scholarly journals Natural convection of Bingham fluids in rectangular cross-sectional cylindrical annuli with differentially heated vertical walls

2019 ◽  
Vol 29 (1) ◽  
pp. 43-77 ◽  
Author(s):  
Sahin Yigit ◽  
Nilanjan Chakraborty
Keyword(s):  
Boundary Condition ◽  
Nusselt Number ◽  
Natural Convection ◽  
Yield Stress ◽  
Thermal Transport ◽  
Second Order ◽  
Bingham Fluids ◽  
Cross Sectional ◽  
Content Type ◽  
The Mean

PurposeThis paper aims to numerically analyse natural convection of yield stress fluids in rectangular cross-sectional cylindrical annular enclosures. The laminar steady-state simulations have been conducted for a range of different values of normalised internal radius (ri/L1/8 to 16, whereLis the difference between outer and inner radii); aspect ratio (AR=H/Lfrom 1/8 to 8 whereHis the enclosure height); and nominal Rayleigh number (Rafrom 103to 106) for a single representative value of Prandtl number (Pris 500).Design/methodology/approachThe Bingham model has been used to mimic the yield stress fluid motion, and numerical simulations have been conducted for both constant wall temperature (CWT) and constant wall heat flux (CWHF) boundary conditions for the vertical side walls. The conservation equations of mass, momentum and energy have been solved in a coupled manner using the finite volume method where a second-order central differencing scheme is used for the diffusive terms and a second-order up-wind scheme is used for the convective terms. The well-known semi-implicit method for pressure-linked equations algorithm is used for the coupling of the pressure and velocity.FindingsIt is found that the mean Nusselt number based on the inner peripheryNu¯iincreases (decreases) with an increase inRa(Bn) due to augmented buoyancy (viscous) forces irrespective of the boundary condition. The ratio of convective to diffusive thermal transport increases with increasingri/Lfor both Newtonian (i.e.Bn= 0) and Bingham fluids regardless of the boundary condition. Moreover, the mean Nusselt numberNu¯inormalised by the corresponding Nusselt number due to pure conductive transport (i.e.Nu¯i/(Nu¯i)cond) shows a non-monotonic trend with increasingARin the CWT configuration for a given set of values ofRa,Pr,Lifor both Newtonian (i.e.Bn= 0) and Bingham fluids, whereasNu¯i/(Nu¯i)condincreases monotonically with increasingARin the CWHF configuration. The influences of convective thermal transport strengthen while thermal diffusive transport weakens with increasingAR, and these competing effects are responsible for the non-monotonicNu¯i/(Nu¯i)condvariation withARin the CWT configuration.Originality/valueDetailed scaling analysis is utilised to explain the observed influences ofRa,BN,ri/LandAR, which along with the simulation data has been used to propose correlations forNu¯i.

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.

scholarly journals Natural convection of Casson fluid in a square enclosure

2020 ◽  
Vol 16 (5) ◽  
pp. 1245-1259
Author(s):  
Mohammad Saeid Aghighi ◽  
Christel Metivier ◽  
Hamed Masoumi
Keyword(s):  
Natural Convection ◽  
Yield Stress ◽  
Casson Fluid ◽  
Small Degree ◽  
Content Type ◽  
Square Enclosure ◽  
Casson Model ◽  
Side Walls ◽  
The Mean ◽  
Viscoplastic Models

PurposeThe purpose of this paper is to analyze the natural convection of a yield stress fluid in a square enclosure with differentially heated side walls. In particular, the Casson model is considered which is a commonly used model.Design/methodology/approachThe coupled conservation equations of mass, momentum and energy related to the two-dimensional steady-state natural convection within square enclosures are solved numerically by using the Galerkin's weighted residual finite element method with quadrilateral, eight nodes elements.FindingsResults highlight a small degree of the shear-thinning in the Casson fluids. It is shown that the yield stress has a stabilizing effect since the convection can stop for yield stress fluids while this is not the case for Newtonian fluids. The heat transfer rate, velocity and Yc obtained with the Casson model have the smallest values compared to other viscoplastic models. Results highlight a weak dependence of Yc with the Rayleigh number: Yc∼Ra0.07. A supercritical bifurcation at the transition between the convective and the conductive regimes is found.Originality/valueThe originality of the present study concerns the comprehensive and detailed solutions of the natural convection of Casson fluids in square enclosures with differentially heated side walls. It is shown that there exists a major difference between the cases of Casson and Bingham models, and hence using the Bingham model for analyzing the viscoplastic behavior of the fluids which follow the Casson model (such as blood) may not be accurate. Finally, a correlation is proposed for the mean Nusselt number Nu¯.

