Combined Forced and Free Convection in the Entrance Region of an Isothermally Heated Horizontal Pipe

1982 ◽  
Vol 104 (1) ◽  
pp. 153-159 ◽  
Author(s):  
Mikio Hishida ◽  
Yasutaka Nagano ◽  
M. S. Montesclaros
Keyword(s):  
Numerical Solutions ◽  
Entrance Region ◽  
Temperature Fields ◽  
Horizontal Pipe ◽  
Uniform Wall Temperature ◽  
Nusselt Numbers ◽  
Developing Flow ◽  
Uniform Wall ◽  
Secondary Velocity ◽  
Laminar Convection

Numerical solutions are given without the aid of a large Prandtl number assumption for combined forced and free laminar convection in the entrance region of a horizontal pipe with uniform wall temperature. The steady-state solutions have been obtained from the asymptotic time solutions of the time-dependent equations of momentum and energy with the Poisson equation for pressure. Results are presented for the developing primary and secondary velocity profiles, developing temperature fields, local wall shear stress, and local and average Nusselt numbers, which reveal how the developing flow and heat transfer in the entrance region are affected by the secondary flow due to buoyancy forces.

Vorticity-Velocity Method for the Graetz Problem and the Effect of Natural Convection in a Horizontal Rectangular Channel With Uniform Wall Heat Flux

1987 ◽  
Vol 109 (3) ◽  
pp. 704-710 ◽  
Author(s):  
F. C. Chou ◽  
G. J. Hwang
Keyword(s):  
Heat Flux ◽  
Prandtl Number ◽  
Numerical Solutions ◽  
Rectangular Channel ◽  
Wall Heat Flux ◽  
Entrance Region ◽  
Grashof Number ◽  
Uniform Wall ◽  
Laminar Convection ◽  
Uniform Wall Heat Flux

Numerical solutions given by a vorticity-velocity method are presented for combined free and forced laminar convection in the thermal entrance region of a horizontal rectangular channel without the assumptions of large Prandtl number and small Grashof number. The channel wall is heated with a uniform wall heat flux. Typical developments of temperature profile, secondary flow, and axial velocity at various axial positions in the entrance region are presented. Local friction factor and Nusselt number variations are shown for Rayleigh numbers Ra = 104, 3×104, 6×104, and 105 with the Prandtl number as a parameter. The solution for the limiting case of large Prandtl number and small Grashof number obtained from the present study confirms the data of existing literature. It is observed that the large Prandtl number assumption is valid for Pr = 10 when Ra ≤ 3×104 but for a larger Prandtl number when the Rayleigh number is higher.

scholarly journals Numerical Investigation of Thermally Developing and Fully Developed Electro-Osmotic Flow in Channels with Rounded Corners

Fluids ◽  
2021 ◽  
Vol 6 (1) ◽  
pp. 22
Author(s):  
Nicola Suzzi ◽  
Marco Lorenzini
Keyword(s):  
Cross Sections ◽  
Joule Heating ◽  
Rectangular Cross Section ◽  
Entry Length ◽  
Osmotic Flow ◽  
Uniform Wall Temperature ◽  
Nusselt Numbers ◽  
Developing Flow ◽  
Uniform Wall ◽  
Electro Osmotic Flow

Electro-osmotic flow, that is, the motion of a polar fluid in microducts induced by an external electric field, is one micro-effect which allows fluid circulation without the use of mechanical pumping. This is of interest in the thermal management of electronic devices, as microchannels with cross sections of almost arbitrary shape can easily be integrated on the chips. It is therefore important to assess how the geometry of the channel influences the heat transfer performance. In this paper, the thermal entry region and the fully developed electro-osmotic flow in a microchannel of rectangular cross section with smoothed corners is investigated for uniform wall temperature. For the fully developed region, correlations for the Poiseuille and Nusselt numbers considering the aspect ratio and nondimensional smoothing radius are given, which can be used for practical design purposes. For thermally developing flow, it is highlighted how smoothing the corners increases the value of the local Nusselt number, with increases up to 18% over sharp corners, but that it also shortens the thermal entry length. It is also found that Joule heating in the fluid may cause a reversal of the heat flux, and that the thermal entry length has a linear dependence on the Reynolds number and the hydraulic diameter and on the logarithm of the nondimensional Joule heating.

High Rayleigh Number Laminar Convection in Low Aspect Ratio Enclosures With Adiabatic Horizontal Walls and Differentially Heated Vertical Walls

1982 ◽  
Vol 104 (1) ◽  
pp. 103-110 ◽  
Author(s):  
J. Tichy ◽  
A. Gadgil
Keyword(s):  
Aspect Ratio ◽  
Flow Regime ◽  
Numerical Solutions ◽  
Temperature Profiles ◽  
Approximate Analysis ◽  
Nusselt Numbers ◽  
Numerical Studies ◽  
Vertical Walls ◽  
Laminar Convection ◽  
Rayleigh Numbers

Laminar flow in shallow horizontal cavities (aspect ratio a < < 1) at high Rayleigh numbers (> 106) is investigated using an approximate analysis based on first principles, and also with numerical solutions to the full equations. A Prandtl number of approximately one is assumed. It is found that the flow regime at such high values of Ra is characterized by boundary layers lining both vertical as well as horizontal walls of the enclosure, and is qualitatively different from the flow regimes at lower Rayleigh numbers. The internal region of the core (near to the horizontal centerline) exhibits linear velocity and temperature profiles. Typical isotherms and streamlines characteristic of this flow regime are presented, based on the numerical solutions. The velocity and temperature profiles predicted from the approximate analysis are found to compare well with those obtained from the numerically obtained solutions. The Nusselt numbers predicted from the analysis are also in good agreement with the numerical solutions, and with the limited experimental data in the literature. The various physical processes in this type of flow are discussed based on the findings of the analytical and numerical studies.

Laminar Heat Transfer in Tubes Under Slip-Flow Conditions

1962 ◽  
Vol 84 (4) ◽  
pp. 363-369 ◽  
Author(s):  
E. M. Sparrow ◽  
S. H. Lin
Keyword(s):  
Heat Transfer ◽  
Wall Temperature ◽  
Slip Flow ◽  
Mean Free Path ◽  
Uniform Wall Temperature ◽  
Nusselt Numbers ◽  
Temperature Jumps ◽  
Uniform Wall ◽  
Moving Fluid ◽  
Uniform Wall Heat Flux

The effects of low-density phenomena on the fully developed heat-transfer characteristics for laminar flow in tubes has been studied analytically. Consideration is given to the slip-flow regime wherein the major rarefaction effects are manifested as velocity and temperature jumps at the tube wall. The analysis is carried out for both uniform wall temperature and uniform wall heat flux. In both cases, the slip-flow Nusselt numbers are lower than those for continuum flow and decrease with increasing mean free path. Extension of the results is made to include the effects of shear work at the wall, temperature jump modifications for a moving fluid, and thermal creep.

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