Results of a theoretical and experimental study of the thermal dynamics of a distributed parameter nonadiabatic humidification process are presented. A wetted-wall column was selected for study to ensure standard and reproducible velocity profiles and a definable area for heat and mass transfer. Four mathematical models which consider various heat and mass transfer effects were derived in the time domain and solved in the frequency domain. All models, including a simple model previously tested for the adiabatic humidification case, were in good agreement with experimental results obtained by pulse testing.Few dynamic studies of distributed parameter simultaneous heat and mass transfer systems have been reported. Bruley and Prados (2, 3 ) performed a frequency response analysis of a wetted-wall adiabatic humidifier. Both laminar and turbulent air flow were studied with water used in countercurrent laminar flow. Lewis (11) experimentally studied adiabatic column d namics by the pulse testing method. Hunt (10) extendeJ the frequency range of previous studies and investigated the effect of various input pulse characteristics.For the adiabatic humidification case, the liquid temperature can be assumed constant and independent of axial position. This means that the mathematical analysis can be restricted to the gas phase alone with a boundary condition of constant temperature at the gas-liquid interface. The present study deals with the thermal dynamics of the nonadiabatic humidification case. Here, nonadiabatic implies the existence of axial temperature gradients in both the gas and liquid phases. Mass transfer and liquid phase dynamics are considered in the theoretical development in addition to the gas phase dynamics.A wetted wall-column was selected for study because of its comparatively well-defined area for heat and mass transfer. A reasonably accurate estimate of this variable was deemed necessary for testing the theoretical models. An air-water system with turbulent gas and liquid flow was investigated. THEORETICAL DEVELOPMENTAll mathematical models are based upon the following 1. Flat velocity and temperature prdles exist in both 2. Gas A mathematical description of the system is obtained from energy balances on the gas and liquid phases and the interface. The following dynamic equations for the gas and liquid phase temperature changes are obtained from these energy balances after a sequence of algebraic manipulations :Solution of Equations (1) and (2) is complicated by the presence of the dynamic humidities H',i and H'Q. The following assumptions are made to simplify the analaysis and still include the dynamics of mass transfer:1. The bulk gas phase humidity remains constant upon inlet gas temperature forcing, that is, H', = 0. H'gi = cvtiThese two assumptions are substituted into Equation ( 2 ) . Next, several time constants T are defined and are included in the resulting gas and liquid phase equations. The following equations are obtained after taking the Laplace transformation with respect to time:Four t...

Many studies dealing with the process dynamics of distributed parameter counterflow systems have been reported in the literature. Nearly all of the investigators have considered counterflow systems whose dynamic performance can be described mathematically by a partial differential equation having only two independent variables. For example, in previous studies of double pipe heat exchanger dynamics (11, 12) an accurate mathematical description of the system was obtained with time and axial position as the independent variables. As a result of these and other studies, methods of extracting the theoretical process dynamics from mathematical models of distributed parameter counterflow systems having time and a single space dimension as independent variables are well known.Several papers dealing with steady state solutions of countercurrent laminar flow problems have been reported. Nunge and Gill (10) presented a separation of variables solution for a laminar counterflow double-pipe heat exchanger at steady state. Their solution required a convergent series in both positive and negative eigenvalues in order to satisfy the split boundary conditions. The negative set of eigenvalues occurs because one of the fluid velocities is negative with respect to a fixed coordinate system. The split boundary conditions occur because the axial position boundary conditions are usually known at the fluid inlets which are at opposite ends of the system. The eigenvalues for this steady state case were evaluated numerically using an iterative integration procedure.In the present study of an unsteady state case, Laplace transformed energy balance equations result which are similar in form to the energy balance equations for the steady state case, for example, Equations ( 3 ) and (6) herein. However, these transformed equations for the unsteady state case contain an additional term which includes the Laplace transform variable, s, as a parameter. Because the steady state solution of Nunge and Gill involved a numerical integration step to determine the eigenvalues and because the complex parameter, s, complicates the unsteady state equations, the direct transfer function substitution method (2, 3) and the use of a completely numerical solution was chosen for the unsteady state equations.Completely numerical solutions for the steady ,state case have been reported, also by Nunge and Gill (9). Their numerical procedure was a modification of the work of King (6). The present study extends the method of King, as modified by Nunge and Gill, to the unsteady state case.The present study is concerned with mathematical modeling and theoretical calculation of process dynamics for distributed parameter counterflow systems which require two space variables and time for an accurate mathematical description. Most distributed parameter counterflow heat and mass transfer systems having radially dependent velocity, temperature, and/or concentration profiles fall into this category.A wetted wall column using air and water in countercurrent laminar flow was s...