scholarly journals Numerical investigation of aspect ratio influences on Rayleigh–Bénard convection of Bingham fluids in vertical cylindrical annuli

2019 ◽  
Vol 29 (1) ◽  
pp. 251-279 ◽  
Author(s):  
Sahin Yigit ◽  
Nilanjan Chakraborty
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Bingham Fluids ◽  
Bingham Model ◽  
Content Type ◽  
Bénard Convection ◽  
Benard Convection ◽  
The Mean ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Purpose This paper aims to conduct numerical simulations to investigate steady-state laminar Rayleigh–Bénard convection of yield stress fluids obeying Bingham model in rectangular cross-sectional cylindrical annular enclosures. In this investigation, axisymmetric simulations have been carried out for nominal Rayleigh number range Ra = 103 to 105, aspect ratio range AR = 0.25 to 4 (i.e. AR = H/L where H is the enclosure height and L is the difference between outer and inner radii) and normalised inner radius range ri/L = 0 to 16 (where ri is internal cylinder radius) for a nominal representative Prandtl number Pr = 500. Both constant wall temperature (CWT) and constant wall heat flux (CWHF) boundary conditions have been considered for differentially heated horizontal walls to analyse the effects of wall boundary condition. Design/methodology/approach The bi-viscosity Bingham model is used to mimic Bingham fluids for Rayleigh–Bénard convection of Bingham fluids in vertical cylindrical annuli. The conservation equations of mass, momentum and energy have been solved in a coupled manner using the finite volume method where a second-order central differencing scheme is used for the diffusive terms and a second-order up-wind scheme is used for the convective terms. The well-known semi-implicit method for pressure-linked equations algorithm is used for the coupling of the pressure and velocity. Findings It is found that the convective transport strengthens (weakens) with an increase in Ra (AR) for both Newtonian (i.e. Bn = 0) and Bingham fluids, regardless of the boundary conditions. Moreover, the strength of convection is stronger in the CWT configuration than that is for CWHF boundary condition due to higher temperature difference between horizontal walls for both Newtonian (i.e. Bn = 0) and Bingham fluids. The mean Nusselt number Nūcy does not show a monotonic increase with increasing Ra for AR = 1 and ri/L = 4 because of the change in flow pattern (i.e. number of convection rolls/cells) in the CWT boundary condition, whereas a monotonic increase of Nūcy with increasing Ra is obtained for the CWHF configuration. In addition, Nūcy increases with increasing ri/L and asymptotically approaches the corresponding value obtained for rectangular enclosures (ri/L → ∞) for both CWT and CWHF boundary conditions for large values of ri/L. It is also found that both the flow pattern and the mean Nusselt number Nūcy are dependent on the initial conditions for Bingham fluid cases, as hysteresis is evident for AR = 1 for both CWT and CWHF boundary conditions. Originality value Finally, the numerical findings have been used to propose a correlation for Nūcy in the range of 0.25 ≤ ri/L ≤ 16, 0.25 ≤ AR ≤ 2 and 5 × 104 ≤ Ra ≤ 105 for the CWHF configuration.

scholarly journals Natural convection of Newtonian fluids between two concentric cylinders of a special cross-sectional form

2020 ◽  
pp. 190-190
Author(s):  
Houssem Laidoudi ◽  
Mustapha Helmaoui ◽  
Mohamed Bouzit ◽  
Abdellah Ghenaim
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Prandtl Number ◽  
Inclination Angle ◽  
Average Nusselt Number ◽  
Outer Cylinder ◽  
Cross Sectional ◽  
The Mean

In this paper, we performed a numerical simulation of natural convection of Newtonian fluids between two cylinders of different cross-sectional form. The inner cylinder is supposed to be hot and the outer cylinder is assumed to be cold. The diameter of inner cylinder to the diameter of outer cylinder defines the radii ratio (RR= 2.5). The governing equations describing the physical behavior of fluid flow and heat transfer are solved using finite volume method. The effects of Prandtl number (Pr = 0.71 to 100), Rayleigh number (Ra = 103 to 105) and inclination angle of inner cylinder (? = 0? to 80?) on streamlines, isotherms and dimensionless velocity are presented and discussed. Also, the mean average Nusselt number of inner cylinder is plotted versus the governing parameters. All present simulations are considered in two-dimensions for steady laminar flow regime. The obtained results showed that the flow between cylinders is more stable for the inclination angle ? = 0?. Increase in Rayleigh number increases the heat transfer rate for all values of inclination angle. Furthermore, the effect of Prandtl number on the mean average Nusselt number becomes negligible when Pr is over the value 7.01. For example at Pr = 0.71 and Ra =105, increase in inclination from 0? to 40?decreases the average Nusselt number by 5.4%. A new correlation is also provided to describe the average Nusselt number as function of Pr and Ra at ? = 0?.

