Rapid calculation of temperature in a regenerative heat exchanger having arbitrary initial solid and entering fluid temperatures

Abstract By means of simple hand calculations it is possible to determine fluid and solid temperatures at any time and location in the regenerative heat exchanger. The methods described apply to cases where the initial temperature varies arbitrarily with longitudinal position in the matrix and the entering fluid temperature varies arbitrarily with time. The solution to the problem with uniform initial matrix temperature and constant entering fluid temperature has been published previously [1–4] and is presented herein in the form of tables and curves for values of the parameters η and ξ from 0 to 20. The solutions for the linear initial matrix temperature and linear entering fluid temperatures are also presented in the form of tables and curves for the same range of parameters. By superposition, these results are extended to the cases of arbitrary initial matrix temperature and arbitrary entering fluid temperature. Either of two methods is useful in obtaining numerical results. One is to evaluate a convolution integral which involves the arbitrary condition. The other is to approximate the arbitrary initial (and/or boundary) condition by a number of linear segments and to superimpose the tabulated solutions.