Numerical Investigation of Laminar Natural Convection in a Square Cavity With Wavy Wall and Horizontal Fin Attached to the Hot Wall

2018 ◽  
Vol 140 (7) ◽  
Author(s):  
Ahmed Kadari ◽  
Nord-Eddine Sad Chemloul ◽  
Said Mekroussi
Keyword(s):  
Thermal Conductivity ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Average Nusselt Number ◽  
Thermal Conductivity Ratio ◽  
Wavy Wall ◽  
Square Cavity ◽  
Laminar Natural Convection ◽  
Fin Length

Laminar natural convection in differentially heated square cavity with right cold wavy wall and horizontal conducting fin attached to its left hot wall has been investigated numerically. The vertical walls are maintained at different isothermal temperatures, while the horizontal walls are insulated. The fluid that filled the cavity is air with Prandtl number of 0.71. The investigation has been performed for Rayleigh number in the range of 103–106, the thermal conductivity ratio was varied from 10 to 105, three fin lengths and positions have been examined (0.25, 0.5, and 0.75), and three numbers of undulation were tested (one, two, and three undulations). The wave amplitude and the fin thickness were kept constant at 0.05 and 0.04, respectively. The results obtained show that increasing the fin thermal conductivity or the Rayleigh number increases the average Nusselt number especially when the fin length increases. It was also found that the fin position enhances the heat transfer when the fin is placed opposite to the crest of the wavy wall. The trend of the local Nusselt number is wavy. The effect of undulations number appears when the fin length is greater than 0.5. The average Nusselt number enhanced when a conducting fin is added to the cavity with wavy wall and without fin by 51.23% and 56.85% for one and three undulations, respectively, when the Rayleigh number is 105 and the fin length is 0.75.

Numerical Study of Laminar Natural Convection From a Plate to its Cylindrical Enclosure

1991 ◽  
Vol 113 (3) ◽  
pp. 194-199 ◽  
Author(s):  
M. M. Elshamy ◽  
M. N. Ozisik
Keyword(s):  
Nusselt Number ◽  
Steady State ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Average Nusselt Number ◽  
Numerical Study ◽  
Hot Plate ◽  
Cell Pattern ◽  
Laminar Natural Convection

The steady-state laminar natural convection for air bounded by a hot plate and a cold cylindrical enclosure has been studied numerically for the case of cold isothermal cylinder and hot isothermal plate. A correlation is presented for the average Nusselt number over the range of Rayleigh number from 105 to 106 for different values of the width-aspect ratio Sw and thickness aspect-ratio St of the plate. It is found that the average Nusselt number increases with increasing Sw and Rayleigh number. A two-cell pattern is observed for Sw=1.5 and less. The effect of Sw on the average Nusselt number is found to be stronger than that of St.

scholarly journals Numerical Investigation of the Effect of Baffle Inclination Angle on Nanofluid Natural Convection Heat Transfer in A Square Enclosure

2019 ◽  
Vol 12 (2) ◽  
pp. 61-71 ◽  
Author(s):  
Barik AL-Muhjaa ◽  
Khaled Al-Farhany
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Nusselt Number ◽  
Fluid Flow ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Average Nusselt Number ◽  
Solid Wall ◽  
Convection Heat Transfer ◽  
Convection Heat

