A sensor for heat transfer measurements

Koschmieder, E. L.; Pallas, S. G.

doi:10.1063/1.1686833

Cited by 7 publications

(8 citation statements)

References 2 publications

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“…However, in his experiments the top surface of fluid was free, and subsequent analysis (Koschmieder [1974]) has shown that in his experiments surface tension had a larger effect than density variations. Most modern experiments are performed in closed containers, so that they may be more carefully controlled.…”

Section: (A) Description Of the Experimentsmentioning

confidence: 93%

“…Most modern experiments are performed in closed containers, so that they may be more carefully controlled. It is now understood both theoretically and experimentally, (see Koschmieder [1974]) that in a closed container with fixed temperatures at top and bottom, rolls are generally the preferred motion. (We qualify this statement with "generally" since, because of various small effects such as temperaturedependent viscosity, the hexagonal pattern may be preferred over a short range of Rayleigh numbers.)…”

Section: (A) Description Of the Experimentsmentioning

confidence: 99%

“…Of course, such experiments are intended to shed light on more dramatic geophysical occurrences of convection, such as in the atmosphere and in the interior of the earth (plate tectonics). See Koschmieder [1974], Schluter et al [1965], Sattinger [1978]. In this section we (a) describe the experiments, (b) discuss how symmetry enters the problem, (c) show how to use Fourier analysis to obtain the group action, and (d) combine these ideas to obtain the appropriate symmetry in a suitably reduced model bifurcation problem.…”

Section: The Planar Benard Pro Blern §O Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Singularities and Groups in Bifurcation Theory

Golubitsky¹,

Stewart²,

Schaeffer³

1988

Applied Mathematical Sciences

1,809

1,250

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Section: (A) Description Of the Experimentsmentioning

confidence: 93%

Section: (A) Description Of the Experimentsmentioning

confidence: 99%

Section: The Planar Benard Pro Blern §O Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Singularities and Groups in Bifurcation Theory

Golubitsky¹,

Stewart²,

Schaeffer³

1988

Applied Mathematical Sciences

1,809

1,250

View full text Add to dashboard Cite

“…By means of a special cooling device (Koschmieder & Pallas 1974) water of temperature 18.0 • C is supplied to the centre of the sapphire-disc, from where it flows radially outwards, thereby ensuring axisymmetric cooling. The cooling water, pumped with a flow rate of 95 l h −1 , is provided from a 0.2 m 3 thermally insulated tank.…”

mentioning

confidence: 99%

Square cells in surface-tension-driven Bénard convection: experiment and theory

1998

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The convective flow in a thin liquid layer with a free surface heated from below is studied using a combination of accurate experiments with silicone oil (v=0.1 cm2 s−1) and high-resolution direct numerical simulations of the time-dependent governing equations. It is demonstrated that above a certain value εs of the threshold of primary instability, ε=0, square convection cells rather than the seemingly all-embracing hexagons are the persistent dominant features of Bénard convection. The transition from hexagonal to square cells sets in via a subcritical bifurcation and is accompanied by a sudden rapid increase of the Nusselt number. This implies that square cells are the more efficient mode of heat transport. Their wavenumber exceeds that of hexagonal cells by about 8%. The transition depends on the Prandtl number and it is shifted towards higher εs if the Prandtl number is increased. The replacement of hexagonal by square cells is mediated by pentagonal cells. In the transitional regime from hexagonal to square cells, characterized by the presence of all three planforms, the system exhibits complex irregular dynamics on large spatial and temporal scales. The time dependence becomes more vivid with decreasing Prandtl number until finally non-stationary square cells appear. The simulations agree with the experimental observations in the phenomenology of the transition, and in the prediction of both the higher Nusselt number of square Bénard cells and the subcritical nature of the transition. Quantitative differences occur with respect to the values of εs and the Prandtl number beyond which the time dependence vanishes. These differences are the result of a considerably weaker mean flow in the simulation and of residual inhomogeneities in the lateral boundary conditions of the experiment which are below the threshold of control.

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“…The thermoelectric sensitivity (TES) is employed in the above mentioned heat flux studies [16,20,17]. It is commonly measured with the differential method (described in [8]) [17,21,22,23,24,25].…”

Section: Introductionmentioning

confidence: 99%

Optimized thermoelectric sensitivity measurement for differential thermometry with thermopiles

Prangemeier

Nejati

Müller

et al. 2015

Experimental Thermal and Fluid Science

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A novel approach to calibrate the sensitivity of a differential thermometer, consisting of several thermocouples connected in series (thermopile), has been developed. The goal of this method is to increase the accuracy of small temperature difference measurements (∆T ≤ 1 K), without invoking higher sensor complexity. To this end, a method to determine the optimal temperature difference employed during the differential measurement of thermoelectric sensitivities has been developed. This calibration temperature difference is found at the minimum of combined measurement and linearization error for a given mean temperature. The developed procedure is demonstrated in an illustrative example calibration of a nine-junction thermopile. For mean temperatures between −10 • C and 15 • C, the thermoelectric sensitivity was measured with an uncertainty of less than ±2 %. Subsequently, temperature differences as low as 0.01 K can be resolved, while the thermometer used for the example calibration was accurate only to ±0.3 K. This and higher degrees of accuracy are required in certain research applications, for example to detect heat flux modulations in bifurcating fluidic systems.

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A sensor for heat transfer measurements

Abstract: A device is described which permits accurate measurements of the heat flow through a horizontal fluid layer. The heat sensor provides for a uniform cooling of the fluid layer and prevents heat losses to ambient air or other parts of the apparatus.

Cited by 7 publications

References 2 publications

Singularities and Groups in Bifurcation Theory

Singularities and Groups in Bifurcation Theory

Square cells in surface-tension-driven Bénard convection: experiment and theory

Optimized thermoelectric sensitivity measurement for differential thermometry with thermopiles

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