Analytical solution for the multidimensional degradation of a packed bed thermocline
A multidimensional, time-dependent model of the thermocline degradation in a packed bed thermal storage tank is presented. The formulation includes the effects of finite tank length, multidimensional thermal conduction, heat transfer between the fluid and solid portions of the bed, and heat losses across all tank surfaces. The technique used to solve the coupled pair of parabolic partial differential equations describing the degradation of the thermocline is based on a vectorized separation of variables approach. Assuming cylindrical geometry, the analysis leads to separate eigenvalue problems for the radial, angular, and axial spatial dependencies of the fluid and solid temperatures in the bed. The eigenvalues are readily calculated and the corresponding eigenfunctions are shown to form a complete set of spatial basis functions for the solution space. The method and results are illustrated by several examples.
- Research Organization:
- Sandia Labs., Livermore, CA
- DOE Contract Number:
- AT-(29-1)-789
- OSTI ID:
- 5924050
- Journal Information:
- J. Franklin Inst.; (United States), Vol. 307:1
- Country of Publication:
- United States
- Language:
- English
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Anharmonic analysis of a time-dependent packed bed thermocline
Anharmonic analysis of a time-dependent packed bed thermocline
Related Subjects
25 ENERGY STORAGE
PACKED BED
HEAT STORAGE
MATHEMATICAL MODELS
ANALYTICAL SOLUTION
DIFFERENTIAL EQUATIONS
EIGENFUNCTIONS
EIGENVALUES
GEOMETRY
HEAT LOSSES
HEAT TRANSFER
LAYERS
SPATIAL DEPENDENCE
STRATIFICATION
TANKS
THERMAL ENERGY STORAGE EQUIPMENT
TIME DEPENDENCE
TOWER FOCUS POWER PLANTS
CONTAINERS
ENERGY LOSSES
ENERGY STORAGE
ENERGY TRANSFER
EQUATIONS
EQUIPMENT
FUNCTIONS
LOSSES
MATHEMATICS
POWER PLANTS
SOLAR POWER PLANTS
SOLAR THERMAL POWER PLANTS
STORAGE
142000* - Solar Energy- Heat Storage- (1980-)
250600 - Energy Storage- Thermal
140702 - Solar Thermal Power Systems- Central Receiver