Asymmetric-unbalanced counterflow thermal regenerator problem: solution by the Galerkin method and meaning of dimensionless parameters

Abstract

The asymmetric-unbalanced counterflow thermal regenerator problem described by the classical idealizations is solved by the Galerkin method. The integral equations relating to the reversal conditions at cyclic equilibrium of the regenerator matrix are transformed into a set of algebraic equations. This permits the determination of the expansion coefficients associated with the representation of the matrix temperature distributions at the start of each period of the cycle in the form of a power series in terms of the space variable. The method is easy and straightforward to apply and leads to explicit analytical expressions for the expansion coefficients for any combination of the four dimensionless parameters of the asymmetric-unbalanced regenerator. Excellent agreement has been found between the results of this new solution and those reported in the literature for different numerical solutions. Convergence towards the exact results by computations to higher order terms is discussed. The solution has been used to predict the effectiveness of a wide range of the four dimensionless parameters. Thermodynamic reasons for an alternative but rational and meaningful way of defining the four regenerator parameters are presented.