Natural Convection of Viscoplastic Fluids in a Square Enclosure

2013 ◽  
Vol 135 (12) ◽  
Author(s):  
M. A. Hassan ◽  
Manabendra Pathak ◽  
Mohd. Kaleem Khan
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Yield Stress ◽  
Average Nusselt Number ◽  
Critical Value ◽  
Square Enclosure ◽  
Bingham Number ◽  
Viscoplastic Fluids

Viscoplastic fluids are special kind of non-Newtonian materials which deform or flow only when applied stresses are more than a critical value known as yield stress. In this work, a numerical investigation of natural convection in a square enclosure filled with viscoplastic fluids has been reported. The enclosure has been partially heated from the bottom wall by a heating source and symmetrically cooled from both the side walls. The rheology of the viscoplastic fluids has been modeled with Bingham fluid model. A scaling analysis has been presented to establish the gross dependence of heat transfer on different values of operating parameters of the problem. The effects of yield stress of the fluid on heat and fluid transport inside the enclosure have been investigated for different values of temperature difference, across the hot and cold surfaces and also for different fluids. The effects of different lengths of heated zone on the flow phenomena and heat transfer characteristics have been investigated for three different values of the heated zones. All the important results have been expressed in terms of Bingham number (Bn), Rayleigh number (Ra), and Prandtl number (Pr). It has been observed that with the increase in Bingham number, the buoyancy induced fluid circulation and convection effect decreases inside the enclosure. For each Rayleigh number, there correspond a critical Bingham number for which the heat transfer inside the enclosure takes place solely by conduction mode. This critical value increases with the increase in Rayleigh number. For fixed value of Bingham number, i.e., fixed value of yield stress, the effects of Rayleigh number and heated length on heat transfer have been observed similar to the case of natural convection in Newtonian fluid. It has been also observed that at high Bingham number the effect of increase in Rayleigh number on average Nusselt number is lesser compared to the effect of increasing Rayleigh number at low Bingham number. Using the present numerical results, a correlation of average Nusselt number as a function of other nondimensional numbers has been established.

Combined Effects of Fluid Yield Stress and Geometrical Arrangement on Natural Convection in a Square Duct From Two Differentially Heated Horizontal Cylinders

2019 ◽  
Vol 12 (1) ◽  
Author(s):  
Lubhani Mishra ◽  
R. P. Chhabra
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Average Nusselt Number ◽  
Square Duct ◽  
Bingham Plastic ◽  
Square Enclosure ◽  
Bingham Number ◽  
Heated Cylinder

Abstract Laminar natural convection in Bingham plastic fluids has been investigated from two differentially heated cylinders arranged either one above the other or along the diagonal of the square enclosure. The coupled momentum and energy equations have been solved to elucidate the effect of Rayleigh number (104–106), Prandtl number (10–100), Bingham number (0.01 to Bnmax), and the gap between the two cylinders in terms of the geometric parameters (0 to −0.25 for vertical alignment and 0.15 to 0.35 for diagonal alignment) on the detailed structure of the flow field and the overall heat transfer characteristics of the system. New extensive results are visualized in terms of streamlines, isotherm contours, and variation of the local Nusselt number along various surfaces. Additional insights are developed by examining the shear-rate contours and the yield surfaces delineating the fluid-like and solid-like regions in the flow domain. At high values of the Bingham number, the average Nusselt number reaches its asymptotic value corresponding to the conduction limit. The increasing Rayleigh number promotes fluid-like behavior which promotes heat transfer. The augmentation in heat transfer depends on the volume of fluid participating in the buoyancy-induced flow. For the vertical arrangement, the average Nusselt number (for the heated cylinder) decreases a little as these are moved slightly away from the center of the enclosure, followed by an increase as the two cylinders approach one of the sidewalls; this is so even in the conduction limit. In contrast, when the two cylinders are arranged along the diagonal, the Nusselt number progressively decreases as the gap between the two cylinders increases. Finally, predictive correlations have been developed for the average Nusselt number and the limiting Bingham number thereby enabling their estimation in a new application.

