Numerical Solution of the Three-Dimensional Equations of Motion for Laminar Natural Convection

1967 ◽  
Vol 10 (2) ◽  
pp. 314 ◽  
Author(s):  
K. Aziz
Keyword(s):  
Natural Convection ◽  
Numerical Solution ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Laminar Natural Convection

Three-Dimensional Laminar Natural Convection in a Vertical Air Slot With Hexagonal Honeycomb Core

1990 ◽  
Vol 112 (1) ◽  
pp. 130-136 ◽  
Author(s):  
Y. Asako ◽  
H. Nakamura ◽  
M. Faghri
Keyword(s):  
Natural Convection ◽  
Numerical Solutions ◽  
Transfer Problem ◽  
Three Dimensional ◽  
Convection Heat Transfer ◽  
Side Wall ◽  
Temperature Fields ◽  
Honeycomb Core ◽  
Wall Boundary Conditions ◽  
Laminar Natural Convection

Numerical solutions are obtained for a three-dimensional natural convection heat transfer problem in a vertical air slot with a thin hexagonal honeycomb core. The air slot is assumed to be of such dimensions that the velocity and temperature fields repeat themselves in successive enclosures. The numerical methodology is based on an algebraic coordinate transformation technique, which maps the complex cross section onto a rectangle, coupled with a calculation procedure for fully elliptic three-dimensional flows. The calculations are performed for the Rayleigh number in the range of 103 to 105, for a Prandtl number of 0.7, and for five values of the aspect ratio of the honeycomb enclosure. The average Nusselt number results for the case of a thin honeycomb core are compared with the previously obtained results for a thick honeycomb core with conduction and adiabatic side wall boundary conditions.

Laminar Natural Convection in a Discretely Heated Cavity: I—Assessment of Three-Dimensional Effects

1995 ◽  
Vol 117 (4) ◽  
pp. 902-909 ◽  
Author(s):  
T. J. Heindel ◽  
S. Ramadhyani ◽  
F. P. Incropera
Keyword(s):  
Natural Convection ◽  
Vertical Wall ◽  
Three Dimensional ◽  
Companion Paper ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Nusselt Numbers ◽  
Aspect Ratios ◽  
Laminar Natural Convection

Two and three-dimensional calculations have been performed for laminar natural convection induced by a 3 × 3 array of discrete heat sources flush-mounted to one vertical wall of a rectangular cavity whose opposite wall was isothermally cooled. Edge effects predicted by the three-dimensional model yielded local and average Nusselt numbers that exceeded those obtained from the two-dimensional model, as well as average surface temperatures that were smaller than the two-dimensional predictions. For heater aspect ratios Ahtr ≲ 3, average Nusselt numbers increased with decreasing Ahtr. However, for Ahtr ≳ 3, the two and three-dimensional predictions were within 5 percent of each other and results were approximately independent of Ahtr. In a companion paper (Heindel et al., 1995a), predictions are compared with experimental results and heat transfer correlations are developed.

scholarly journals UNIVERSAL SOFTWARE SYSTEM “STADYO” FOR THE NUMERICAL SOLUTION OF LINEAR AND NONLINEAR PROBLEMS OF THE FIELD THEORY, STATICS, STABILITY AND DYNAMICS OF SPATIAL COMBINED SYSTEMS: GENERAL PARAMETERS AND SUPERELEMENTAL FEATURES

2018 ◽  
Vol 14 (3) ◽  
pp. 26-41 ◽  
Author(s):  
Alexander M. Belostotsky ◽  
Alexey L. Potapenko ◽  
Pavel A. Akimov
Keyword(s):  
Field Theory ◽  
Numerical Solution ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Rigid Bodies ◽  
Orthotropic Materials ◽  
Software System ◽  
Natural Oscillations ◽  
Dynamic Synthesis ◽  
Linear And Nonlinear

The distinctive paper presents the general papers of the science-based universal software system “STADYO” intended for the numerical solution of stationary and nonstationary problems of field theory, analy-sis of static, temperature and dynamic stress-strain state (SSS), stability and strength of arbitrary combined me-chanical systems (massive-shell-lamellar-membrane-rod with “rigid” bodies, fluid cavities and internal bonds, isotropic and orthotropic materials) into a flat axis, axisymmetric and three-dimensional linear and nonlinear formulations. The composition of the “STADYO” software system is briefly described; in terms of its theoretical foundations, the main provisions and matrix relationships of the superelement method (which is known to be one of the most effective ways to increase the universality and increase the computational efficiency of finite element algorithms) are presented, as well as methods for dynamic synthesis of substructures and submodelling. The su-perelement algorithm is also extended to solving a system of linear equations at each step of the implicit scheme of direct integration of the equations of motion, and at each iteration in the calculation of natural oscillations; however, an alternative and more efficient approach consists in constructing special superelement algorithms based on the direct condensation of the equations of motion and ideologically close to the method of dynamic synthesis of substructures. The submodelling options, in particular, are important for the refined analysis of the three-dimensional SSS of heavily loaded component parts of the objects under consideration. In general, the presentation of the global design model of the system as a set of substructures is also very convenient for its de-scription and creates the prerequisite for the creation (application) of effective pre- and postprocessor software. The paper also provides information on verification and experience in the use of the “STADYO” software sys-tem, as well as prospects for development. 

Sign in / Sign up

Export Citation Format

Share Document