scholarly journals Sinc Approximation of the Heat Flux on the Boundary of a Two-Dimensional Finite Slab

2006 ◽  
Vol 27 (5-6) ◽  
pp. 685-695 ◽  
Author(s):  
P. H. Quan ◽  
D. D. Trong ◽  
P. N. Dinh Alain
2005 ◽  
Vol 46 (6) ◽  
pp. 881-892 ◽  
Author(s):  
Yu-Ching Yang ◽  
Haw-Long Lee ◽  
Eing-Jer Wei ◽  
Jenn-Fa Lee ◽  
Tser-Son Wu

1992 ◽  
Vol 114 (3) ◽  
pp. 553-557 ◽  
Author(s):  
T. R. Hsu ◽  
N. S. Sun ◽  
G. G. Chen ◽  
Z. L. Gong

This paper presents a finite element algorithm for two-dimensional nonlinear inverse heat conduction analysis. The proposed method is capable of handling both unknown surface heat flux and unknown surface temperature of solids using temperature histories measured at a few discrete point. The proposed algorithms were used in the study of the thermofracture behavior of leaking pipelines with experimental verifications.


2004 ◽  
Vol 61 (21) ◽  
pp. 2528-2543 ◽  
Author(s):  
Glenn M. Auslander ◽  
Peter R. Bannon

Abstract This study examines the diurnal response of a mixed-layer model of the dryline system to localized anomalies of surface heat flux, topography, mixed-layer depth, and inversion strength. The two-dimensional, mixed-layer model is used to simulate the dynamics of a cool, moist layer east of the dryline capped by an inversion under synoptically quiescent conditions. The modeled domain simulates the sloping topography of the U.S. Great Plains. The importance of this study can be related to dryline bulges that are areas with enhanced convergence that may trigger convection in suitable environmental conditions. All anomalies are represented by a Gaussian function in the horizontal whose amplitude, size, and orientation can be altered. A positive, surface-heat-flux anomaly produces increased mixing that creates a bulge toward the east, while a negative anomaly produces a westward bulge. Anomalies in topography show a similar trend in bulge direction with a peak giving an eastward bulge, and a valley giving a westward bulge. Anomalies in the initial mixed-layer depth yield an eastward bulge in the presence of a minimum and a westward bulge for a maximum. An anomaly in the initial inversion strength results in a westward bulge when the inversion is stronger, and an eastward bulge when the inversion is weak. The bulges observed in this study at 1800 LT ranged from 400 to 600 km along the dryline and from 25 to 80 km across the dryline. When the heating ceases at night, the entrainment and eastward movement of the line stops, and the line surges westward. This westward surge at night has little dependence on the type of anomaly applied. Whether a westward or eastward bulge was present at 1800 LT, the surge travels an equal distance toward the west. However, the inclusion of weak nocturnal friction reduces the westward surge by 100 to 200 km due to mechanical mixing of the very shallow leading edge of the surge. All model runs exhibit peaks in the mixed-layer depth along the dryline at 1800 LT caused by enhanced boundary layer convergence and entrainment of elevated mixed-layer air into the mixed layer. These peaks appear along the section of the dryline that is least parallel to the southerly flow. They vary in amplitude from 4 to 9 km depending on the amplitude of the anomaly. However, the surface-heat-flux anomalies generally result in peaks at the higher end of this interval. It is hypothesized that the formation of these peaks may be the trigger for deep convection along the dryline in the late afternoon.


Author(s):  
Thomas B. Gradinger ◽  
T. Laneryd

Natural-convection cooling with oil or other fluids of high Prandtl number plays an important role in many technical applications such as transformers or other electric equipment. For design and optimization, one-dimensional (1D) flow models are of great value. A standard configuration in such models is flow between vertical parallel plates. Accurate modeling of heat transfer, buoyancy, and pressure drop for this configuration is therefore of high importance but gets challenging as the influence of buoyancy rises. For increasing ratio of Grashof to Reynolds number, the accuracy of one-dimensional models based on the locally forced-flow assumption drops. In the present work, buoyancy corrections for use in one-dimensional models are developed and verified. Based on two-dimensional (2D) simulations of buoyant flow using finite-element solver COMSOL Multiphysics, corrections are derived for the local Nusselt number, the local friction coefficient, and a parameter relating velocity-weighted and volumetric mean temperature. The corrections are expressed in terms of the ratio of local Grashof to Reynolds number and a normalized distance from the channel inlet, both readily available in a one-dimensional model. The corrections universally apply to constant wall temperature, constant wall heat flux, and mixed boundary conditions. The developed correlations are tested against two-dimensional simulations for a case of mixed boundary conditions and are found to yield high accuracy in temperature, wall heat flux, and wall shear stress. An application example of a natural-convection loop with two finned heat exchangers shows the influence on mass-flow rate and top-to-bottom temperature difference.


Author(s):  
Patrick H. Oosthuizen ◽  
Jane T. Paul

Two-dimensional natural convective heat transfer from vertical plates has been extensively studied. However, when the width of the plate is relatively small compared to its height, the heat transfer rate can be greater than that predicted by these two-dimensional flow results. Because situations that can be approximately modelled as narrow vertical plates occur in a number of practical situations, there exists a need to be able to predict heat transfer rates from such narrow plates. Attention has here been given to a plate with a uniform surface heat flux. The magnitude of the edge effects will, in general, depend on the boundary conditions existing near the edge of the plate. To examine this effect, two situations have been considered. In one, the heated plate is imbedded in a large plane adiabatic surface, the surfaces of the heated plane and the adiabatic surface being in the same plane while in the second there are plane adiabatic surfaces above and below the heated plate but the edge of the plate is directly exposed to the surrounding fluid. The flow has been assumed to be steady and laminar and it has been assumed that the fluid properties are constant except for the density change with temperature which gives rise to the buoyancy forces, this having been treated by using the Boussinesq approach. It has also been assumed that the flow is symmetrical about the vertical centre-plane of the plate. The solution has been obtained by numerically solving the full three-dimensional form of the governing equations, these equations being written in terms of dimensionless variables. Results have only been obtained for a Prandtl number of 0.7. A wide range of the other governing parameters have been considered for both edge situations and the conditions under which three dimensional flow effects can be neglected have been deduced.


Author(s):  
Kamyar Mansour

We consider the two-dimensional problem of steady natural convection in a narrow (Micro size) Horizontal Cylindrical annulus filled with viscous fluid and periodic volumetric heat flux. The solution is expanded in powers of a single combined similarity parameter, which is the product of the Gap ratio to the power of four, and Rayleigh number and the series extended by means of symbolic calculation up to 16 terms. Analysis of these expansions allows the exact computation for arbitrarily accuracy up to 50000 figures. Although the range of the radius of convergence is almost zero but Pade approximation lead our result to be good even for much higher value of the similarity parameter.


Sign in / Sign up

Export Citation Format

Share Document