Laminar Combined Convection in a Horizontal Annulus Subject to Constant Heat Flux Inner Wall and Adiabatic Outer Wall

1986 ◽  
Vol 108 (2) ◽  
pp. 392-397 ◽  
Author(s):  
M. Kaviany
Keyword(s):  
Heat Flux ◽  
Rayleigh Number ◽  
Outer Wall ◽  
Constant Heat Flux ◽  
Lateral Flow ◽  
Temperature Fields ◽  
Constant Heat ◽  
Average Temperature ◽  
Finite Difference Approximations ◽  
Structure Changes

Steady-state, fully developed velocity and temperature fields in mixed convection through a horizontal annulus (ratio of outside to inside radii of 1.25), with a prescribed constant heat flux on the inner cylinder and an adiabatic outside cylinder are analyzed using finite difference approximations. The effects of the buoyancy-driven lateral flow on the temperature of the inner surface are studied in detail. The results show that, as the buoyancy potential (Rayleigh number) increases, the lateral flow structure changes from one cell (on each side) to two cells. The consequence of these flow regimes is that as Rayleigh number increases the temperature of the upper portion of the inner cylinder first increases significantly above its value for pure forced convection and then decreases significantly as the number of cells increases. The average temperature of the inner cylinder decreases monotonically as the Rayleigh number increases.

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.

scholarly journals Double-diffusive instabilities at a horizontal boundary after the sudden onset of heating

2018 ◽  
Vol 859 ◽  
pp. 126-159
Author(s):  
Oliver S. Kerr
Keyword(s):  
Heat Flux ◽  
Rayleigh Number ◽  
Salinity Gradient ◽  
Constant Heat Flux ◽  
Initial Time ◽  
Sudden Increase ◽  
Constant Heat ◽  
Diffusive Convection ◽  
Double Diffusive ◽  
Thermal Rayleigh Number

When a deep body of fluid with a stable salinity gradient is heated from below at a horizontal boundary a destabilizing temperature gradient develops and can lead to instabilities. We will focus on two variants of this problem: the sudden increase in the boundary temperature at the initial time and the sudden turning on of a constant heat flux. These generate time-dependent temperature profiles. We look at the growing phase of the linear instabilities as an initial value problem where the initial time for the instabilities is a parameter to be determined. We determine numerically the optimal initial conditions and the optimal starting time for the instabilities to ensure that the maximum growth occurs at some given later time. The method that is used is an extension of the method developed by Kerr & Gumm (J. Fluid Mech., vol. 825, 2017, pp. 1002–1034) in their investigation of the stability of developing temperature boundary layers at horizontal and vertical boundaries. This requires the use of an appropriate measure of the amplitude of the disturbances which is identified. The effectiveness of this approach is verified by looking at the classic problem of double-diffusive convection in a horizontal layer, where we look at both the salt-finger regime and the diffusive regime. We show that this approach is an effective way of investigating instabilities where the background gradients time dependent. For the problem of heating a salinity gradient from below, as the heat diffuses into the fluid the effective thermal Rayleigh number based on the instantaneous diffusion length scale grows. For the case of a sudden increase in the temperature by a fixed amount the effective thermal Rayleigh number is proportional to $t^{3/2}$, and for a constant heat flux it is proportional to $t^{2}$, where $t$ is the time since the onset of heating. However, the effective salt Rayleigh number also grows as $t^{2}$. We will show that for the constant temperature case the thermal Rayleigh number initially dominates and the instabilities undergo a phase where the convection is essentially thermal, and the onset is essentially instantaneous. As the salt Rayleigh number becomes more significant the instability undergoes a transition to oscillatory double-diffusive convection. For the constant heat flux the ratio of the thermal and salt Rayleigh numbers is constant, and the instabilities are always double diffusive in their nature. These instabilities initially decay. Hence, to achieve the largest growth at some given fixed time, there is an optimal time after the onset of heating for the instabilities to be initiated. These instabilities are essentially double diffusive throughout their growth.

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.

scholarly journals EXPERIMENTAL AND NUMERICAL STUDY OF NATURAL CONVECTION BETWEEN TILTED WALLS WITH ATTACHED FINS

2018 ◽  
Vol 18 (2) ◽  
pp. 253-276
Author(s):  
Kadhum A Jehhef ◽  
Mohamed A Al Abas Siba
Keyword(s):  
Heat Flux ◽  
Rayleigh Number ◽  
Transfer Rate ◽  
Numerical Study ◽  
Constant Heat Flux ◽  
Governing Equations ◽  
Constant Heat ◽  
Ansys Fluent ◽  
The Right ◽  
Volume Method

The free convection between two tilted adiabatic plates with centered heated horizontalcylinder with attached plate fin was investigated experimentally and numerically. Theexperimental rig constructed from vertical adiabatic was filled with air plates with aspectratio of (A= 12) tilted by angles of (15o, 30o, 45o, 60o, 75o, and 90o). A horizontal heatedcylinder with diameter of (16 cm) subjected under constant heat flux of (100, 500, 700, and1000 W/m2), the Rayleigh number ranging from (3.5 ×107 to 4.5 ×109). At the bottom of therig left an opining with distance of (2, 4, 6, and 8 cm) but the upper left open to theatmosphere. The tested cases was of (without fin, smooth, triangular, square, and semi-circlefin) was attached to the right wall of the cavity. The numerical solution of the case wasperformed by solving the governing equations by ANSYS-FLUENT 14.0 package thatdependent upon the finite volume method. The experimental results show that the Nusseltnumber increases with increasing Rayleigh number, decreasing the inclination angle,increasing heat flux and with increasing the bottom opining distance. Basically, the resultsshowed that the using fins with any geometry will lead to increase the heat transfer rate. Theoptimum increasing in the Nusselt number was found by using triangular plat fin. Finally,the experimental data was compared with a numerical calculation and found that there is agood agreement in the same conditions.