The characteristics of the conjugate natural convection of (Al2O3-water) nanofluid inside differentially heated enclosure is numerically analyzed using COMSOL Multiphysics (5.3a). The enclosure consists of two vertical walls, the left wall has a thickness and maintain at a uniform hot temperature, while the opposite wall at cold temperature and the horizontal walls are isolated. A high thermal conductivity thin baffle has been added on the insulated bottom wall at a different inclination angles. The effect of the volume fractions of nanoparticles (f), Rayleigh number (Ra), solid wall thermal conductivity ratio (Kr), baffle incline angles (Ø) and the thickness of solid wall (D) on the isothermal lines, fluid flow patterns and the average Nusselt number (Nu)  has been investigated. At low Rayleigh number (Ra=103 to 104) the Isothermal lines are parallel with the vertical wall which is characteristic of conduction heat transfer. on the other hand, when Rayleigh number increase to (Ra=106),  the isotherms lines distribution in the inner fluid become parallel curves with the adiabatic horizontal walls of the enclosure and smooth in this case convection heat transfer becomes dominant. As the Rayleigh number further increases, the average Nusselt number enhance because of buoyancy force become stronger. In addition, the fluid flow within the space is affected by the presence of a fin attached to the lower wall that causes blockage and obstruction of flow near the hot wall, hence the recirculation cores become weak and effect on the buoyant force. The maximum value of the stream function can be noticed in case of nanofluid at (Ø=60), whereas they decrease when (Ø > 60), where the baffle obstruction causing decreases in flow movement. So that the left region temperature increases which cause reduction of the convective heat transfer by the inner fluid temperatures. This is an indication of enhancing of insulation. When the inclination angle increases (Ø >90), the baffle obstruction on flow and fluid resistance becomes smaller and the buoyancy strength increase, as a result, the heat transfer is increasing in this case. As a result of increasing the thermal conductivity from 1 to 10, an increase in the amount of heat transferred through the solid wall to the internal fluid have been noticed. This change can be seen in the isothermal lines, also, there was growth and an increase in the temperature gradient. The increasing of wall thickness from (D=0.1 to 0.4) leads to reduce the intensive heating through the solid wall as well as small heat transferred to the inner fluid. Therefore, it can be noticed that when the wall thickness increases the stream function decrease.

A Numerical Study of Conjugate Heat Transfer by Natural Convection and Surface Radiation in a Square Enclosure With Thick Adiabatic Walls

2013 ◽  
Author(s):  
H. Hadim ◽  
K. Blecker
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Nusselt Number ◽  
Natural Convection ◽  
Average Nusselt Number ◽  
Surface Radiation ◽  
Thick Wall ◽  
Thermal Conductivity Ratio ◽  
Conductivity Ratio ◽  
Square Enclosure

A numerical solution of heat transfer by combined natural convection and surface radiation in a square enclosure with thick adiabatic top and bottom walls and isothermal vertical walls is presented. The present model was used to obtain new results with the addition of thermal conduction at the thick top and bottom walls for a thermal conductivity ratio, K = ksolid/kfluid, that ranges from 0 to 10, emissivity of the adiabatic walls that ranges from 0 to 1, and the Rayleigh Number that ranges from 103 to 106. The model was validated by comparing the results to a benchmark solution and other solutions found in the literature. The results showed that with an increase in thermal conductivity ratio, the flow circulation decreases while the average Nusselt Number increases indicating increased heat transfer across the thick walls and the fluid in the corners. The results indicate that while past studies have shown negligible impact of the emissivity of the adiabatic walls on characteristics of the flow and heat transfer within the cavity, when a wall with moderate heat capacity and conductivity is considered, the resulting flow velocity and temperature distribution within the cavity are found to be significantly influenced by the thick wall emissivity. As the conductivity ratio increases this discrepancy between thin and thick walls becomes greater, there is further need for a more complex and accurate model including the thick walls. The results also showed that an increase in the emissivity of the adiabatic walls results in a slight decrease in the average Nusselt Number.

A Numerical Study of Natural Convection in a Cavity With Two Fins Attached to Its Vertical Walls

2007 ◽  
Author(s):  
G. A. Sheikhzadeh ◽  
M. Pirmohammadi ◽  
M. Ghassemi
Keyword(s):  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Numerical Study ◽  
Convection Heat Transfer ◽  
Square Cavity ◽  
Vertical Walls ◽  
The Mean ◽  
Energy Equations ◽  
Rayleigh Numbers

Numerical study natural convection heat transfer inside a differentially heated square cavity with adiabatic horizontal walls and vertical isothermal walls is investigated. Two perfectly conductive thin fins are attached to the isothermal walls. To solve the governing differential mass, momentum and energy equations a finite volume code based on Pantenkar’s simpler method is developed and utilized. The results are presented in form of streamlines, isotherms as well as Nusselt number for Rayleigh number ranging from 104 up to 107. It is shown that the mean Nusselt number is affected by the position of the fins and length of the fins as well as the Rayleigh number. It is also observed that maximum Nusselt number occurs about the middle of the enclosure where Lf is grater the 0.5. In addition the Nusselt number stays constant and does not varies with width of the cavity (lf) when Lf is equal to 0.5 and Rayleigh number is equal to 104 and 107 as well as when Lf is equal to 0.6 and low Rayleigh numbers.