Numerical investigation of steady-state laminar natural convection of power-law fluids in square cross-sectioned cylindrical annular cavity with differentially-heated vertical walls

2016 ◽  
Vol 26 (1) ◽  
pp. 85-107 ◽  
Author(s):  
Sahin Yigit ◽  
Timothy Graham ◽  
Robert J Poole ◽  
Nilanjan Chakraborty
Keyword(s):  
Nusselt Number ◽  
Steady State ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Power Law ◽  
Content Type ◽  
Power Law Fluids ◽  
Power Law Exponent ◽  
Vertical Walls ◽  
The Mean

Purpose – Numerical simulations have been used to analyse steady-state natural convection of non-Newtonian power-law fluids in a square cross-sectioned cylindrical annular cavity for differentially heated vertical walls for a range of different values of nominal Rayleigh number, nominal Prandtl number and power-law exponent (i.e. 103 < Ra < 106, 102 < Pr < 104 and 0.6 < n < 1.8). The paper aims to discuss these issues. Design/methodology/approach – Analysis is carried out using finite-volume based numerical simulations. Findings – Under the assumption of axisymmetry, it has been shown that the mean Nusselt number on the inner periphery Nu i increases with decreasing (increasing) power-law exponent (nominal Rayleigh number) due to strengthening of thermal advection. However, Nu i is observed to be essentially independent of nominal Prandtl number. It has been demonstrated that Nu i decreases with increasing internal cylinder radius normalised by its height r i /L before asymptotically approaching the mean Nusselt number for a two-dimensional square enclosure in the limit r i /L→infinity. By contrast, the mean Nusselt number normalised by the corresponding Nusselt number for pure conductive transport (i.e. Nu i /Nu cond ) increases with increasing r i /L. Originality/value – A correlation for Nu i has been proposed based on scaling arguments, which satisfactorily captures the mean Nusselt number obtained from the steady-state axisymmetric simulations.

Effects of complex boundary conditions on natural convection of a viscoplastic fluid

2019 ◽  
Vol 29 (8) ◽  
pp. 2792-2808 ◽  
Author(s):  
Behnam Rafiei ◽  
Hamed Masoumi ◽  
Mohammad Saeid Aghighi ◽  
Amine Ammar
Keyword(s):  
Heat Transfer ◽  
Finite Element ◽  
Natural Convection ◽  
Boundary Conditions ◽  
Yield Stress ◽  
Heated Wall ◽  
Uniform Heating ◽  
Content Type ◽  
Yield Stress Fluids ◽  
Complex Boundary

Purpose The purpose of this paper is to analyze the effects of complex boundary conditions on natural convection of a yield stress fluid in a square enclosure heated from below (uniformly and non-uniformly) and symmetrically cooled from the sides. Design/methodology/approach The governing equations are solved numerically subject to continuous and discontinuous Dirichlet boundary conditions by Galerkin’s weighted residuals scheme of finite element method and using a non-uniform unstructured triangular grid. Findings Results show that the overall heat transfer from the heated wall decreases in the case of non-uniform heating for both Newtonian and yield stress fluids. It is found that the effect of yield stress on heat transfer is almost similar in both uniform and non-uniform heating cases. The yield stress has a stabilizing effect, reducing the convection intensity in both cases. Above a certain value of yield number Y, heat transfer is only due to conduction. It is found that a transition of different modes of stability may occur as Rayleigh number changes; this fact gives rise to a discontinuity in the variation of critical yield number. Originality/value Besides the new numerical method based on the finite element and using a non-uniform unstructured grid for analyzing natural convection of viscoplastic materials with complex boundary conditions, the originality of the present work concerns the treatment of the yield stress fluids under the influence of complex boundary conditions.

