TY - JOUR

T1 - Steady and transient thermal convection in a fluid layer with uniform volumetric energy sources

AU - Kulacki, F. A.

AU - Emara, A. A.

PY - 1977/11

Y1 - 1977/11

N2 - Measurements of the overall heat flux in steady convection have been made in a horizontal layer of dilute aqueous electrolyte. The layer is bounded below by a rigid zero-heat-flux surface and above by a rigid isothermal surface. Joule heating by an alternating current passing horizontally through the layer provides a uniformly distributed volumetric energy source. The Nusselt number at the upper surface is found to be proportional to Ra0.227 in the range 1.4 ≤ Ra/Rac ≤ 1.6 × 109, which covers the laminar, transitional and turbulent flow regimes. Eight discrete transitions in the heat flux are found in this Rayleigh number range. Extrapolation of the heat-transfer correlation to the conduction value of the Nusselt number yields a critical Rayleigh number which is within -6.7% of the value given by linearized stability theory. Measurements have been made of the time scales of developing convection after a sudden start of volumetric heating and of decaying convection when volumetric heating is suddenly stopped. In both cases, the steady-state temperature difference across the layer appears to be the controlling physical parameter, with both processes exhibiting the same time scale for a given steady-state temperature difference, or ·δRa·. For step changes in Ra such that ·δRa· > 100Rac, the time scales for both processes can be represented by Fo ·δRa·m, where Fo is the Fourier number of the layer. Temperature profiles of developing convection exhibit a temperature excess in the upper 15–20 % of the layer in the early stages of flow development for Rayleigh numbers corresponding to turbulent convection. This excess disappears when the average core temperature becomes large enough to permit eddy transport and mixing processes near the upper surface. The steady-state limits in the transient experiments yield heat-transfer data in agreement with the results of the steady-state experiments.

AB - Measurements of the overall heat flux in steady convection have been made in a horizontal layer of dilute aqueous electrolyte. The layer is bounded below by a rigid zero-heat-flux surface and above by a rigid isothermal surface. Joule heating by an alternating current passing horizontally through the layer provides a uniformly distributed volumetric energy source. The Nusselt number at the upper surface is found to be proportional to Ra0.227 in the range 1.4 ≤ Ra/Rac ≤ 1.6 × 109, which covers the laminar, transitional and turbulent flow regimes. Eight discrete transitions in the heat flux are found in this Rayleigh number range. Extrapolation of the heat-transfer correlation to the conduction value of the Nusselt number yields a critical Rayleigh number which is within -6.7% of the value given by linearized stability theory. Measurements have been made of the time scales of developing convection after a sudden start of volumetric heating and of decaying convection when volumetric heating is suddenly stopped. In both cases, the steady-state temperature difference across the layer appears to be the controlling physical parameter, with both processes exhibiting the same time scale for a given steady-state temperature difference, or ·δRa·. For step changes in Ra such that ·δRa· > 100Rac, the time scales for both processes can be represented by Fo ·δRa·m, where Fo is the Fourier number of the layer. Temperature profiles of developing convection exhibit a temperature excess in the upper 15–20 % of the layer in the early stages of flow development for Rayleigh numbers corresponding to turbulent convection. This excess disappears when the average core temperature becomes large enough to permit eddy transport and mixing processes near the upper surface. The steady-state limits in the transient experiments yield heat-transfer data in agreement with the results of the steady-state experiments.

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U2 - 10.1017/S0022112077001244

DO - 10.1017/S0022112077001244

M3 - Article

AN - SCOPUS:84974159387

VL - 83

SP - 375

EP - 395

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

IS - 2

ER -