The non-adiabatic calorimeter problem and its application to transfer processes in suspensions of solids

Abstract

The problem of simultaneous transfer of heat from a fluid of finite extent to the ambient and to a solid of finite thermal conductivity is solved. The general solution is in the form of an infinite series with the Biot number, the thermal extent ratio H, the ambient loss parameter E and the ambient temperature V a as parameters; the series shows strong exponential decay so that a few terms suffice for most applications. The solution is an extension and refinement of the classical calorimeter problem. The results find application in the analysis of (and design of equipment for) continuous exchange involving suspended solids. The form of the solution is sufficiently simple for optimisation of insulation thickness, residence time and other process parameters. For limiting values of the parameters simplified solutions are presented, for instance for the double pipe heat exchanger with ambient loss.