Thermodynamics and melting ice flow

by Dan Hughes

Recently I came across Isenko’s article et al. [2005] listed below. The second paragraph of the introduction states:

“According to conservation of energy, the potential energy loss of a mass of water is enough to warm it by 0.2 C for every 100 m of descent.”

The described process corresponds to isotropic compression of liquid water by a pressure increase of about 1 MPa, through a change in elevation of 100.0 m. Note that the change in temperature is provided independent of any other information regarding flow velocity, kinetic energy, viscosity, dissipation or any details of the flow channel that may affect the flow rate. affects the conversion to heat by viscous dissipation of kinetic energy. Note in particular that for the case of flow in horizontal channels, where the change in potential energy is zero, there will not be any change in temperature obviously. The same can be said for upward flows against gravity.

The authors’ calculations are related to the same concept that is the subject of this previous post. That is, the total potential energy at the top of the water column is converted into heat by the effect of viscous dissipation. As in the topic of the previous lesson, the temperature rises too high.

When this process is considered as the compression of liquid water cooled under isolation from interactions with its surroundings, the temperature rise is estimated to be about 0.01 K per 100 m.

In general, the textbook recommends that the temperature rise due to the oil dissipation can be ignored for all but a few special cases. The recommendation is especially valid whenever there is thermal interaction between the liquid and the channel wall, IE heat transfer, is the focus of the application.

The temperature rise when compressing the bottom cooled liquid water is estimated in the attached PDF file. [WorkPost03]

Authority to solve

Evgeni Isenko, Renji Naruse and Bulat Mavlyudov, “Water temperature in glacial and super-glacial channels: Changes along the flow and contribution to thawing on the channel walls” Cold Zone Science and TechnologyVol. 42, pp. 53–62, 2005.

Herbert B. Callen, Thermodynamics: An introduction to the physical theories of thermal equilibrium statistics and irreversible thermodynamics.John Wiley & Sons, Incorporated, New York, (1960).

W. Bridgman, “Complete Collection of Thermodynamic Formulas,” Physical assessment, Volume 3, no. 4, pp. 273–281, (1914). doi: 10.1103/PhysRev.3.273.

W. Bridgeman, Thermodynamics of electrical phenomena in metals and a condensed set of thermodynamic formulas, Dover Publications, Inc. New York. (In 1961).

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