Performance of Counterflow, Parallel Plate Heat Exchangers under Laminar Flow Conditions
TL;DR: In this paper, multilayered heat exchangers were analyzed theoretically and their heat transfer characteristics were clarified, and the problem was treated as a two-dimensional, conjugated one with three phases-two fully developed laminar flows and the exchanger wall.
Abstract: Multilayered heat exchangers were analyzed theoretically and their heat transfer characteristics were clarified. The problem was treated as a two-dimensional, conjugated one with three phases-two fully developed laminar flows and the exchanger wall. From numerical results, the exchanger effectiveness was found to be definitely influenced by the following parameters: Graetz number, heat capacity flow rate ratio, dimensionless wall thickness, and conductance ratios between fluid and wall and between both fluids. Examination of mixed-mean temperature distributions in the exchanger showed that longitudinal wall conduction significantly reduces exchanger effectiveness in the low-Graetz-number region. Experimental results were in fairly good agreement with theoretical predictions.
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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 paper, the effects of wall axial heat conduction on laminar flow heat transfer were investigated and the results satisfactorily compare with predictions by a theoretical method previously developed by the authors.
20 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
TL;DR: In this paper, the wall conduction effects in multilayered, counterflow, parallel-plate heat exchangers are analyzed theoretically and numerically, carried out for constant property fluids, considering a hydrodynamically developed laminar flow and neglects axial conduction both in the fluids and in the plates.
16 citations
TL;DR: In this article, the axial conduction effect in the wall is shown to relax the interference between the two convections in both fluids, and the theoretical predictions describe well the experimental temperature distributions, showing the validity of the present analysis.
14 citations
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112 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 article, an exact solution of the heat transfer problem for a circular channel is presented and the first four eigenvalues and the corresponding eigenfunctions are found for Peclet numbers 100 and 1000.
Abstract: In a recent paper1) a method for determining the discrete set of eigenvalues and the associated eigenfunctions of a certain Sturm-Liouville differential system has been developed and it has been pointed out that by this method the problem of heat transfer by laminar flow in cylindrical channels can be worked out withaxial heat conduction, viscous dissipation and any prescribedheat generation included. In the present paper an exact solution of this problem for a circular channel is presented and the first four eigenvalues and the corresponding eigenfunctions are found for Peclet numbers 100 and 1000 (hitherto worked out by assuming thatδ2T/δx2 ≪δ2T/δr2 + (1/r)δT/δr, and also neglecting the viscous dissipation). It is found that the effect of axial heat-conduction is almost negligible for higher Peclet numbers (Pe>100), and hence it can be definitely stated that the approximate solution is good enough under the usual experimental conditions. The heat transfer problem for plug flow is also solved exactly, and it is concluded that the effect of axial heat conduction is negligible forPe>100. The mean mixed temperature and the Nusselt numbers are tabulated and plotted against the Graetz number.
79 citations
TL;DR: In this article, a solution to the Graetz problem in an annulus with a heated core and an insulated outer wall is presented, where both uniform temperature and uniform heat input on the inside wall are considered for a number of arbitrarily chosen radius ratios.
57 citations