Counterflow double-pipe heat exchanger analysis using a mixed lumped-differential formulation
01 Jul 1992-International Journal of Heat and Mass Transfer (Pergamon)-Vol. 35, Iss: 7, pp 1723-1731
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.
About: This article is published in International Journal of Heat and Mass Transfer.The article was published on 1992-07-01. It has received 11 citations till now. The article focuses on the topics: Heat transfer & Bulk temperature.
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TL;DR: In this article, a detailed one-dimensional steady and transient numerical simulation of the thermal and fluid-dynamic behavior of double-pipe heat exchangers (evaporators and condensers) has been carried out.
Abstract: A detailed one-dimensional steady and transient numerical simulation of the thermal and fluid-dynamic behaviour of double-pipe heat exchangers (evaporators and condensers) has been carried out. The governing equations (continuity, momentum and energy) inside the internal tube and the annulus, together with the energy equation in the internal tube wall, external tube wall and insulation, are solved iteratively in a segregated manner. The discretized governing equations in the zones with fluid flow are efficiently coupled using an implicit step by step method. This formulation requires the use of empirical correlations for the evaluation of convective heat transfer, shear stress and void fraction. An implicit central difference numerical scheme and a line-by-line solver was used in the internal and external tube walls and insulation. A special treatment has been implemented in order to consider transitions (single-phase/two-phase, dry-out,…). All the flow variables (enthalpies, temperatures, pressures, mass fractions, velocities, heat fluxes,…) together with the thermophysical properties are evaluated at each point of the grid in which the domain is discretized. Different numerical aspects and comparisons with analytical and experimental results are presented in order to verify and validate the model.
51 citations
TL;DR: In this paper, a multilayered, counterflow, parallel-plate heat exchanger is analyzed numerically and theoretically for constant property fluids, carried out for constant-property fluids, considering a hydrodynamically developed laminar flow and neglects longitudinal conduction both in the fluid and in the plates.
40 citations
TL;DR: In this article, a generalized Leveque solution is presented for the conjugate fluid-fluid problem that arises in the thermal entrance region of laminar counterflow heat exchangers.
17 citations
Cites background from "Counterflow double-pipe heat exchan..."
...Specifically, several investigations have been reported dealing with both the co-current [36, 37, 38, 39, 40] and counter-current [41, 42, 43, 44, 45, 46, 47, 48, 49] flow configurations....
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TL;DR: In this article, a precision method for attenuating temperature variations in a high-throughput control fluid stream is described and analyzed in contrast to earlier investigations, the authors emphasize heat transfer analysis of the constituent control device and derive theoretical descriptions of system responses to time-varying fluid temperatures.
Abstract: A precision method for attenuating temperature variations in a high-throughput control fluid stream is described and analyzed In contrast to earlier investigations, the present study emphasizes heat transfer analysis of the constituent control device and derives theoretical descriptions of system responses to time-varying fluid temperatures. Experiments demonstrate that the technique provides: (1) frequency-dependent attenuation which is several orders of magnitude greater than that obtained via a perfect mixing volume; (2) attenuation, over two decades of disturbance frequency, that reduces in-flow temperature variations by factors ranging from 10 to 10 4 ; (3) asymptotic attenuation greater than three orders of magnitude for spectral components having periods less than the device thermal equilibrium time; and (4) attenuation which is fully consistent with theoretical predictions. The model developed provides design criteria for tailoring system performance. In particular, it is shown that for a given control stream flow rate, the magnitude of maximal attenuation can be adjusted by varying the thermal resistance between the flow and attenuating medium, while the range of frequencies maximally attenuated can he adjusted by varying the product of thermal resistance and attenuating medium heat capacity. The analysis and design are general and should prove useful in the design and analysis of other high-throughput precision temperature control systems.
9 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
References
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Book•
01 Jan 1950
TL;DR: In this article, the authors provide fundamental instruction in heat transfer while employing the methods and language of industry using a course given at the Polytechnic Institute of Brooklyn over a period of years.
Abstract: It is the object of this text to provide fundamental instruction in heat transfer while employing the methods and language of industry. This treatment of the subject has evolved from a course given at the Polytechnic Institute of Brooklyn over a period of years. The possibilities of collegiate instruction patterned after the requirements of the practicing process engineer were suggested and encouraged by Dr. Donald F. Othmer, Head of the Department of Chemical Engineering. The inclusion of the practical aspects of the subject as an integral part of the pedagogy was intended to serve as a supplement rather than a substitute for a strong foundation in engineering fundamentals. These points of view have been retained throughout the writing of the book.
955 citations
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 paper, a class of nonlinear diffusion-type problems is handled through a hybrid method incorporating the ideas in the generalized integral transform technique to reduce the original partial differential equation into a denumerable system of coupled ordinary differential equations.
Abstract: A class of nonlinear diffusion-type problems is handled through a hybrid method. This method incorporates the ideas in the generalized integral transform technique to reduce the original partial differential equation into a denumerable system of coupled ordinary differential equations. These equations can then be solved through standard numerical techniques, once the system is truncated to a finite order. Sufficient conditions for the convergence of the truncated finite system are then examined. An application is considered that deals with a transient radiative fin problem, which is quite suitable for illustrating the solution methodology and convergence behavior.
106 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 generalized integral transform (GIFT) was used to solve convection-diffusion problems with non-separable eigenvalue problems in the thermal entry region, for a wide range of axial variable and various aspect ratios.
61 citations