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 Fin Length and Location on Natural Convection Heat Transfer in a Wavy Cavity

2020 ◽  
Vol 7 (3) ◽  
Author(s):  
M. Fayz-Al-Asad ◽  
M. J. H. Munshi ◽  
M.M.A. Sarker
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Fluid Flow ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Flow Structure ◽  
Model Parameters ◽  
Flow And Heat Transfer ◽  
Wavy Cavity ◽  
Fin Length

The present study aims to analyze the natural convection flow and heat transfer in a wavy cavity with a single horizontal fin attached to its hot wall. Galerkin weighted residual finite element technique has been employed to solve the governing nonlinear dimensionless equations. The effects of model parameters like Rayleigh number, fin length and location on the fluid flow and heat transfer are investigated. The obtained results are exhibited graphically in terms of flow structure, temperature dispersion, velocity field, fin effectiveness, local Nusselt number, and average Nusselt number. It is observed that the different fin length and location have a substantial effect on flow structure and temperature field. Fin effectiveness is also studied and the highest fin effectiveness was found at fin length (L = 0.75). Besides, it is also found that the mean Nusselt number increases significantly with the increase of Rayleigh number and fin length. Wavy cavity becomes more effective on heat transfer behaviors and fluid flow than that of a square cavity.

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.

Laminar Natural Convection Between a Vertical Surface With Uniform Heat Flux and Pseudoplastic and Dilatant Fluids

2014 ◽  
Vol 136 (9) ◽  
Author(s):  
Massimo Capobianchi ◽  
A. Aziz
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Natural Convection ◽  
Shear Rate ◽  
Power Law ◽  
Average Nusselt Number ◽  
Vertical Surface ◽  
Flux Boundary Condition ◽  
Shear Rates ◽  
Laminar Natural Convection

This paper reports the average Nusselt number for steady, laminar natural convection between a vertical surface and otherwise quiescent pseudoplastic and dilatant fluids under a constant and uniform surface heat flux boundary condition. Models for the fluids' apparent viscosity were utilized that are valid in all five regions of the flow curve. The results are thus applicable for whatever shear rates may exist within the flow field and a dimensionless shear rate parameter was identified that quantifies the shear rate region where the given system is operating. The data indicate that the average Nusselt numbers approach the corresponding Newtonian values when the shear rates are predominantly in either the zero or the infinite shear rate Newtonian regions. However, power law values are approached only when both of the following two conditions are met: (1) the shear rates are principally in the power law region and (2) the fluid's limiting zero and infinite shear rate Newtonian viscosities differ sufficiently, by approximately 4 orders of magnitude or more. For all other cases, the average Nusselt number was found to reside between the Newtonian and the power law asymptotes. Results are provided in both graphical and tabular form over a broad range of system parameters.

MHD natural convection flow in cavities filled with square solid blocks

2014 ◽  
Vol 24 (8) ◽  
pp. 1813-1830 ◽  
Author(s):  
Majid Ashouri ◽  
Mohammad Behshad Shafii ◽  
Hossein Rajabi Kokande
Keyword(s):  
Magnetic Field ◽  
Thermal Conductivity ◽  
Nusselt Number ◽  
Natural Convection ◽  
Numerical Code ◽  
Thermal Conductivity Ratio ◽  
Convection Flow ◽  
Conductivity Ratio ◽  
Natural Convection Flow ◽  
Content Type

Purpose – The purpose of this paper is to study the influence of magnetic field on natural convection inside the enclosures partially filled with conducting square solid obstacles. Also, the effect of thermal conductivity ratio between the solid and fluid materials is investigated for different number of solid blocks. Design/methodology/approach – The dimensionless governing equations are transformed into sets of algebraic equations using finite volume method and momentum equations are solved by the SIMPLE algorithm with the hybrid scheme. The validation of the numerical code was conducted by comparing the results of average Nusselt number with previously published works. Findings – The results indicate that both the magnetic field and solid blocks can significantly affect the flow and temperature fields. It is shown that for a given Rayleigh number, variation of Nusselt number might be increasing or decreasing with change in solid-to-fluid thermal conductivity ratio depending on magnetic field strength and number of solid blocks. Originality/value – No work has been reported previously on the effect of magnetic field on natural convection flow in a cavity partially filled with square solid blocks. The numerical analysis of conductivity ratio between the solid and fluid materials under the effect of magnetic field have been carried out for the first time.

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