Laminar counterflow parallel-plate heat exchangers: Exact and approximate solutions

Abstract

Multilayered, counterflow, parallel-plate heat exchangers are analyzed numerically and theoretically. The analysis, carried out for constant property fluids, considers a hydrodynamically developed laminar flow and neglects longitudinal conduction both in the fluid and in the plates. The solution for the temperature field involves eigenfunction expansions that can be solved in terms of Whittaker functions using standard symbolic algebra packages, leading to analytical expressions that provide the eigenvalues numerically. It is seen that the approximate solution obtained by retaining the first two modes in the eigenfunction expansion provides an accurate representation for the temperature away from the entrance regions, specially for long heat exchangers, thereby enabling simplified expressions for the wall and bulk temperatures, local heat-transfer rate, overall heat-transfer coefficient, and outlet bulk temperatures. The agreement between the numerical and theoretical results suggests the possibility of using the analytical solutions presented herein as benchmark problems for computational heat-transfer codes.

Modified effectiveness and linear regression based models for heat exchangers under heat gain/loss to the environment

“…More detailed but considerably more technical and hard to handle mathematical descriptions of the corresponding physical phenomena can be gained by means of ordinary differential equations (ODEs) or partial differential equations (PDEs). A system of ODEs models the temperature of the working fluids in [12] and systems of PDEs model the temperature distribution inside a heat exchanger in [13,14]. In [13], the PDEs for a unitary cell of parallel plate heat exchangers is solved analytically by means of eigenfunctions technique taking into account longitudinal and transverse wall conduction effects.…”

“…A system of ODEs models the temperature of the working fluids in [12] and systems of PDEs model the temperature distribution inside a heat exchanger in [13,14]. In [13], the PDEs for a unitary cell of parallel plate heat exchangers is solved analytically by means of eigenfunctions technique taking into account longitudinal and transverse wall conduction effects. Then the truncated form of the solution is compared numerically with another approximate solution (based on problem discretization) showing small difference.…”

Numerical computation of 3D heat transfer in complex parallel heat exchangers using generalized Graetz modes

“…Parallel convective heat exchangers are relevant in various applications such as heating or cooling systems [1], haemodialysis [2], and convective heat exchangers [3]. Since the seminal contributions of Nunge et al [4,5] there has been a number of works devoted to parallel convective heat exchangers in simple two dimensional configurations among which [6,7,8,9,10,11] to cite only a few, whilst many other can be found in a recent review [12]. As quoted in [12] conjugate heat transfer are mixed parabolic/hyperbolic problems which makes them numerically challenging.…”

Analysis of the temperature, humidity, and total efficiency of the air handling unit with a periodic counterflow heat exchanger

“…In most solutions, parallel-plate heat exchangers are used. This type of heat exchanger was analysed by Vera and Linan [9] to provide formulations for construction design. Authors developed a 2-D model to evaluate expressions able to describe parallel-plate heat exchangers.…”