摘要:

When finite-difference methods are used to solve the benchmark problem of natural convection in a square cavity, a very fine grid is required to obtain predictions that are accurate to 1-2%. The derivation of the finite-difference equations requires the introduction of many approximations; this study systematically evaluates these approximations to establish which are mainly responsible for the fine-grid requirement. The poorest approximations are then improved one by one, resulting in a scheme that yields highly accurate predictions using a relatively coarse grid. The method of evaluating the accuracy of the approximations, the improved approximations themselves, and the solution method used all contain novel features. Storage and computing time requirements for a new sparse matrix solver, which was used in the current study to simultaneously solve for stream function and vorticity, are presented.

ISSN:0149-5720    

DOI:10.1080/10407787908913404

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor

摘要:

A simple and rapidly converging method has been developed to study laminar natural convection in enclosures. The method is a combination of the Gauss-Seidel iterative technique and optimum under-relaxation with ω < 1. Three nonlinear elliptic equations for the conservation of mass, momentum, and energy in an enclosure are solved simultaneously in the finite-difference form on a computer. The results are in very good agreement with experimental data. An internal checking procedure, based on the physics of the problem, is strongly recommended. This computational method can probably be applied to other engineering problems involving more than three elliptic equations. The effect of the Prandtl number on the heat transfer across the enclosure is discussed. Correlations are presented for the Nusselt number as a function of the Prandtl number, Rayleigh number, and enclosure height-to-width ratio.

ISSN:0149-5720    

DOI:10.1080/10407787908913405

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor

摘要:

A noniterative method has been developed to solve nonlinear two-point boundary-value problems efficiently and accurately. The original ordinary differential equations are linearized by a parametric differentiation procedure and are then transformed into an initial value problem. Solutions at any value of either an inherent parameter or an artificial parameter can be obtained once first-order, second-order, and remainder terms in a Taylor series expanded with respect to the parameter are computed. To illustrate this new method, mixed-mode convection boundary-layer flows and flames and Troesch's problem are analyzed. Numerical results are presented and discussed. Application of the present method proves most beneficial when (1) solutions of many parametric values are of interest or (1) solutions are highly sensitive to the missing initial conditions.

ISSN:0149-5720    

DOI:10.1080/10407787908913406

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor

摘要:

The problem of laminar free convection in an air-filled rectangular cavity is studied numerically. A numerical method that was Initially designed for low Prandtl number convection is described and then applied to parameter values for which detailed experimental results are available. The comparison between the numerical predictions and the experimental results is very good.

ISSN:0149-5720    

DOI:10.1080/10407787908913407

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor

摘要:

The effects of the temperature dependence of properties on laminar natural convection transport from an isothermal vertical surface in water are calculated. Bounding temperature conditions in the range 0–100°C are considered in the laminar boundary-layer equations. Results are compared with those obtained assuming constant properties. Large effects on flow and transport arise. These predictions are in good agreement with the limited experimental data available. For bounding temperatures greater than 20°C, heat transfer is correctly predicted by a constant-property solution to within 5% when the film temperature is used to evaluate properties. Detailed transport parameters are tabulated and plotted over the whole temperature range.

ISSN:0149-5720    

DOI:10.1080/10407787908913408

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor

摘要:

The combined heat and mass transfer characteristics of natural convection flow along inclined surfaces are studied analytically. The buoyancy forces arise from both temperature and concentration variations in the fluid. In the analysis, the diffusion-thermo and thermo-diffusion effects are neglected, as are the interfacial velocities resulting from mass diffusion. The surfaces are either maintained at a uniform temperature/concentration or subjected to a uniform heat/mass flux. The important parameters of the problem include Prandtl and Schmidt numbers, thermal and concentration Grashof numbers, the relative buoyancy force effect between species and thermal diffusion, and the angle of inclination from the vertical. Numerical results are presented for diffusion of common species into air and water. For both heating/diffusing conditions, the wall shear stress and the local Nusselt number are found to increase and decrease as the buoyancy force from species diffusion assists and opposes, respectively, the thermal buoyancy force. The mass transfer parameter or the local Sherwood number increases as the thermal buoyancy force increases. In addition, the net effect of the combined buoyancy forces on the surface heat and mass transfer diminishes as the angle of inclination from the vertical increases. Finally, a comparison is made between results from the uniform wall temperature/concentration and the uniform surface heat/mass flux.

ISSN:0149-5720    

DOI:10.1080/10407787908913409

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor

摘要:

Effects of convective boundary conditions on the thermal instability of the conduction regime of natural flow in an inclined slender slot having very thin waits are investigated analytically for the type of instabilities occurring as longitudinal rolls, transverse rolls, and traveling waves. The Biot number H has a significant effect on the stability criterion when the instability sets in either as longitudinal rolls or as transverse waves in the form of traveling waves, but it has practically no effect on instability during the formation of stationary transverse rolls. When the transverse waves are dominant, the transition Prandtl number Prt, that is, the Prandtl number at which a changeover occurs from the stationary cells to the traveling waves, varies from a value of Prt= 12.7 when the vertical walls have prescribed temperatures to Prt= 0.95 when the walls have prescribed heat fluxes. The critical internal Grashof number decreases with decreasing Biot number. The transition angle, that is, the angle at which a changeover takes place from the longitudinal rolls to the transverse rolls, changes from δt= 72°(measured from the horizontal) with H →∞ to δt= 82°with H = 0 at both walls, for Pr = 0.72.

ISSN:0149-5720    

DOI:10.1080/10407787908913410

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor

摘要:

A mesh for use with polar coordinates is described that avoids the difficulties and complexities occurring at the origin when a conventional mesh is employed.

ISSN:0149-5720    

DOI:10.1080/10407787908913411

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor