scholarly journals The Effect of Internal and External Heating on the Free Convective Flow of a Bingham Fluid in a Vertical Porous Channel

Fluids ◽  
2019 ◽  
Vol 4 (2) ◽  
pp. 95 ◽  
Author(s):  
D. Andrew S. Rees ◽  
Andrew P. Bassom
Keyword(s):  
Convective Flow ◽  
Internal Heat ◽  
Bingham Fluid ◽  
Relative Strength ◽  
Porous Channel ◽  
Free Convective Flow ◽  
Bingham Number ◽  
Different Types ◽  
Yield Surfaces ◽  
Rayleigh Numbers

We study the steady free convective flow of a Bingham fluid in a porous channel where heat is supplied by both differential heating of the sidewalls and by means of a uniform internal heat generation. The detailed temperature profile is governing by an external and an internal Darcy-Rayleigh number. The presence of the Bingham fluid is characterised by means of a body force threshold as given by the Rees-Bingham number. The resulting flow field may then exhibit between two and four yield surfaces depending on the balance of magnitudes of the three nondimensional parameters. Some indication is given of how the locations of the yield surfaces evolve with the relative strength of the Darcy-Rayleigh numbers and the Rees-Bingham number. Finally, parameter space is delimited into those regions within which the different types of flow and stagnation patterns arise.

Laminar convection in uniformly heated vertical pipes

1960 ◽  
Vol 8 (2) ◽  
pp. 227-240 ◽  
Author(s):  
B. R. Morton
Keyword(s):  
Exact Solution ◽  
Rayleigh Number ◽  
Pressure Gradient ◽  
Poiseuille Flow ◽  
Convective Flow ◽  
Vertical Pipe ◽  
Buoyancy Forces ◽  
Different Types ◽  
Laminar Convection ◽  
Rayleigh Numbers

An exact solution is presented in this paper for the problem of laminar convective flow under a pressure gradient along a vertical pipe, the walls of which are heated or cooled uniformly; the solution is based on the assumption that velocity and buoyancy profiles far from the pipe entrance do not change with height, and entry-lengt effects are ignored. Two different types of behaviour are found accordingly as the pressure gradient and buoyancy forces act together or in opposition near the centre of the pipe.When an upflow is heated (or a downflow cooled) the velocity near the walls is increased relatively and that near the axis decreased until, for sufficiently large Rayleigh numbers, definite velocity and thermal boundary layers are formed.In the case of cooled upflow (or heated downflow) there is an increase in the velocity across the whole profile for small Rayleigh numbers. As the Rayleigh number is increased the velocity and buoyancy increase, slowly at first and then rapidly, and the solution ‘runs away’ at a Rayleigh number of about 33. For higher Rayleigh numbers, laminar Poiseuille flow of an increasingly complicated profile is theoretically possible, but is unlikely to be found in practise.

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