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

2000 ◽  
Vol 37 (6) ◽  
pp. 567-586 ◽  
Author(s):  
Chin-Hsiang Cheng, Chin-Yung Lin, W
Keyword(s):  
Flow Separation ◽  
Parabolic Model ◽  
Rectangular Duct ◽  
Developing Flow ◽  
Elliptic Model ◽  
Model Versus

A Numerical Study of Developing Buoyancy-Assisted Mixed Convection With Spatially Periodic Wall Heating

2017 ◽  
Vol 139 (8) ◽  
Author(s):  
Chris D. Dritselis
Keyword(s):  
Mixed Convection ◽  
Richardson Number ◽  
Numerical Study ◽  
Heat Fluxes ◽  
Computational Time ◽  
Convection Flow ◽  
Parabolic Model ◽  
Flow Modification ◽  
Elliptic Model ◽  
Spatially Periodic

The validity of a parabolic model for simulating the developing buoyancy-assisted mixed convection flow in a vertical channel with spatially periodic wall temperature is verified by a full elliptic model of the momentum and energy equations. A detailed assessment of the effects of the grid resolution, the Richardson number, the Reynolds number, and the preheating zone is presented through extensive comparisons of the velocity and temperature fields and spatial variations of pressure and local heat fluxes at the walls yielded by both models. The parabolic model is capable of reproducing the flow modification into a pattern consisting of a recirculating zone with increasing Richardson number, capturing adequately the main trends of the flow and heat transfer results. For certain combinations of the relevant nondimensional parameters, the solutions of the parabolic model agree reasonably well with those of the elliptic model from a quantitative point of view. In all the cases examined here, the computational time needed by the parabolic model is significantly smaller than that of the elliptic model.

Modeling of on Shore Propagation of Random Water Waves

2011 ◽  
Vol 2011 ◽  
pp. 1-7 ◽  
Author(s):  
K. M. Fassieh ◽  
O. Fahmy ◽  
M. M. El-Shabrawy ◽  
M. A. Zaki
Keyword(s):  
Water Waves ◽  
Wave Breaking ◽  
Small Amplitude ◽  
Wave Reflection ◽  
Numerical Models ◽  
Superposition Principle ◽  
Test Cases ◽  
Parabolic Model ◽  
Depth Variation ◽  
Elliptic Model

Two numerical models are investigated to model random water waves (RWWs) transformation due to mild depth variation. Modelling of steady on-shore propagation of small-amplitude RWWs is based on superposition principle of waves of different heights and directions. Each component is simulated through either the parabolic model (PM) or the elliptic model (EM). PM simulates weak refraction, diffraction, shoaling, and wave breaking. EM simulates strong refraction, diffraction, and shoaling. Both models neglect wave reflection. Comparison between PM and EM, in test cases that are experimentally measured, proved that both models give good results for unidirectional and narrow-directional RWW. However, EM is more accurate in modelling broad-directional RWWs.

Thermal Modeling and Analysis for Grinding Operation

2010 ◽  
Vol 426-427 ◽  
pp. 624-628
Author(s):  
Yan Ding Qin ◽  
Yan Ling Tian ◽  
Da Wei Zhang
Keyword(s):  
Thermal Analysis ◽  
Heat Source ◽  
Peak Temperature ◽  
Parabolic Model ◽  
Element Analysis ◽  
Modeling And Analysis ◽  
Temperature Distributions ◽  
Elliptic Model ◽  
Triangular Model ◽  
Peak Value

This paper focuses on the effects of heat source profiles during thermal analysis of grinding. Three different models of heat source, namely triangular model, parabolic model and elliptic model, have been suggested and their numeric formulas are provided. These models take into account of the variation of heat flux along the contact zone, so as to improve the accuracy of numeric results. Finite Element Analysis (FEA) is utilized to investigate the temperature distributions under different thermal models and the effects of two profile parameters (η and ξ). The result is a) peak temperature decreases as η increases and the location of peak value moves backwards simultaneously; b) peak temperature decreases as ξ increases and the location of peak value moves forwards simultaneously.

Turbulent Heat Transfer in a Symmetrically or Asymmetrically Heated Flat Rectangular Duct With Flow Separation at Inlet

1982 ◽  
Vol 104 (1) ◽  
pp. 82-89 ◽  
Author(s):  
E. M. Sparrow ◽  
N. Cur
Keyword(s):  
Heat Transfer ◽  
Flow Separation ◽  
Entrance Region ◽  
Turbulent Heat Transfer ◽  
Rectangular Duct ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Thermal Entrance Region ◽  
Asymmetric Heating ◽  
Thermal Entrance

Heat transfer experiments were performed for a high-aspect-ratio (∼18) rectangular duct having a sharp-edged inlet, with air being drawn into the inlet from a large upstream space. The experiments encompassed data runs where both of the principal walls of the duct were isothermal (at the same temperature) and other runs where one wall was isothermal while the other was adiabatic. Local heat transfer coefficients were determined for all runs. It was found that flow separation at the duct inlet played a decisive role in shaping the axial distribution of the heat transfer coefficient in the thermal entrance region. Of particular note is a high heat transfer peak at the point of flow reattachment. The peak is situated at an axial station less than one hydraulic diameter from the inlet and moves upstream with increasing Reynolds number. The heat transfer coefficients for symmetric and asymmetric heating are identical in the initial portion of the thermal entrance region. Deviations occur farther downstream but do not exceed more than about 7 percent. The entrance length for asymmetric heating is significantly greater than that for symmetric heating.

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