Natural Convective Heat Transfer in a Divided Vertical Channel: Part II—Experimental Study

1993 ◽  
Vol 115 (2) ◽  
pp. 388-394 ◽  
Author(s):  
D. Naylor ◽  
J. D. Tarasuk
Keyword(s):  
Heat Transfer ◽  
Convection Heat Transfer ◽  
Vertical Channel ◽  
Channel Length ◽  
Nusselt Numbers ◽  
Numerical Predictions ◽  
Interferometric Study ◽  
Laminar Natural Convection ◽  
Nusselt Number Correlation ◽  
Good Agreement

An interferometric study has been conducted on two-dimensional laminar natural convection heat transfer in an isothermal vertical divided channel. Interferograms were obtained for air and a plate-to-channel length ratio of Lp/Lc= 1/3. Data are presented for the dividing plate located at the bottom (Li/Lc = 0) and top of the channel (Li/Lc=2/3). Comparisons of local and average Nusselt numbers are made with the numerical predictions from Part I. Although the experimental average Nusselt numbers are typically about 10 percent lower than the numerical results, the general trends of the data are in good agreement. Average Nusselt number correlation equations are presented.

Investigation of Natural Convection Heat Transfer in Converging Channel Flows Using a Specklegram Technique

1993 ◽  
Vol 115 (1) ◽  
pp. 140-148 ◽  
Author(s):  
K. D. Kihm ◽  
J. H. Kim ◽  
L. S. Fletcher
Keyword(s):  
Heat Transfer ◽  
Convection Heat Transfer ◽  
Vertical Channel ◽  
Channel Length ◽  
Heat Transfer Characteristics ◽  
Grashof Number ◽  
Nusselt Numbers ◽  
Single Plate ◽  
Converging Channel ◽  
Inclination Angles

Natural convection heat transfer characteristics in converging vertical channel flows were studied by nonintrusively measuring the wall temperature gradients using a laser specklegram technique. Local and average heat transfer coefficients were obtained for forty different configurations, including five different inclination angles from the vertical, γ = 0, 15, 30, 45 and 60 deg, with eight different channel exit openings for each inclination angle. Correlations for both local and average Nusselt numbers, based on the channel length L, were determined as functions of Grashof number, where the local Grashof number, based on the channel length L, ranged up to 7.16×106 and the overall Grashof number varied from 3.58×106 (γ = 60 deg) to 7.16×106 (γ = 0), depending upon the inclination angle. As the top opening was decreased, both local and average Nusselt numbers deviated from the single inclined plate theory and significant reductions in heat transfer resulted. The minimum opening ratio, at which the average Nusselt number started decreasing from that for the single plate, was determined as (b/L)min = 0.07, 0.1, 0.3, 0.35, and 0.4 for inclination angles of 0, 15, 30, 45 and 60 deg, respectively. For Ra* larger than 105, average Nusselt numbers, based on the channel opening b, approached the single-plate limit of the vertical channel flow theory, which was modified to incorporate the reduced gravity due to the inclination. When Ra* was smaller than 105, however, neither the single-plate limit nor the fully developed limit properly described the heat transfer characteristics in the converging channel.

Natural Convective Heat Transfer in a Divided Vertical Channel: Part I—Numerical Study

1993 ◽  
Vol 115 (2) ◽  
pp. 377-387 ◽  
Author(s):  
D. Naylor ◽  
J. D. Tarasuk
Keyword(s):  
Heat Transfer ◽  
Numerical Study ◽  
Plate Thickness ◽  
Convection Heat Transfer ◽  
Vertical Channel ◽  
Channel Length ◽  
Navier Stokes ◽  
Nusselt Numbers ◽  
Data Correlations ◽  
Energy Equations

This is a two-part study of two-dimensional laminar natural convection heat transfer in a divided vertical channel. The divided channel consists of an isothermal dividing plate located on the center line of a vertical channel formed by two isothermal walls. The study examines the effect of Rayleigh number, plate-to-channel length ratio, vertical plate position, and plate thickness on the heat transfer rate from the channel walls, the dividing plate, and the channel as a whole. In Part I, solutions to both the full elliptic and parabolic forms of the Navier–Stokes and energy equations are obtained for Prandtl number Pr = 0.7 (air). Positioning the plate at the bottom of the channel was found to give the highest average Nusselt numbers for the plate and channel. Dividing plate average Nusselt numbers as much as two times higher than the isolated plate Nusselt number were predicted numerically. Experimental measurements and data correlations for the divided channel are presented in Part II of this paper.

Laminar Natural Convection From Isothermal Vertical Cylinders: A Revisit to a Classical Subject

2011 ◽  
Author(s):  
Jerod C. Day ◽  
Matthew J. Traum ◽  
Sandra K. S. Boetcher
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Convection Heat Transfer ◽  
Vertical Cylinder ◽  
Vertical Surface ◽  
Nusselt Numbers ◽  
Laminar Natural Convection ◽  
Nusselt Number Correlation ◽  
Vertical Cylinders ◽  
Classical Subject

Laminar natural convection heat transfer from the vertical surface of a cylinder is a classical subject, which has been studied extensively. Furthermore, this subject has generated some recent interest in the literature. In the present investigation, numerical experiments were performed to determine average Nusselt numbers for isothermal vertical cylinders (103 < RaL < 109, 0.5 < L/D <10, and Pr = 0.7) situated on an adiabatic surface in a quiescent ambient environment which will allow for plume growth. Results will be compared with commonly used correlations and a new average Nusselt number correlation will be presented. Furthermore, the limit for which the heat transfer results for a vertical flat plate may be used as an approximation for the heat transfer from a vertical cylinder will be investigated.