Influence of Partition Length on Natural Convection in Partially Divided Square Enclosure

2007 ◽  
Vol 129 (11) ◽  
pp. 1592-1599 ◽  
Author(s):  
C. D. Sankhavara ◽  
H. J. Shukla
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Average Nusselt Number ◽  
Square Enclosure ◽  
Thermal Boundary Conditions ◽  
Different Temperatures ◽  
Vertical Walls ◽  
Good Agreement

Numerical investigation is carried out for natural convection in square enclosures consisting of partitions protruding from the end walls with different thermal boundary conditions at the end walls and partitions. The vertical walls were maintained isothermal at different temperatures. The Rayleigh number varies from 104 to 106 and the Prandtl number is 0.71. The thickness of the partition is fixed and is equal to one-tenth of the width of the enclosure. Their nondimensional length (l∕H) varies from 0 (a nonpartitioned enclosure) to 0.5 (two separate enclosures). A good agreement was found between the results in the present study and those published previously. The partitions were found to significantly influence the convective heat transfer. The average Nusselt number is less in the presence of partitions, and it decreases with increasing partition length (l∕H) from 0 to 0.5.

scholarly journals Natural convection in a differentially heated enclosure with triangular roof

1970 ◽  
Vol 39 (1) ◽  
pp. 1-7 ◽  
Author(s):  
Sumon Saha ◽  
Noman Hasan ◽  
Chowdhury Md Feroz
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Fluid Flow ◽  
Natural Convection ◽  
Average Nusselt Number ◽  
Numerical Study ◽  
Convection Heat Transfer ◽  
Element Analysis ◽  
Left Wall ◽  
Square Enclosure

A numerical study has been carried out for laminar natural convection heat transfer within a two-dimensional modified square enclosure having a triangular roof. The vertical sidewalls are differentially heated considering a constant flux heat source strip is flush mounted with the left wall. The opposite wall is considered isothermal having a temperature of the surrounding fluid. The rest of the walls are adiabatic. Air is considered as the fluid inside the enclosure. The solution has been carried out on the basis of finite element analysis by a non-linear parametric solver to examine the heat transfer and fluid flow characteristics. Different heights of the triangular roof have been considered for the present analysis. Fluid flow fields and isotherm patterns and the average Nusselt number are presented for the Rayleigh numbers ranging from 103 to 106 in order to show the effects of these governing parameters. The average Nusselt number computed for the case of isoflux heating is also compared with the case of isothermal heating as available in the literature. The outcome of the present investigation shows that the convective phenomenon is greatly influenced by the inclined roof height. Keywords: Natural convection, triangular roof, Rayleigh number, isoflux heating. Doi:10.3329/jme.v39i1.1826 Journal of Mechanical Engineering, vol. ME39, No. 1, June 2008 1-7

scholarly journals Prediction of Natural Convection Heat Transfer Phenomena of Nanofluids in Corrugated Annulus

2020 ◽  
Author(s):  
Sattar Aljobair ◽  
Akeel Abdullah Mohammed ◽  
Israa Alesbe
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Average Nusselt Number ◽  
Volume Fraction ◽  
Outer Cylinder ◽  
Convection Heat Transfer ◽  
Natural Convection Heat Transfer ◽  
Convection Heat

Abstract The natural convection heat transfer and fluid flow characteristic of water based Al2O3 nano-fluids in a symmetrical and unsymmetrical corrugated annulus enclosure has been studied numerically using CFD. The inner cylinder is heated isothermally while the outer cylinder is kept constant cold temperature. The study includes eight models of corrugated annulus enclosure with constant aspect ratio of 1.5. The governing equations of fluid motion and heat transfer are solved using stream-vorticity formulation in curvilinear coordinates. The range of solid volume fractions of nanoparticles extends from PHI=0 to 0.25, and Rayleigh number varies from 104 to 107. Streamlines, isotherms, local and average Nusselt number of inner and outer cylinder has been investigated in this study. Sixty-four correlations have been deduced for the average Nusselt number for the inner and outer cylinders as a function of Rayleigh number have been deduced for eight models and five values of volume fraction of nano particles with an accuracy range 6-12 %. The results show that, the average heat transfer rate increases significantly as particle volume fraction and Rayleigh number increase. Also, increase the number of undulations in unsymmetrical annuli reduces the heat transfer rates which remain higher than that in symmetrical annuli. There is no remarkable change in isotherms contour with increase of volume fraction of nanofluid.

