Non-Darcy Natural Convection in a Saturated Horizontal Porous Annulus

1988 ◽  
Vol 110 (1) ◽  
pp. 133-139 ◽  
Author(s):  
K. Muralidhar ◽  
F. A. Kulacki
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Computational Study ◽  
Viscous Friction ◽  
Fluid Phase ◽  
Outer Wall ◽  
Constant Heat Flux ◽  
Darcy Flow ◽  
Constant Heat ◽  
Nusselt Numbers

A computational study of free convective flow and heat transfer in a saturated porous horizontal annulus is reported. Both isothermal and constant heat flux boundary conditions have been considered on the inner walls while the outer wall is held at a constant temperature. The calculation of the flow field involves consideration of non-Darcy effects, such as inertial and viscous forces, and also the variation of porosity near the walls. While the literature shows that Darcy flow model is inadequate in predicting average Nusselt numbers, the present study examines whether non-Darcy effects, and in particular the presence of the boundary, could play a significant role in explaining this discrepancy. Average Nusselt numbers have been obtained for Rayleigh–Darcy numbers from 20 to 4000 for the case of isothermal boundaries, and 20 to 20,000 for the case of constant heat flux on the inner wall. Radius ratio has been varied from 1.1 to 3. Over this range of parameters, inertia and viscous friction in the fluid phase have been found to produce a small effect on the Darcy flow. The effect of including variable porosity near a boundary is seen to produce channeling near the wall which in turn substantially increases the heat transfer coefficient.

Effects of Nanoparticle Migration on Water/Alumina Nanofluid Flow Inside a Horizontal Annulus with a Moving Core

2014 ◽  
Vol 31 (3) ◽  
pp. 291-305 ◽  
Author(s):  
A. Malvandi ◽  
D. D. Ganji
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Boundary Conditions ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Outer Wall ◽  
Constant Heat Flux ◽  
Constant Heat ◽  
Thermal Boundary Conditions ◽  
Alumina Nanofluid

AbstractThe present study is a theoretical investigation of the laminar flow and convective heat transfer of water/alumina nanofluid inside a horizontal annulus with a streamwise moving inner cylinder. A modified, two-component, four-equation, nonhomogeneous equilibrium model is employed for the alumina/water nanofluid, which fully accounts for the effect of the nanoparticle volume fraction distribution. To determine the effects of thermal boundary conditions on the migration of the nanoparticles, two cases are considered: constant heat flux at the outer wall with an adiabatic inner wall (Case A) and constant heat flux at the inner wall with an adiabatic outer wall (Case B). The numerical results indicate that the thermal boundary conditions at the pipe walls significantly affect the nanoparticle distribution, particularly in cases where the ratio of Brownian motion to thermophoretic diffusivities is small. Moreover, increasing the velocity of the moving inner cylinder reduces the heat transfer rate for Case A. Conversely, in Case B, the movement of the inner cylinder enhances the heat transfer rate, and anomalous heat transfer enhancement occurs when the thermophoretic force is dominant (in larger nanoparticles).

Heat Transfer Characteristics of Gaseous Slip Flow in Concentric Micro Annular Tubes

2009 ◽  
Author(s):  
Chungpyo Hong ◽  
Yutaka Asako ◽  
Koichi Suzuki
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Incompressible Flow ◽  
Slip Flow ◽  
Outer Wall ◽  
Constant Heat Flux ◽  
Heat Transfer Characteristics ◽  
Constant Heat ◽  
Transfer Characteristics ◽  
Adiabatic Case

