The Laplace transform solution of equation (A.2) is where the time constant is tc = mcR^. such that the magnitude of the transfer function for the oscillation output flux is where = cotc is the frequency ratio and co is the frequency of oscillation of the source flux. The solution is a typical first-order lag, as expected from the first-order equation (A.2). This behavior was found previously for an axial-flow receiver [7], where the receiver storage material acted thermally as one "lump" of mass even though the heat input to it was distributed. To increase the order of the thermal response we consider the mass in Figure A-1(a) divided into two masses, each of mass f-m/2, and interconnected by conductor Kj = 1/Rj, as shown in Figure A-1(b). The factor f is a mass fraction to be determined (for f = 1, the masses of the two systems are the same, whereas for f < 1 the total mass of the two-block system is less than the mass of the single-block system). The input flux is concentrated at block 1, but some steady energy loss occurs from both blocks. where the conductance ratio is k = Kj/K0 = Rq/R], and x is the fraction of energy loss from block 1. Energy balances on the two blocks then yield equations for the oscillating components:
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