Analysis of Heat Transfer and Fluid Flow Through a Spirally Fluted Tube Using a Porous Substrate Approach

1994 ◽  
Vol 116 (3) ◽  
pp. 543-551 ◽  
Author(s):  
Vijayaragham Srinivasan ◽  
Kambiz Vafai ◽  
Richard N. Christensen
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Porous Substrate ◽  
The Finite Element Method ◽  
Nusselt Numbers ◽  
Flow And Heat Transfer ◽  
Numerical Predictions ◽  
Friction Factors ◽  
Flow Through ◽  
Good Agreement

An innovative approach was opted for modeling the flow and heat transfer through spirally fluted tubes. The model divided the flow domain into two regions. The flutes were modeled as a porous substrate with direction-dependent permeabilities. This enabled modeling the swirl component in the fluted tube. The properties of the porous substrate such as its thickness, porosity, and ratio of the direction-dependent permeabilities were obtained from the geometry of the fluted tube. Experimental data on laminar Nusselt numbers and friction factors for different types of fluted tubes representing a broad range of flute geometry were available. Experimental data from a few of the tubes tested were used to propose a relationship between the permeability of the porous substrate and the flute parameters, particularly the flute spacing. The governing equations were discretized using the Finite Element Method. The model was verified and applied to the other tubes in the test matrix. Very good agreement was found between the numerical predictions and the experimental data.

Laminar Natural Convection From Isothermal Vertical Cylinders: Revisting a Classical Subject

2013 ◽  
Vol 135 (2) ◽  
Author(s):  
Jerod C. Day ◽  
Matthew K. Zemler ◽  
Matthew J. Traum ◽  
Sandra K. S. Boetcher
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Convection Heat Transfer ◽  
Vertical Cylinder ◽  
Vertical Surface ◽  
Nusselt Numbers ◽  
Recent Interest ◽  
Laminar Natural Convection ◽  
Vertical Cylinders ◽  
Classical Subject

Although an extensively studied classical subject, laminar natural convection heat transfer from the vertical surface of a cylinder has generated some recent interest in the literature. In this investigation, numerical experiments are performed to determine average Nusselt numbers for isothermal vertical cylinders (102<RaL<109,0.1<L/D<10, and Pr = 0.7) situated on an adiabatic surface in a quiescent ambient environment. Average Nusselt numbers for various cases will be presented and compared with commonly used correlations. Using Nusselt numbers for isothermal tops to approximate Nusselt numbers for heated tops will also be examined. Furthermore, the limit for which the heat transfer results for a vertical flat plate may be used as an approximation for the heat transfer from a vertical cylinder will be investigated.

Laminar Natural Convection Heat Transfer From Vertical 7 × 7 Rod Bundles in Liquid Sodium

2019 ◽  
Vol 5 (2) ◽  
Author(s):  
Koichi Hata ◽  
Katsuya Fukuda ◽  
Tohru Mizuuchi
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Convection Heat Transfer ◽  
Liquid Sodium ◽  
Natural Convection Heat Transfer ◽  
Convection Heat ◽  
Rod Bundles ◽  
Nusselt Numbers ◽  
Rod Bundle ◽  
Laminar Natural Convection

Laminar natural convection heat transfer from vertical 7 × 7 rod bundle in liquid sodium was numerically analyzed to optimize the thermal–hydraulic design for the bundle geometry with equilateral square array (ESA). The unsteady laminar three-dimensional basic equations for natural convection heat transfer caused by a step heat flux were numerically solved until the solution reaches a steady-state. The code of the parabolic hyperbolic or elliptic numerical integration code series (PHOENICS) was used for the calculation considering the temperature dependence of thermophysical properties concerned. The 7 × 7 heated rods for diameter (D = 0.0076 m), length (L = 0.2 m) and L/D (=26.32) were used in this work. The surface heat fluxes for each cylinder, which was uniformly heated along the length, were equally given for a modified Rayleigh number, (Raf,L)ij and (Raf,L)Nx×Ny,S/D, ranging from 3.08 × 104 to 4.28 × 107 (q = 1 × 104∼7 × 106 W/m2) in liquid temperature (TL = 673.15 K). The values of ratio of the diagonal center-line distance between rods for bundle geometry to the rod diameter (S/D) for vertical 7 × 7 rod bundle were ranged from 1.8 to 6 on the bundle geometry with ESA. The spatial distribution of average Nusselt numbers for a vertical single cylinder of a rod bundle, (Nuav)ij, and average Nusselt numbers for a vertical rod bundle, (Nuav,B)Nx×Ny,S/D, were clarified. The average values of Nusselt number, (Nuav)ij and (Nuav,B)Nx×Ny,S/D, for the bundle geometry with various values of S/D were calculated to examine the effect of array size, bundle geometry, S/D, (Raf,L)ij and (Raf,L)Nx×Ny,S/D on heat transfer. The bundle geometry for the higher (Nuav,B)Nx×Ny,S/D value under the condition of S/D = constant was examined. The general correlations for natural convection heat transfer from a vertical Nx×Ny rod bundle with the ESA and equilateral triangle array (ETA), including the effects of array size, (Raf,L)Nx×Ny,S/D and S/D were derived. The correlations for vertical Nx×Ny rod bundles can describe the theoretical values of (Nuav,B)Nx×Ny,S/D for each bundle geometry in the wide analytical range of S/D (=1.8–6) and the modified Rayleigh number ((Raf,L)Nx×Ny,S/D = 3.08 × 104 to 4.28 × 107) within −9.49 to 10.6% differences.