A concentric micro annular passage is a basic and important micro-geometry of micro-fluidic-systems from simple heat exchanger to the most complicated nuclear reactors. Therefore, heat transfer characteristics of gaseous flows in concentric micro annular tubes with constant heat flux whose value was positive or negative were numerically investigated. The slip velocity, temperature jump and shear stress work were considered on the slip boundary. The numerical methodology was based on the Arbitrary-Lagrangian-Eulerian (ALE) method. The computations were performed for two thermal cases. This is, the heat flux was constant at the inner wall and outer wall was adiabatic (Case 1) and the heat flux was constant at the outer wall and the inner wall was adiabatic (Case 2). Each constant heat flux of 104 Wm−2 for the positive value and −104 Wm−2 for the negative value was chosen. The outer tube radius ranged from 20 to 150 μm with the radius ratio 0.02, 0.05, 0.1, 0.25 and 0.5 and the ratio of length to hydraulic diameter was 100. The stagnation pressure was chosen in such a way that the exit Mach number ranges from 0.1 to 0.7. The outlet pressure was fixed at the atmospheric pressure. The heat transfer characteristics in concentric micro annular tubes were obtained. The wall and bulk temperatures with positive heat flux are compared with those of negative heat flux cases and also compared with those of the simultaneously developing incompressible flow. The results show that the compressible slip flow Nusselt number is different from that of incompressible flow. And, the temperatures normalized by heat flux have different trends whether heat flux value is positive or negative. A correlation for the prediction of the heat transfer characteristics of gas slip flow in concentric micro annular tubes is proposed.

Natural Convection in a Rectangular Porous Cavity With Constant Heat Flux on One Vertical Wall

1984 ◽  
Vol 106 (1) ◽  
pp. 152-157 ◽  
Author(s):  
V. Prasad ◽  
F. A. Kulacki
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Numerical Solutions ◽  
Vertical Wall ◽  
Local Heat ◽  
Constant Heat Flux ◽  
Heated Wall ◽  
Width Ratio ◽  
Constant Heat ◽  
Nusselt Numbers

Numerical solutions for two-dimensional, steady, free convection are presented for a rectangular cavity with constant heat flux on one vertical wall, the other vertical wall being isothermally cooled. The horizontal walls are insulated. Results are presented in terms of streamlines and isotherms, local and average Nusselt numbers at the heated wall, and the local heat flux at the cooled wall. Flow patterns are observed to be quite different from those in the case of a cavity with both vertical walls at constant temperatures. Specifically, symmetry in the flow field is absent and any increase in applied heat flux is not accompanied by linearly proportional increase in the temperature on the heated wall. Also, for low Prandtl number, the heat transfer rate based upon the mean temperature difference is higher as compared to experimental results for the isothermal case. Heat transfer results, further, indicate that the average Nusselt number is correlated by a relation of the form Nu = constant Ra*mAn, where Ra* is the Rayleigh number and A the height-to-width ratio of the cavity.

Heat Transfer Characteristics of Gaseous Slip Flow in Concentric Micro-Annular Tubes

2011 ◽  
Vol 133 (7) ◽  
Author(s):  
Chungpyo Hong ◽  
Yutaka Asako ◽  
Koichi Suzuki
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Incompressible Flow ◽  
Slip Flow ◽  
Outer Wall ◽  
Constant Heat Flux ◽  
Heat Transfer Characteristics ◽  
Constant Heat ◽  
Transfer Characteristics ◽  
Adiabatic Case

A concentric micro-annular passage is a basic and important microgeometry of microfluidic-systems from simple heat exchanger to the most complicated nuclear reactors. Therefore, heat transfer characteristics of gaseous flows in concentric micro-annular tubes with constant heat flux whose value was positive or negative were numerically investigated. The slip velocity, temperature jump, and shear stress work were considered on the slip boundary conditions. The numerical methodology was based on the arbitrary-Lagrangian–Eulerian method. The computations were performed for two thermal cases. That is, the heat flux that was constant at the inner wall and outer wall was adiabatic (case 1) and the heat flux that was constant at the outer wall and the inner wall was adiabatic (case 2). Each constant heat flux of 104 Wm−2 for the positive value and −104 Wm−2 for the negative value was chosen. The outer tube radius ranged from 20 μm to 150 μm with the radius ratios of 0.02, 0.05, 0.1, 0.25, and 0.5 and the ratio of length to hydraulic diameter was 100. The stagnation pressure was chosen in such a way that the exit Mach number ranges from 0.1 to 0.8. The outlet pressure was fixed at the atmospheric pressure. The heat transfer characteristics in concentric micro-annular tubes were obtained. The wall and bulk temperatures with positive heat flux are compared with those of negative heat flux cases and also compared with those of the simultaneously developing incompressible flow. The results show that the Nusselt number of compressible slip flow is different from that of incompressible flow. However, the temperatures normalized by heat flux have different trends whether heat flux value is positive or negative. A correlation for the prediction of the heat transfer characteristics of gas slip flow in concentric micro annular tubes is proposed.

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