Influences of Boundary Conditions on Laminar Natural Convection of Bingham Fluids in Rectangular Enclosures With Differentially Heated Side Walls

2013 ◽  
Vol 35 (9) ◽  
pp. 822-849 ◽  
Author(s):  
Osman Turan ◽  
Robert J. Poole ◽  
Nilanjan Chakraborty
Keyword(s):  
Natural Convection ◽  
Boundary Conditions ◽  
Bingham Fluids ◽  
Side Walls ◽  
Laminar Natural Convection

A Pseudospectral Analysis of Laminar Natural Convection Flow and Heat Transfer Between Two Inclined Parallel Plates

2006 ◽  
Author(s):  
Serkan Kasapoglu ◽  
Ilker Tari
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Boundary Conditions ◽  
Boussinesq Approximation ◽  
Temperature Fields ◽  
Convection Flow ◽  
Parallel Plates ◽  
Natural Convection Flow ◽  
Constant Wall Temperature ◽  
Laminar Natural Convection

Three dimensional laminar natural convection flow of and heat transfer in incompressible air between two inclined parallel plates are analyzed with the Boussinesq approximation by using spectral methods. The plates are assumed to be infinitely long in streamwise (x) and spanwise (z) directions. For these directions, periodic boundary conditions are used and for the normal direction (y), constant wall temperature and no slip boundary conditions are used. Unsteady Navier-Stokes and energy equations are solved using a pseudospectral approach in order to obtain velocity and temperature fields inside the channel. Fourier series are used to expand the variables in × and z directions, while Chebyshev polynomials are used to expand the variables in y direction. By using the temperature distribution between the plates, local and average Nusselt numbers (Nu) are calculated. Nu values are correlated with φ, which is the inclination angle, and with Ra·cosφ to compare the results with the literature.

Laminar Natural Convection of Bingham Fluids in Inclined Differentially Heated Square Enclosures Subjected to Uniform Wall Temperatures

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
Şahin Yİğİt ◽  
Robert J. Poole ◽  
Nilanjan Chakraborty
Keyword(s):  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Yield Stress ◽  
Local Minimum ◽  
Bingham Fluids ◽  
Bingham Number ◽  
Yield Stress Fluids ◽  
Laminar Natural Convection ◽  
The Mean

The effects of inclination 180deg≥φ≥0deg on steady-state laminar natural convection of yield-stress fluids, modeled assuming a Bingham approach, have been numerically analyzed for nominal values of Rayleigh number Ra ranging from 103 to 105 in a square enclosure of infinite span lying horizontally at φ=0deg, then rotated about its axis for φ>0deg cases. It has been found that the mean Nusselt number Nu¯ increases with increasing values of Rayleigh number but Nu¯ values for yield-stress fluids are smaller than that obtained in the case of Newtonian fluids with the same nominal value of Rayleigh number Ra due to the weakening of convective transport. For large values of Bingham number Bn (i.e., nondimensional yield stress), the mean Nusselt number Nu¯ value settles to unity (Nu¯=1.0) as heat transfer takes place principally due to thermal conduction. The mean Nusselt number Nu¯ for both Newtonian and Bingham fluids decreases with increasing φ until reaching a local minimum at an angle φ* before rising with increasing φ until φ=90deg. For φ>90deg the mean Nusselt number Nu¯ decreases with increasing φ before assuming Nu¯=1.0 at φ=180deg for all values of Ra. The Bingham number above which Nu¯ becomes unity (denoted Bnmax) has been found to decrease with increasing φ until a local minimum is obtained at an angle φ* before rising with increasing φ until φ=90deg. However, Bnmax decreases monotonically with increasing φ for 90deg<φ<180deg. A correlation has been proposed in terms of φ, Ra, and Bn, which has been shown to satisfactorily capture Nu¯ obtained from simulation data for the range of Ra and φ considered here.

Sign in / Sign up

Export Citation Format

Share Document