scholarly journals Effect of Various Tilted Positions of a Thin Fin on Natural Convection of Laminar Viscous Flow in a Square Cavity

2021 ◽  
Vol 39 (5) ◽  
pp. 1634-1642
Author(s):  
Syed Fazuruddin ◽  
Seelam Sreekanth ◽  
G Sankara Sekhar Raju
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Fluid Flow ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Finite Difference ◽  
Average Nusselt Number ◽  
Vertical Position ◽  
Inclination Angles ◽  
Rayleigh Numbers

An exhaustive numerical investigation is carried out to analyze the role of an isothermal heated thin fin on fluid flow and temperature distribution visualization in an enclosure. Natural convection within square enclosures finds remarkable pragmatic applications. In the present study, a finite difference approach is performed on two-dimensional laminar flow inside an enclosure with cold side walls and adiabatic horizontal walls. The fluid flow equations are reconstructed into vorticity - stream function formulation and these equations are employed utilizing the finite-difference strategy with incremental time steps. The parametric study includes a wide scope of Rayleigh number, Ra, and inclination angle ϴ of the thin fin. The effect of different Rayleigh numbers ranging Ra = 104-106 with Pr=0.71 for all the inclination angles from 0°-360° with uniform rotational length of angle 450 of an inclined heated fin on fluid flow and heat transfer have been investigated. The heat transfer rate within the enclosure is measured by means of local and average Nusselt numbers. Regardless of inclination angles of the thin fin, a slight enhancement in the average Nusselt number is observed when Rayleigh number increased for both the cases of the horizontal and vertical position of the thin fin. When the fin has inclined no change in average Nusselt number is noticed for distinct Rayleigh numbers.

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.

Natural Convection in Yield Stress Fluids From a Confined Horizontal Plate

2019 ◽  
Author(s):  
S. A. Patel ◽  
A. H. Raja ◽  
R. P. Chhabra
Keyword(s):  
Heat Transfer ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Yield Stress ◽  
Boussinesq Approximation ◽  
Critical Value ◽  
Heated Plate ◽  
Bingham Number ◽  
Wide Range ◽  
Energy Equations

Abstract The heat transfer characteristics from an isothermal heated plate in a quiescent yield stress fluid in a cavity was investigated over a wide range of parameters (Rayleigh number, 102 ≤ Ra ≤ 105, Prandtl number, 10 ≤ Pr ≤ 100, and Bingham number, Bn ≥ 0) where the flow is known to be laminar and steady. The coupled momentum and energy equations have solved here numerically within the framework of Boussinesq approximation to capture the temperature-dependent fluid density. The results demonstrate that for a given value of the Rayleigh number, there exists a critical value of the Bingham number, above which the fluid is completely unyielded and heat transfer occurs solely by conduction. In order to delineate the effect of domain geometry on the conduction limit, the study was extended over a range of geometrical aspects by varying the aspect ratio (λ = diameter of the cavity/ a length of the plate), 2 ≤ λ ≤ 5. This work shows that the critical value of the Bingham number can be described as a function of geometry of domain, Ra and Pr. The value of critical Bingham number increases with the increasing aspect ratio and Rayleigh number in order to approach the conduction limit. The yield surfaces show that the increasing values of Rayleigh number induce fluid-like behaviour whereas Bingham number opposes this propensity. The average Nusselt number decreases with the increasing Bingham number due to the suppression of the advective component of heat transfer.

