Anharmonic analysis of a time-dependent packed bed thermocline
Author:
Stephen B. Margolis
Journal:
Quart. Appl. Math. 36 (1978), 97-114
MSC:
Primary 80.35
DOI:
https://doi.org/10.1090/qam/479055
MathSciNet review:
479055
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Abstract: A vectorized separation of variables approach is applied to a coupled pair of parabolic partial differential equations describing the degradation of a thermocline in a packed bed thermal storage tank. The time-dependent quasi-one-dimensional model includes the effects of finite tank length, thermal conduction in the direction parallel to the tank walls, and heat transfer between the fluid and solid components of the bed. For certain classes of boundary conditions, the analysis leads to an eigenvalue problem for the spatial dependence of the fluid and solid temperatures in the bed. The eigenvalues and corresponding eigenfunctions are readily calculated, and completeness of the eigenfunctions follows from a transformation to an integral equation by the construction of a Green’s tensor function. The method is illustrated by an example which arises in the analysis of the thermal storage subsystem of a central solar receiver power plant.
T. E. W. Schumann, Heat transfer: a liquid flowing through a porous prism, J. Franklin Inst. 208, 405–416 (1929)
S. B. Margolis, Thermocline degradation in a packed bed thermal storage tank, Sandia Laboratories, SAND77-8032, 1977, to appear J. Heat Transfer
---, Central solar receiver thermal power system, Vol. 5, McDonnell Douglas Corporation Contractor’s Report MDC G6776, 1977
- Gilbert Helmberg, Introduction to spectral theory in Hilbert space, North-Holland Series in Applied Mathematics and Mechanics, Vol. 6, North-Holland Publishing Co., Amsterdam-London; Wiley Interscience Division John Wiley & Sons, Inc., New York, 1969. MR 0243367
- R. Courant and D. Hilbert, Methods of mathematical physics. Vol. I, Interscience Publishers, Inc., New York, N.Y., 1953. MR 0065391
- I. G. Petrovskii, Partial differential equations, Iliffe Books Ltd., London (distributed by W. B. Saunders Co., Philadelphia, Pa.), 1967. Translated from the Russian by Scripta Technica, Ltd. MR 0211021
T. E. W. Schumann, Heat transfer: a liquid flowing through a porous prism, J. Franklin Inst. 208, 405–416 (1929)
S. B. Margolis, Thermocline degradation in a packed bed thermal storage tank, Sandia Laboratories, SAND77-8032, 1977, to appear J. Heat Transfer
---, Central solar receiver thermal power system, Vol. 5, McDonnell Douglas Corporation Contractor’s Report MDC G6776, 1977
G. Helmberg, Introduction to spectral theory in Hilbert space, North-Holland Publishing Co., Amsterdam, 1969, pp. 182, 202
R. Courant and D. Hilbert, Methods of mathematical physics, Vol. I, Wiley-Interscience, New York, 1953, pp. 356, 394
I. G. Petrovskii, Partial differential equations, W. B. Saunders Co., Philadelphia, 1967, p. 343
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Article copyright:
© Copyright 1978
American Mathematical Society