., Lohse, D.: Comparison between two- and three-dimensional Rayleigh-Bénard convection. J. Fluid Mech. 736, 177–194 (2013)CrossRefMATH van der Poel, E.P., Stevens, R.J.A.M., Lohse, D.: Comparison between two- and three-dimensional Rayleigh-Bénard convection. J. Fluid Mech. 736, 177–194 (2013)CrossRefMATH
83.
go back to reference Vel’tishchev, N.F.: Convection in a horizontal fluid layer with a uniform internal heat source. Fluid Dyn. 39(2), 189–197 (2004)CrossRefMATH Vel’tishchev, N.F.: Convection in a horizontal fluid layer with a uniform internal heat source. Fluid Dyn. 39(2), 189–197 (2004)CrossRefMATH
84.
go back to reference Wörner, M., Schmidt, M., Grötzbach, G.: Direct numerical simulation of turbulence in an internally heated convective fluid layer and implications for statistical modeling. 35(6), 773–797 (1997) Wörner, M., Schmidt, M., Grötzbach, G.: Direct numerical simulation of turbulence in an internally heated convective fluid layer and implications for statistical modeling. 35(6), 773–797 (1997)
Metadata
Title
Internally Heated Convection Experiments and Simulations
Author
David Goluskin
Copyright Year
2016
DOI
https://doi.org/10.1007/978-3-319-23941-5_3

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