Transient analysis of packed-bed thermal storage systems

A model, including longitudinal thermal dispersion and intraparticle conduction, is developed to describe the transient response of a packed column with a time-varying inlet temperature. The model can be applied to a diabatic column with uniform and constant ambient temperature, or to a perfectly insulated system. The expression for the temperature response within the column as a function of time and axial position is obtained by expanding the solution to an impulse of heat at the inlet in terms of either Hermite or Laguerre polynomials. The response to an arbitrary inlet temperature transient, found via a convolution integral, is expressed as a single quadrature. The response to a step input is an algebraic expression.