Heat Transfer in a Surfactant Drag-Reducing Solution—A Comparison With Predictions for Laminar Flow

2005 ◽  
Vol 128 (6) ◽  
pp. 557-563 ◽  
Author(s):  
Paul L. Sears ◽  
Libing Yang
Keyword(s):  
Heat Transfer ◽  
Laminar Flow ◽  
Reynolds Numbers ◽  
High Heat ◽  
High Heat Flux ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Nusselt Numbers ◽  
Drag Reducing Additive ◽  
Good Agreement

Heat transfer coefficients were measured for a solution of surfactant drag-reducing additive in the entrance region of a uniformly heated horizontal cylindrical pipe with Reynolds numbers from 25,000 to 140,000 and temperatures from 30to70°C. In the absence of circumferential buoyancy effects, the measured Nusselt numbers were found to be in good agreement with theoretical results for laminar flow. Buoyancy effects, manifested as substantially higher Nusselt numbers, were seen in experiments carried out at high heat flux.

Effects of Free Convection and Axial Conduction on Forced-Convection Heat Transfer Inside a Vertical Channel at Low Peclet Numbers

1984 ◽  
Vol 106 (2) ◽  
pp. 297-303 ◽  
Author(s):  
L. C. Chow ◽  
S. R. Husain ◽  
A. Campo
Keyword(s):  
Heat Transfer ◽  
Free Convection ◽  
Forced Convection ◽  
Convection Heat Transfer ◽  
Vertical Channel ◽  
Reynolds Numbers ◽  
Convection Heat ◽  
Constant Property ◽  
Axial Conduction ◽  
Forced Convection Heat Transfer

A numerical investigation was conducted to study the simultaneous effects of free convection and axial conduction on forced-convection heat transfer inside a vertical channel at low Peclet numbers. Insulated entry and exit lengths were provided in order to assess the effect of upstream and downstream energy penetration due to axial conduction. The fluid enters the channel with a parabolic velocity and uniform temperature profiles. A constant-property (except for the buoyancy term), steady-state case was assumed for the analysis. Results were categorized into two main groups, the first being the case where the channel walls were hotter than the entering fluid (heating), and the second being the reverse of the first (cooling). For each group, heat transfer between the fluid and the walls were given as functions of the Grashof, Peclet, and Reynolds numbers.

Laminar Natural Convection Heat Transfer in a Differentially Heated Square Cavity Due to a Thin Fin on the Hot Wall

2003 ◽  
Vol 125 (4) ◽  
pp. 624-634 ◽  
Author(s):  
Xundan Shi ◽  
J. M. Khodadadi
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Computational Study ◽  
Convection Heat Transfer ◽  
Square Cavity ◽  
Left Wall ◽  
Flow Modification ◽  
Laminar Natural Convection ◽  
Rayleigh Numbers ◽  
Blockage Effect

A finite-volume-based computational study of steady laminar natural convection (using Boussinesq approximation) within a differentially heated square cavity due to the presence of a single thin fin is presented. Attachment of highly conductive thin fins with lengths equal to 20, 35 and 50 percent of the side, positioned at 7 locations on the hot left wall were examined for Ra=104,105,106, and 107 and Pr=0.707 (total of 84 cases). Placing a fin on the hot left wall generally alters the clockwise rotating vortex that is established due to buoyancy-induced convection. Two competing mechanisms that are responsible for flow and thermal modifications are identified. One is due to the blockage effect of the fin, whereas the other is due to extra heating of the fluid that is accommodated by the fin. The degree of flow modification due to blockage is enhanced by increasing the length of the fin. Under certain conditions, smaller vortices are formed between the fin and the top insulated wall. Viewing the minimum value of the stream function field as a measure of the strength of flow modification, it is shown that for high Rayleigh numbers the flow field is enhanced regardless of the fin’s length and position. This suggests that the extra heating mechanism outweighs the blockage effect for high Rayleigh numbers. By introducing a fin, the heat transfer capacity on the anchoring wall is always degraded, however heat transfer on the cold wall without the fin can be promoted for high Rayleigh numbers and with the fins placed closer to the insulated walls. A correlation among the mean Nu, Ra, fin’s length and its position is proposed.

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