Lumped-differential analysis of concurrent flow double-pipe heat exchanger
TL;DR: In this article, a mixed lumped-differential formulation for double-pipe heat exchangers is presented that radially lumps the temperature distribution in the outer channel, providing a differential problem for the inner channel that involves a more general type of boundary condition for the wall temperature.
Abstract: A mixed lumped-differential formulation for double-pipe heat exchangers is presented that radially lumps the temperature distribution in the outer channel, providing a differential problem for the inner channel that involves a more general type of boundary condition for the wall temperature. The generalized integral transform technique is extended to allow for the analytical solution of this class of problems. Applicability limits for the simplified model are then established in terms of related parameters, based on numerical results obtained for bulk temperatures and Nusselt numbers, as compared to more involved approaches for the complete differential model.
Une formulation mixte differentielle-globale est presentee pour les echangeurs de chaleur a double conduite; cette formulation basee sur une valeur moyenne de la distribution radiale de temperature dans le canal exterieur permet d'etablir une equation differentielle pour le canal interieur qui necessite un type de conditions limites plus general pour la temperature aux parois. La technique des transformees integrales generalisees est etendue de facon a permettre la resolution analytique de cette categorie de problemes. Les limites d'applicabilite pour le modele simplifie sont ensuite etablies en termes de parametres connexes, a partir des resultats obtenus pour les temperatures et les nombres de Nusselt en masse, par comparaison a des techniques plus complexes pour le modele differentiel complet.
Citations
More filters
TL;DR: Mean-squared error (MSE) is used to analyse nine commonly used model selection criteria (MSC) for their performance when selecting simplified models (SMs) as discussed by the authors.
Abstract: Mean-squared error (MSE) is used to analyse nine commonly used model-selection criteria (MSC) for their performance when selecting simplified models (SMs). Expressions are derived to enable exact calculations of the probability that a particular MSC will select a SM. For several common MSC, the relative propensities to select SMs are independent of model structure and data. It is shown that MSC that are effective in preventing overfitting are prone to underfitting when information content of the data is low. In a subsequent article, results are extended to develop a new MSE-based MSC for selecting nonlinear multi-response SMs.
L'erreur quadratique moyenne (EQM) est utilisee pour analyser neuf criteres de selection de modeles (CSM) couramment utilises pour leur rendement lors de la selection de modeles simplifies (MS). Des expressions sont trouvees pour permettre des calculs exacts de la probabilite qu'un CSM particulier choisisse un MS. Pour plusieurs CSM communs, les propensions relatives pour choisir des MS sont independantes de la structure et des donnees des modeles. On a demontre que les CSM qui sont efficaces pour empecher le surajustement sont enclins au sous-ajustement lorsque le contenu de l'information des donnees est faible. Dans un article ulterieur, les resultats sont etendus pour creer un nouveau CSM fonde sur l'EQM pour la selection de MS non lineaires a reponses multiples.
27 citations
Cites background from "Lumped-differential analysis of con..."
...There are many reasons to choose a simplified model (SM) with fewer parameters and terms than the trulystructured complex model (Neto and Cotta, 1992; Talukdar and Basu, 1995; Gray, 1997; Zhang, 1997; Ismail, 2004; Jaree et al., 2004; Forney et al., 2005; Marquardt, 2005)....
[...]
TL;DR: In this article, an analysis of double-pipe heat exchangers under a thermally developing countercurrent flow condition is made, by radially lumping the temperature field in the outer channel, which results in a more involved boundary condition for the inner differential system involving the axially varying outer channel bulk temperature.
11 citations
01 Aug 1993
TL;DR: In this article, a mixed lumped-differential formulation is employed to model the transient energy equations for fully developed laminar-laminar or laminor-turbulent flow situations in concurrent or countercurrent double-pipe heat exchangers.
Abstract: A mixed lumped-differential formulation is employed to model the transient energy equations for fully developed laminar-laminar or laminar-turbulent flow situations in concurrent or countercurrent double-pipe heat exchangers. The temperature distribution in the outer annular channel is radially lumped, providing a more general boundary condition for the inner channel differential energy equation, coupled through the interface condition. The case of periodically varying inlet temperatures is more closely considered, and the dynamic response of the exchanger is established in terms of the governing dimensionless parameters, such as heat capacity flow rate ratio, dimensionless inlet temperature oscillation frequency, and relative wall thermal resistence. The ideas in the generalized integral transform technique are extended to yield analytical solutions to the related periodic problem defined in the complex domain, and offer highly accurate numerical results for quantities of practical interest, such as fluids bulk temperatures.
