Analytical Solution of Dynamic Response of Heat Exchanger (original) (raw)

Heat Exchangers-Basics Design Applications 54 in which both fluids are gases. The paper (Gvozdenac, 1987) shows analytical solution for transient response of parallel and counter flow heat exchangers. However, these solutions are limited to the case in which heat capacities of both fluids are negligibly small in relation to the heat exchanger's separating wall capacity. Moreover, it is important to mention that papers (Romie, 1983), (Gvozdenac, 1986), (Spiga & Spiga, 1987) and (Spiga & Spiga, 1988) deal with two-dimensional problems of transition for cross flow heat exchangers with both fluids unmixed throughout. The last paper is the most general one and provides opportunities for calculating transient temperatures of wall temperatures and of both fluids by an analytical method for finite flow velocities and finite wall capacity. The paper (Gvozdenac, 1990) shows analytical solution of transient response of the parallel heat exchanger with finite heat capacity of the wall. The procedure presented in the above paper is also used for resolving dynamic response of the cross flow heat exchanger with the finite wall capacity (Gvozdenac, 1991). A very important book is that of Roetzel W and Xuan Y (Roetzel & Xuan, 1999) which provides detailed analysis of all important aspects of the heat exchanger's dynamic behavior in general. It also gives detailed overview and analysis of literature. This paper shows solutions for energy functions which describe convective heat transfer between the wall of a heat exchanger and fluid streams of constant velocities. The analysis refers to parallel, counter and cross flow heat exchangers. Initial fluids and wall temperatures are equal but at the starting moment, there is unit step change of inlet temperature of one of the fluids. The presented model is valid for finite fluid velocities and finite heat capacity of the wall. The mathematical model is comprised of three linear partial differential equations which are resolved by manifold Laplace transforms. To a certain extent, this paper presents a synthesis of the author's pervious papers with some simplified and improved final solutions. The availability of such analytical solutions enables engineers and designers a much better insight into the nature of heat transfers in parallel, counter and cross flow heat exchangers. For the purpose of easier practical application of these solutions, the potential users are offered MS Excel program at the web address: www.peec.uns.ac.rs. This program is open and can be not only adjusted to special requirements but also modified. 2. Mathematical formulation Regardless of seeming similarity of partial differential equations arising from mathematical modeling, this paper analyzes parallel, cross and counter flow heat exchangers separately. However, simplifying assumptions in the derivation of differential equations are the same and are as follows: a. Heat transfer characteristics and physical properties are independent of temperature, position and time; b. The fluid velocity is constant in each flow passage; c. Axial conduction is negligible in both fluids and the wall; d. Overall heat losses are negligible; e. The heat generation and viscous dissipation within the fluids are negligible; f. Fluids are assumed to be finite-velocity liquids or gases. This means that the fluid transit or dwell times are not small compared to the duration of transience.