Analysis of heat or mass transfer in some countercurrent flows

Nunge, Richard J.; Gill, William N.

doi:10.1016/0017-9310(65)90072-4

Cited by 68 publications

(30 citation statements)

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“…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.…”

Section: Motivation Context and Brief Overviewmentioning

confidence: 99%

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

Pierre

Bouyssier

Gournay

et al. 2014

Journal of Computational Physics

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We propose and develop a variational formulation dedicated to the simulation of parallel convective heat exchangers that handles possibly complex input/output conditions as well as connection between pipes. It is based on a spectral method that allows to re-cast three-dimensional heat exchangers into a two-dimensional eigenvalue problem, named the generalized Graetz problem. Our formulation handles either convective, adiabatic, or prescribed temperature at the entrance or at the exit of the exchanger. This formulation is robust to mode truncation, offering a huge reduction in computational cost, and providing insights into the most contributing structure to exchanges and transfers. Several examples of heat exchangers are analyzed, their numerical convergence is tested and the numerical efficiency of the approach is illustrated in the case of Poiseuille flow in tubes.

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Section: Motivation Context and Brief Overviewmentioning

confidence: 99%

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

Pierre

Bouyssier

Gournay

et al. 2014

Journal of Computational Physics

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“…The laminar force convection heat transfer problem neglecting thermal conduction in the axial direction under equal wall temperatures, was firstly proposed by Graetz [1], and is therefore called the classical Graetz problem [2,3]. The extension of classical Graetz problems by considering the axial thermal conduction for low Prandtl number fluids, such as liquid metal, has also been studied by many researchers [4][5][6][7][8], and are referred to as extended Graetz problems. Moreover, conjugated Graetz problems [9][10][11][12] dealing with heat transfer problems in multistream or multiphase systems must be solved through the mutual conditions at the boundaries.…”

Section: Introductionmentioning

confidence: 99%

Device Performance Improvement of Double‐Pass Concentric Circular Mass Exchangers under Uniform Wall Fluxes

Chuang

2007

Chem Eng & Technol

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A double-pass concentric circular mass exchanger under uniform wall fluxes is produced by inserting a permeable barrier into a circular tube to improve the device performance. The mathematical formulation was developed theoretically for such double-pass, forced-convection, mass-transfer problems which are referred to as conjugated Graetz problems. The analytical solutions are obtained by the linear superposition of an asymptotic solution and a homogeneous solution which are linear in the axial direction and solved with the use of an eigenfunction expansion in a power series. The analytical results show that the mass-transfer rate of a double-pass mass exchanger can be improved compared to that of a single-pass mass exchanger by suitably adjusting the permeable barrier position. Moreover, the ratio of mass-transfer efficiency improvement and power consumption increment is also shown to make good economic sense.

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“…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).…”

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confidence: 98%

Process dynamics of distributed parameter counterflow systems in laminar flow

Stewart

Bruley

1969

AIChE Journal

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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...

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Analysis of heat or mass transfer in some countercurrent flows

Cited by 68 publications

References 1 publication

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

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

Device Performance Improvement of Double‐Pass Concentric Circular Mass Exchangers under Uniform Wall Fluxes

Process dynamics of distributed parameter counterflow systems in laminar flow

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