8 citations
TL;DR: In this article, the authors considered the cross-sectional velocity profile to be piecewise-constant in each stream of a multi-stream heat exchanger for cocurrent thermally developing flow, and solved the related conjugated Graetz problem by using an integral transform method.
Abstract: Considering the cross-sectional velocity profile to be piecewise-constant in each stream of a multi-stream heat exchanger for cocurrent thermally developing flow, this study analytically solves the related conjugated Graetz problem by using an integral transform method. Further, it obtains an analytical solution in an explicit form to the fluid temperatures that vary two-dimensionally. A numerical example is provided for the case of a triple-tube heat exchanger. The numerical results demonstrate the effects of the thermal conductivity ratios of the fluids and the Peclet number ratios on the temperature distribution in the streams. In addition, in order to show the importance of considering streamwise variations in the overall heat transfer coefficients when designing laminar flow heat exchangers, the amount of exchanged heat calculated by the presented analytical solution is compared with that predicted on the basis of bulk temperatures and constant overall heat transfer coefficients.
2 citations
Cites background from "Lumped-differential analysis of con..."
...…with non-negligible effects of thermally developing flow has been analytically investigated by various researchers (Blanco and Gill, 1967; Gill et al., 1968; Mikhailov and Shishedjiev, 1976; Neto and Cotta, 1992; Nunge and Gill, 1966; Pagliarini and Barozzi, 1991; Plaschko, 2000; Stein, 1965a,b)....
[...]
23 Dec 2009
TL;DR: This book is intended to serve as a “roadmap” for future generations of writers to consider the themes of self-confidence, self-consistency, and self-publishing.
Abstract: ........................................................................................................................................... ii Co-Authorship ................................................................................................................................ iii Acknowledgements ......................................................................................................................... iv Chapter
1 citations
Cites background from "Lumped-differential analysis of con..."
...There are many reasons to choose a simplified model (SM) with fewer parameters and terms than the correctly-structured complex model (Neto and Cotta, 1992; Talukdar and Basu, 1995; Gray, 1997; Zhang, 1997; Ismail, 2004; Jaree et al., 2004; Forney et al., 2005; Marquardt, 2005)....
[...]
...There are many reasons to choose a SM with fewer parameters and terms than the correctly-structured complex model (Neto and Cotta, 1992; Talukdar and Basu, 1995; Gray, 1997; Zhang, 1997; Ismail, 2004; Jaree et al., 2004; Forney et al., 2005; Marquardt, 2005)....
[...]
References
More filters
TL;DR: An orthogonal expansion technique for solving a new class of counterflow heat transfer problems is developed and applied to the detailed study of laminar flow concentric tube heat exchangers as discussed by the authors.
Abstract: An orthogonal expansion technique for solving a new class of counterflow heat transfer problems is developed and applied to the detailed study of laminar flow concentric tube heat exchangers. The exchanger problem is solved for fully developed laminar velocity profiles, negligible longitudinal conduction in the fluid streams and in the exchanger walls, and with fluid properties which are independent of the temperature.
A description of the variation of the local Nusselt numbers and the temperature at the wall between the two streams is given. Also reported are bulk temperature changes in the two streams and mean overall Nusselt numbers. It is shown that for long exchangers, which are of some industrial importance, asymptotic Nusselt numbers exist in counterflow as in single-phase and cocurrent systems. Numerical values of asymptotic Nusselt numbers are reported for a wide range of parameters. Comparisons are made with single-stream solutions such as the Graetz problem, with empirical correlations of experimental data, and with cocurrent flow exchangers.
To solve this problem it was necessary to derive new orthogonality relations, and also expressions for determining positive and negative sets of eigenvalues and eigenvectors. Satisfaction of inlet boundary conditions at both ends of counterflow exchangers requires a complete set of eigenfunctions and thus one must use both the positive and negative sets.
110 citations
TL;DR: In this article, the generalized integral transform technique is employed to reduce the original problem to a system of linear first-order differential equations, which is then solved utilizing the related complex matrix eigenvalue problem.
82 citations
TL;DR: In this article, the analytical solutions for coupled at boundary diffusion processes in the entrance region of channel flow are presented and an algorithm for computing the resulting eigenvalue problem and computer program CUPFLOW are developed for studying a class of coupled problems to which belong the ones discussed in [1, 7].
14 citations
01 Jan 1986
9 citations
8 citations