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Nusselt correlation to predict heat transfer from an oscillated vertical annular fluid column through a porous domain

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Abstract

Experimental evaluation of the heat transfer in oscillating flow under the constant heat flux and constant amplitude fluid displacement conditions is presented for a vertical annular flow through a stainless steel wool porous media. The analysis is carried out for two different heat fluxes and for five different frequencies. The data is acquired from the measurements both in the initial transient period and in the pseudo-steady (cyclic) period by the system. The physical and mathematical behavior of the resulting Nusselt numbers are analyzed, according to data acquired from the experiments and in accordance with the results of the Buckingham Pi theorem. A cycle and space averaged Nusselt number correlation is suggested as a function of kinetic Reynolds number for oscillating flows. The suggested correlation is useful in predicting heat transfer from oscillating flows through highly porous and permeable solid media at low actuation frequencies and at low heat fluxes applied in the wall. The validity of the Nusselt numbers acquired by correlation is discussed using experimental Nusselt numbers for the selected kinetic Reynolds number interval. The present investigation has possible applications in moderate sized wicked heat pipes, solid matrix compact heat exchangers compromising of metallic foams, filtration equipment, and steam generators.

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Abbreviations

A0 :

Dimensionless oscillation amplitude

D:

Hydraulic diameter of test duct (m)

h:

Local heat transfer coefficient (W/m2 K)

\(\overline{h}\) :

Cycle and space averaged heat transfer coefficient (W/m2 K)

kw :

Heat conduction coefficient of water (W/m K)

L:

Distance from probe 1 to probe 2 (m)

\(\overline{Nu}\) :

Cycle and space averaged Nusselt number

q″:

Instantaneous heat flux through heater (W/m2)

\(\left\langle {q^{{\prime \prime }} } \right\rangle\) :

Cycle averaged heat flux through heater (W/m2)

\(\overline{{\left\langle {q''} \right\rangle }}\) :

Cycle-space averaged heat flux (W/m2)

Q:

Average heat supplied to heater (W)

r:

Radial coordinate (m)

r0 :

Inner radius of annulus (m)

\(\text{Re}_{\omega }\) :

Kinetic Reynolds number

t:

Time (s)

Tm :

Local bulk temperature of water (°C)

\(\overline{{T_{m} }}\) :

Mean bulk temperature of water (°C)

Tw :

Local wall temperature (°C)

\(\overline{{T_{w} }}\) :

Mean wall temperature (°C)

z:

Vertical coordinate (m)

z0 :

Length from the bottom of the system to the entrance of control volume (m)

zmax :

Maximum vertical coordinate during the oscillations (m)

υ :

Kinetic viscosity (m2/s)

ω :

Angular frequency (rad/s)

Exp:

Experiment no

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Correspondence to Ersin Sayar.

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Ersin Sayar and Ugurcan Sari have contributed equally to this work.

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Sayar, E., Sari, U. Nusselt correlation to predict heat transfer from an oscillated vertical annular fluid column through a porous domain. Heat Mass Transfer 53, 1135–1142 (2017). https://doi.org/10.1007/s00231-016-1887-1

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