A Study on Natural Convection in a Cold Square Enclosure With Two Vertical Eccentric Square Heat Sources Using the IB–LBM Scheme

2019 ◽  
Vol 11 (5) ◽  
Author(s):  
S. M. Dash ◽  
S. Sahoo
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Heat Source ◽  
Lattice Boltzmann Model ◽  
Immersed Boundary ◽  
Heat Sources ◽  
Square Enclosure ◽  
Thermal Lattice Boltzmann

In this article, the natural convection process in a two-dimensional cold square enclosure is numerically investigated in the presence of two inline square heat sources. Two different heat source boundary conditions are analyzed, namely, case 1 (when one heat source is hot) and case 2 (when two heat sources are hot), using the in-house developed flexible forcing immersed boundary–thermal lattice Boltzmann model. The isotherms, streamlines, local, and surface-averaged Nusselt number distributions are analyzed at ten different vertical eccentric locations of the heat sources for Rayleigh number between 103 and 106. Distinct flow regimes including primary, secondary, tertiary, quaternary, and Rayleigh–Benard cells are observed when the mode of heat transfer is changed from conduction to convection and heat sources eccentricity is varied. For Rayleigh number up to 104, the heat transfer from the enclosure is symmetric for the upward and downward eccentricity of the heat sources. At Rayleigh number greater than 104, the heat transfer from the enclosure is better for downward eccentricity cases that attain a maximum when the heat sources are near the bottom enclosure wall. Moreover, the heat transfer rate from the enclosure in case 2 is nearly twice that of case 1 at all Rayleigh numbers and eccentric locations. The correlations for heat transfer are developed by relating Nusselt number, Rayleigh number, and eccentricity of the heat sources.

Natural Convection in a Nano-Fluid Filled Square Enclosure

2020 ◽  
Vol 847 ◽  
pp. 114-119
Author(s):  
Barbie Leena Barhoi ◽  
Ramesh Chandra Borah ◽  
Sandeep Singh
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Volume Fraction ◽  
Control Volume ◽  
Convection Heat Transfer ◽  
Ansys Fluent ◽  
Square Enclosure ◽  
Nano Fluid

The present study relates to numerical investigation of natural convection heat transfer in a nanofluid filled square enclosure. One side of the enclosure is maintained at high temperature and the other side at a low temperature; while the top and bottom sides are adiabatic. The commercial CFD software ANSYS-FLUENT© was used to solve this numerical problem with the governing differential equations discretized by a control volume approach. nanofluids of Cu-water, Al2O3-water and TiO2-water have been simulated for a range of Rayleigh numbers and volume fractions. The results were obtained in the form of streamlines and isotherms. Interpretations of the results are done based on heat transfer rates, volume fraction, Rayleigh number and Nusselt number. It is to be noted that addition of nanoparticles enhances the heat transfer rate. It is also observed that the Nusselt number is highly affected by volume fraction and Rayleigh number.

scholarly journals Numerical Investigation of Laminar Natural Convection in Inclined Square Enclosure with the Influence of Discrete Heat Source

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Chithra Devaraj ◽  
Eswaramurthi Muthuswamy ◽  
Sundararaj Kandasamy
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Heat Source ◽  
Average Nusselt Number ◽  
Convection Heat Transfer ◽  
Correlation Coefficients ◽  
Computational Procedure ◽  
Square Enclosure ◽  
Rayleigh Numbers

Natural convection heat transfer in a two-dimensional square enclosure at various angles of inclination is investigated numerically using a finite volume based computational procedure. The heat transfer is from a constant temperature heat source of finite length centred at one of the walls to the cold wall on the opposite side while the remaining walls are insulated. The effect of area ratio of the heat sourceAfrom 0.2 to 1.0, Rayleigh number Ra from 103to 107, and angle of inclination of the enclosureθvarying from 0° to 360° on the flow field and heat transfer characteristics are investigated. Streamline and isothermal line patterns are found to be similar at low Rayleigh numbers whereas at high Rayleigh numbers the differences are significant due to the influence of the parameters considered. Average Nusselt number decreases drastically as the position of the heat source is moved above the horizontal centre line of the enclosure. Correlation of the average Nusselt number which depends on the parameters of interest is obtained in the general formCRamAn. The correlation coefficients are determined by multiple regression analysis for the entire range of Rayleigh numbers analysed and the values found by correlation equations are in good agreement with the numerical results.

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