Developing Flow with Combined Forced–Free Convection in an Isothermal Vertical Tube

1972 ◽  
Vol 94 (2) ◽  
pp. 211-221 ◽  
Author(s):  
B. Zeldin ◽  
F. W. Schmidt
Keyword(s):  
Numerical Analysis ◽  
Free Convection ◽  
Velocity Profiles ◽  
Vertical Tube ◽  
Test Fluid ◽  
Nusselt Numbers ◽  
Numerical Predictions ◽  
Test Conditions ◽  
Developing Flow ◽  
Entrance Velocity

The influence of gravity on developing forced, laminar flow in a vertical isothermal tube was investigated by means of a numerical analysis and an associated experiment. Numerically predicted velocity profiles and Nusselt numbers for combined forced–free convection with Gr/Re = −30 are compared with their counterparts for pure forced convection, Gr/Re = 0, for air with Re = 500. The analysis was performed for both the uniform irrotational and the fully developed velocity entrance models. Velocity profiles were measured in a vertical-tube apparatus designed to provide an approximately uniform entrance velocity using air as the test fluid. These are compared with numerical predictions based on test conditions.

Free Convection in Antisymmetrically Heated Vertical Channels

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
D. Roeleveld ◽  
D. Naylor ◽  
W. H. Leong
Keyword(s):  
Temperature Field ◽  
Free Convection ◽  
Vertical Channel ◽  
Laser Interferometry ◽  
Measured Temperature ◽  
Ansys Fluent ◽  
Nusselt Numbers ◽  
Numerical Predictions ◽  
Rayleigh Numbers ◽  
Special Case

Free convection in a vertical channel with antisymmetrical heating is a special case that has not received a great deal of attention in the literature. Antisymmetrical heating is where the hot wall is heated above the ambient temperature by the same amount that the cold wall is cooled below the ambient, giving equal but opposing buoyancy forces inside the channel. An experimental model was constructed to study antisymmetrical heating inside an isothermally heated vertical channel. Flow visualization was used to obtain the flow field and laser interferometry was used to obtain the temperature field. Based on the measured temperature field, the local and average Nusselt numbers were determined, which were compared with numerical predictions obtained using ansys fluent. A range of Rayleigh numbers were studied for air with a Prandtl number of 0.71. The results show that an open-ended channel with antisymmetrical heating has some similarities to a tall enclosure. The average convective heat transfer can be approximated using an existing correlation for a tall enclosure from the literature.

NUMERICAL ANALYSIS OF TEMPERATURE AND VELOCITY PROFILES INSIDE AND OUTSIDE OF A DC THERMAL PLASMA TORCH

2021 ◽  
Author(s):  
Akash Yadav ◽  
Mayank Kumar ◽  
Satyananda Kar ◽  
Sujay Karmakar ◽  
Nitin B Lal
Keyword(s):  
Numerical Analysis ◽  
Thermal Plasma ◽  
Plasma Torch ◽  
Velocity Profiles

The Graetz Problem for the Ellis Fluid Model

2018 ◽  
Vol 74 (1) ◽  
pp. 15-24 ◽  
Author(s):  
N. Ali ◽  
M.W.S. Khan
Keyword(s):  
Energy Equation ◽  
Fluid Model ◽  
Separation Of Variables ◽  
Surface Heat ◽  
Thermal Boundary Conditions ◽  
Nusselt Numbers ◽  
Graetz Problem ◽  
Developing Flow ◽  
Sturm Liouville

AbstractThe determination of temperature and auxiliary quantities such as local and average Nusselt numbers for thermally developing flow is referred as the Graetz problem. In the classical Graetz problem, the fluid entering the tube or channel is Newtonian in nature. Here, an extension of the classical Graetz problem is presented by assuming that the fluid entering the tube or channel obeys the Ellis constitutive equation. The energy equation for the considered problem is solved using the separation of variables technique supplemented with the MATLAB routine bvp4c for computation of the eigenvalues and numerical solution of the associated Sturm-Liouville boundary value problem. The problem is solved for two types of thermal boundary conditions, namely, uniform surface temperature and uniform surface heat flux for both flat and circular geometries. Expressions for bulk mean temperature and local and average Nusselt numbers are presented and discussed through tables and graphs.

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