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.

Experimental Investigation of Natural Convective Heat Transfer From Horizontal, Inclined and Vertical Cylinder With Constant Heat Flux

2010 ◽  
Author(s):  
A. Gharehghani ◽  
R. Hoseini ◽  
M. M. Salahi
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Rayleigh Number ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Constant Heat Flux ◽  
Experimental Results ◽  
Constant Heat ◽  
Constant Length

In this study, natural convective heat transfer from cylindrical slender rods with different length and diameters and different angles of inclination (from horizontal to vertical) at constant heat flux condition was measured. For each inclination angle, average natural heat transfer coefficient was obtained. The effects of the angle of inclination and that of the diameter and length of cylinders on heat transfer rates were examined. The angles of 0°, 15°, 30°, 45°, 60°, 75° and 90° were studied. Experimental results show that increasing the diameter of the cylinder, with constant length and the Rayleigh number based on length causes the decrease of the Nusselt number. Increasing the length of the cylinders, with constant diameter and Rayleigh number based on diameter causes the decrease of the Nusselt number. Increasing either the angle of inclination or length decreases the effect of diameter on the heat transfer rate. Experimental results in terms of Nusselt number were correlated as a function of modified Rayleigh number and dimensionless parameters containing diameter, length and orientation angle.

Heat Convection Within an Eccentric Annulus Heated at Either Constant Wall Temperature or Constant Heat Flux

2012 ◽  
Vol 134 (8) ◽  
Author(s):  
F. M. Mahfouz
Keyword(s):  
Heat Flux ◽  
Numerical Solution ◽  
Wall Temperature ◽  
Outer Wall ◽  
Constant Heat Flux ◽  
Heat Convection ◽  
Radius Ratio ◽  
Constant Heat ◽  
Constant Wall Temperature ◽  
Eccentric Annulus

Natural heat convection within an annular annulus bounded by two horizontal vertically eccentric long cylinders has been investigated. The annulus inner wall has been heated and maintained at either constant wall temperature CWT or constant heat flux CHF while the outer wall is cooled and maintained at constant temperature. The induced buoyancy driven flow and the associated heat convection are predicted through solving numerically the full conservation equations for mass, momentum, and energy using Fourier spectral method. Beside Rayleigh and Prandtl numbers, the heat convection process in the annulus depends on the annulus radius ratio and eccentricity (normalized by the radius difference). The study considered a moderate range of Rayleigh numbers up to 105 while Prandtl number is fixed at 0.7. The radius ratio is considered up to 3.2 while the eccentricity is varied between − 0.65 and + 0.65. The study has revealed that at certain radius ratio for a given Rayleigh number and eccentricity, the heat transfer is minimum in case of CWT and the mean inner wall temperature is maximum in case of CHF. The study has also shown, in the range considered for controlling parameters, that multiple convection cells only exist in case of CWT and only for positive eccentricity. Moreover, the study has shown that the present numerical solution of the pure conduction problem is almost identical with the newly presented analytical solution which confirms the high accuracy of the numerical solution.

Temperature Measurements of a Transient Thermal Plume in a Confined Space

1997 ◽  
Vol 119 (2) ◽  
pp. 389-391 ◽  
Author(s):  
C.-H. Hsu ◽  
C.-F. Hsieh ◽  
J.-T. Teng
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Rayleigh Number ◽  
Local Nusselt Number ◽  
Constant Heat Flux ◽  
Thermal Plume ◽  
Confined Space ◽  
Fourier Number ◽  
Constant Heat ◽  
Transient Thermal

Experiments are performed by measuring a developing thermal plume in an enclosure, that is generated by a constant heat flux annular cylinder heater, with six T-type thermocouples. An empirical correlation obtained among local Nusselt number, Fourier number, and modified Rayleigh number is Nux/Rax*1/4 = 0.00422FoL−0.893.

Rate of Sublimation of Ice by Radiative Heating in Freeze-Etching

1980 ◽  
Vol 38 ◽  
pp. 618-619
Author(s):  
Yeshayahu Talmon
Keyword(s):  
Heat Flux ◽  
Freeze Fracture ◽  
Constant Heat Flux ◽  
Radiative Heating ◽  
Constant Heat ◽  
Entire Sample ◽  
Simplified Method ◽  
Freeze Etching ◽  
Sublimation Rates ◽  
Fractured Surface

To bring out details in the fractured surface of a frozen sample in the freeze fracture/freeze-etch technique,the sample or part of it is warmed to enhance water sublimation.One way to do this is to raise the temperature of the entire sample to about -100°C to -90°C. In this case sublimation rates can be calculated by using plots such as Fig.1 (Talmon and Thomas),or by simplified formulae such as that given by Menold and Liittge. To achieve higher rates of sublimation without heating the entire sample a radiative heater can be used (Echlin et al.). In the present paper a simplified method for the calculation of the rates of sublimation under a constant heat flux F [W/m2] at the surface of the sample from a heater placed directly above the sample is described.

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