摘要:

In numerical calculations of fluid flows and heat transfer it is often necessary to solve a system of algebraic equations with a nine-diagonal coefficient matrix. Two examples are the diffusion and pressure-correction equations when discretized on nonorthogonal grids. A method of solving such systems of equations, based on the strongly implicit procedure of Stone [1] for five-diagonal matrices, is presented. It operates on the upper and lower triangular matrices with only seven nonzero diagonals, thus requiring less storage and computing time per iteration than the alternative extensions of the strongly implicit procedure to nine-diagonal coefficient matrices. It is also more efficient than the alternative methods—for the land of equations studied—when the missing diagonals in the upper and lower triangular matrices correspond to points lying in “sharp” corners of a computational molecule. Results of various test calculations and comparisons of performance with alternative solvers are presented to support this view. The proposed solver can also be applied to five-diagonal matrix problems, in which case it reduces to the strongly implicit procedure of Stone [1].

ISSN:0149-5720    

DOI:10.1080/10407788708913554

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

The use of robust general-purpose user-oriented software packages for solving systems of two-point boundary-value problems for ordinary differential equations (BVODEs) is considered for the solution of BVODEs that commonly arise in the modeling of problems in heat transfer. This investigation involves three packages, DVCPR, COLSYS, and DTPTB, which implement the trapezoidal rule with deferred corrections, the method of spline collocation at Gaussian points, and multiple shooting, respectively. The effectiveness of the packages is demonstrated by examining their performance on a variety of BVODEs that have appeared in the literature. In several cases the packages produce results quite different from published results, and since the packages are consistently in agreement with each other, questions must be raised about the validity of the latter. The packages are also used to treat B VODEs that were impossible to solve using techniques presented in the literature. The software packages DVCPR, COLSYS, and DTPTB are widely available and are powerful alternatives to the ad hoc computer programs so often used in the engineering literature for solving BVODEs

ISSN:0149-5720    

DOI:10.1080/10407788708913555

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

Inertia effects on buoyancy-driven flow and heat transfer in a vertical porous cavity are examined by using the Forchheimer-extended Darcy equation of motion for flow through porous media. A dimensional analysis indicates that in the inertial flow regime a new dimensionless parameter, the Forchheimer number Fs, which characterizes the porous matrix structure and its confinement, must be considered together with the Rayleigh and Prandtl numbers, Ra*and Pr*. Finite-difference numerical results obtained for a wide range of parameters indicate that the effect of Prandtl number and aspect ratio remains unchanged with an enhancement in the inertia effects, whereas the dependence on Grashof and Forchheimer numbers changes substantially. Indeed, for a Nusselt number correlation Nu = CGr*pPr*qFs−rA−s, q and s remain the same as those obtained for Darcy flow, but p and r change in such a way that p + r is always equal to the value of p in the Darcy regime. The criteria for the Darcy and inertial flow limits are also obtained, and it is shown that the boundary-layer flow structure does not exist when Fs/Pr*→ ∞. Hence, the applicability of a boundary-layer solution in the inertial flow regime is highly restricted.

ISSN:0149-5720    

DOI:10.1080/10407788708913556

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

The interaction of conduction and radiation is investigated under both transient and steady-state conditions for an absorbing, emitting, and isotropically scattering two-layer slab having opaque coverings at both boundaries. The slab is subjected to an externally applied constant heat flux at one boundary surface and dissipates heat by radiation into external ambients from both boundary surfaces. An analytic approach is applied to solve the radiation part of the problem, and a finite-difference scheme is used to solve the conduction part. The effects of the conduction-to-radiation parameter, the single scattering albedo, the optical thickness, and the surface emissivity on the temperature distribution are examined.

ISSN:0149-5720    

DOI:10.1080/10407788708913557

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

Many important engineering problems Jail into the category of linear operators, with supporting boundary conditions. In this paper a new inner product and norm are developed that enable the numerical modeler to approximate such engineering problems by developing a generalized Fourier series. The resulting approximation is the “best” approximation in that a least-squares (L2) error is minimized simultaneously for fitting both the problem's boundary conditions and satisfying the linear operator relationship (the governing equations) over the problem's domain (both space and time). For slow-moving interface phase change problems where the heat flux balance can be adequately described by the Laplace equation, the generalized Fourier series technique results in a highly accurate solution.

ISSN:0149-5720    

DOI:10.1080/10407788708913558

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

A finite-difference method for heat conduction with phase change proposed by Hsiao [7] is shown to be equivalent to that of Comini et al. [9]. The method is extended to cover the case of gradual phase change and compared to several others. A small but consistent error is found in the method. The fastest method is a Crank-Nicolson version of Pham's method [5]. The explicit enthalpy method, though slower, is suitable for casual users.

ISSN:0149-5720    

DOI:10.1080/10407788708913559

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor