Win Aung

Effect of wall conduction on free convection between asymmetrically heated vertical plates: uniform wall heat flux

Abstract In this study of the effect of wall conduction on laminar free convection between asymmetrically heated vertical plates, an implicit finite difference scheme is used to solve the governing equations. The governing independent parameters are identified to be Prandtl number ( Pr ), Grashof number ( Or ), ratio of thermal conductivity of the solid to air (K), wall thickness to channel width ratio ( t / B ), channel height to width ratio ( L / B ) and the asymmetric heating parameter ( γ H ). The effect of wall conduction on free convective flow of air under asymmetrically heated conditions ( γ H = 1.0, 0.5, and 0) is discussed. Calculations are made for K = 1 and 10, t / B = 0.1 and 0.5, Gr = 10-10 4 , and L / B = 1 and 5. The maximum increase in mass flow rate of air for symmetric heating due to wall conduction is 30%. The maximum decrease in average Nusselt number due to wall conduction is 22%. Wall conduction effects are more significant for low Gr flows than for high Gr flows.

Numerical prediction of lock-on effect on convective heat transfer from a transversely oscillating circular cylinder

Abstract Heat transfer characteristics and the flow behavior of cross flow over a transversely oscillating cylinder are investigated. The lock-on phenomenon has been predicted numerically and its influence on the heat transfer performance of the cylinder is evaluated. The SOLA method is employed to solve the unsteady velocity field in a non-inertial reference frame, and the energy equation is solved by a finite-volume method. Transient variations of the Nusselt number and the drag and lift coefficients are calculated for various oscillation conditions. The ranges of the dominant parameters considered in this study are 0 ⩽ Re ⩽ 300, 0⩽ S c ⩽ 0.3 and 0 ⩽ A / D ⩽ 0.7.. The Prandtl number is considered to be 0.71 or 7.0. In the lock-on regime, an appreciable heat transfer increase caused by the oscillation is observed; however, outside this regime, the heat transfer is almost unaffected by the oscillation. A correlation formula expressing the dependence of heat transfer on these dominant parameters in this lock-on regime is presented. The numerical predictions have been compared with the existing information, and good agreement has been found.

Buoyancy-assisted flow reversal and convective heat transfer in entrance region of a vertical rectangular duct

Abstract In this study, predictions of buoyancy-assisted flow reversal and convective heat transfer in the entrance region of a vertical rectangular duct are reported for the first time. In line with the current trend toward the use of computationally efficient numerical methods, the present study is based on the use of a three-dimensional parabolic, boundary-layer model and the FLARE approximation. Physical situations investigated include cases with various asymmetric heating conditions over wide ranges of parameters. Analytical solutions for the fully developed flows are also presented, and the criteria for the flow reversal to occur are predicted. Solutions for the developing flow obtained in this study agree closely with the elliptic-model solutions, and precisely approach the fully developed solutions downstream.

PREDICTIONS OF DEVELOPING FLOW WITH BUOYANCY-ASSISTED FLOW SEPARATION IN A VERTICAL RECTANGULAR DUCT: PARABOLIC MODEL VERSUS ELLIPTIC MODEL

The relative performance and validity of the parabolic-equation model coupled with a modified FLARE procedure for analyzing three-dimensional buoyancy-assisted flow separation in a vertical duct are verified by the full elliptic Navier ? Stokes model. Numerical solutions for the flow and thermal fields are presented, and a comparison between the two models under various heating conditions and over wide ranges of values of Prandtl number (Pr), aspect ratio of the cross section of the duct (B), and buoyancy parameter (Gr/Re) has been made. Results show that the solutions yielded by the parabolic model agree closely with the elliptic-model solutions within the considered parameter ranges. Computation time required in the full elliptic model is approximately 15,000 CPU seconds on a CRAY XMP EA/116se computer to complete a case, whereas the parabolic-model analysis takes only about 2000 CPU seconds or less.The relative performance and validity of the parabolic-equation model coupled with a modified FLARE procedure for analyzing three-dimensional buoyancy-assisted flow separation in a vertical duct are verified by the full elliptic Navier ? Stokes model. Numerical solutions for the flow and thermal fields are presented, and a comparison between the two models under various heating conditions and over wide ranges of values of Prandtl number (Pr), aspect ratio of the cross section of the duct (B), and buoyancy parameter (Gr/Re) has been made. Results show that the solutions yielded by the parabolic model agree closely with the elliptic-model solutions within the considered parameter ranges. Computation time required in the full elliptic model is approximately 15,000 CPU seconds on a CRAY XMP EA/116se computer to complete a case, whereas the parabolic-model analysis takes only about 2000 CPU seconds or less.

NUMERICAL PREDICTIONS OF MIXED CONVECTION AND FLOW SEPARATION IN A VERTICAL DUCT WITH ARBITRARY CROSS SECTION

Recent studies on an efficient numerical approach for predicting mixed convection heat transfer and buoyancy-induced flow separations in the vertical rectangular ducts have been extended for the duct with complex geometry, testing it in several case studies. In this work, the three-dimensional parabolic model is modified by incorporating the curvilinear-coordinate finite volume method with the parabolic model. The validity of the approach has been demonstrated for several test cases, and the relative performance of the approach is also evaluated by comparing the numerical predictions with the full elliptic model solutions. The approach has been used to seek, in one case, detailed information on heat transfer and reversed flow behavior for the flow within a vertical parabolic duct. Results indicate that the three-dimensional parabolic model can be implemented and applied to predict mixed convective flows in ducts with arbitrary cross-sectional shapes, leading to satisfactory accuracy.

Enhancement of FLARE method for predicting buoyancy-induced flow reversal in vertical ducts via parabolic model

Enhancement of the FLARE method frequently employed in a parabolic-equation model analysis for buoyancy-induced flow reversal within vertical channels is investigated. The present study shows several modifications to the parabolic model and the FLARE method. The relative performance of all these modified parabolic models is evaluated for two-dimensional buayancy- assisted reversed flows. Comparison of the solutions between the parabolic and the full elliptic Navier-Stokes models is also made. Results tend to confirm previously reported findings that analysis based on the parabolic model and the FLARE approximation (B.L.+FLARE) reduces the implementation and computation efforts remarkably yet still retains the accuracy of the numerical solutions. However, when the Richardson number is higher than a treshold number, the traditional B.L. + FLARE procedure leads to an oscillating or even a divergent solution downstream. The numerical instability downstream can be eliminated by introducing a modified numerical algorithm (B.L. + FLAREC method) proposed in this study so as to advance the analysis into the higher Richardson number regime.

Convection and frictional heating in a cone and plate system

Abstract The temperature field resulting from the frictional heating of a fluid confined in the region between a cone and a plate, which are in relative steady rotation, is calculated for prescribed thermal boundary conditions. The convective heat-transfer problem pertaining to the three dimensional velocity field, characteristic of this geometry, is solved as an asymptotic expansion for small Reynolds number and small cone angle. Together with adaptations of previously published results for plane Couette flow of fluids with temperature-dependent transport properties, these solutions provide quantitative measures of the effects of conduction, convection, frictional heating, as well as the temperature sensitivity of the fluid transport properties.