Natural convection in differentially heated enclosures subjected to variable temperature boundaries

2019 ◽  
Vol 29 (11) ◽  
pp. 4130-4141 ◽  
Author(s):  
Abdulmajeed Mohamad ◽  
Mikhail A. Sheremet ◽  
Jan Taler ◽  
Paweł Ocłoń
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Average Nusselt Number ◽  
Uniform Heating ◽  
Content Type ◽  
Left Hand ◽  
Heating And Cooling ◽  
Right Hand ◽  
The Right

Purpose Natural convection in differentially heated enclosures has been extensively investigated due to its importance in many industrial applications and has been used as a benchmark solution for testing numerical schemes. However, most of the published works considered uniform heating and cooling of the vertical boundaries. This paper aims to examine non-uniform heating and cooling of the mentioned boundaries. The mentioned case is very common in many electronic cooling devices, thermal storage systems, energy managements in buildings, material processing, etc. Design/methodology/approach Four cases are considered, the left-hand wall’s temperature linearly decreases along the wall, while the right-hand wall’s temperature is kept at a constant, cold temperature. In the second case, the left-hand wall’s temperature linearly increases along the wall, while the right-hand wall’s temperature is kept a constant, cold temperature. The third case, the left-hand wall’s temperature linearly decreases along the wall, while the right-hand wall’s temperature linearly increases along the wall. In the fourth case, the left-hand and the right-hand walls’ temperatures decrease along the wall, symmetry condition. Hence, four scenarios of natural convection in enclosures were covered. Findings It has been found that the average Nusselt number of the mentioned cases is less than the average Nusselt number of the uniformly heated and cooled enclosure, which reflects the physics of the problem. The work quantifies the deficiency in the rate of the heat transfer. Interestingly one of the mentioned cases showed two counter-rotating horizontal circulations. Such a flow structure can be considered for passively, highly controlled mechanism for species mixing processes application. Originality/value Previous works assumed that the vertical boundary is subjected to a constant temperature or to a sinusoidal varying temperature. The subject of the work is to examine the effect of non-uniformly heating and/or cooling vertical boundaries on the rate of heat transfer and flow structure for natural convection in a square enclosure. The temperature either linearly increases or decreases along the vertical coordinate at the boundary. Four scenarios are explored.

Natural convection flow in a vertical micro-annulus with time-periodic thermal boundary conditions

2018 ◽  
Vol 14 (5) ◽  
pp. 1064-1081
Author(s):  
Basant Kumar Jha ◽  
Michael O. Oni
Keyword(s):  
Nusselt Number ◽  
Natural Convection ◽  
Boundary Conditions ◽  
Skin Friction ◽  
Convection Flow ◽  
Natural Convection Flow ◽  
Content Type ◽  
Thermal Boundary Conditions ◽  
The Impact ◽  
Time Periodic

PurposeThe purpose of this paper is to investigate the impact of time-periodic thermal boundary conditions on natural convection flow in a vertical micro-annulus.Design/methodology/approachAnalytical solution in terms of Bessel’s function and modified Bessel’s function of order 0 and 1 is obtained for velocity, temperature, Nusselt number, skin friction and mass flow rate.FindingsIt is established that the role of Knudsen number and fluid–wall interaction parameter is to decrease fluid temperature, velocity, Nusselt number and skin friction.Research limitations/implicationsNo laboratory practical or experiment was conducted.Practical implicationsCooling device in electronic panels, card and micro-chips is frequently cooled by natural convection.Originality/valueIn view of the amount of works done on natural convection in microchannel, it becomes interesting to investigate the effect that time-periodic heating has on natural convection flow in a vertical micro-annulus. The purpose of this paper is to examine the impact of time-periodic thermal boundary conditions on natural convection flow in a vertical micro-annulus.

Adherence to Mediterranean dietary pattern in female adolescents

2018 ◽  
Vol 48 (5) ◽  
pp. 722-732 ◽  
Author(s):  
Asal Neshatbini Tehrani ◽  
Hossein Farhadnejad ◽  
Amin Salehpour ◽  
Reza Moloodi ◽  
Azita Hekmatdoost ◽  
...  
Keyword(s):  
Dietary Pattern ◽  
Cross Sectional Study ◽  
Basic Knowledge ◽  
Female Adolescents ◽  
Mediterranean Country ◽  
Dietary Intakes ◽  
Cross Sectional ◽  
Content Type ◽  
Mediterranean Dietary Pattern ◽  
The Mean

PurposeTo the best of our knowledge, the studies on determining adherence to the Mediterranean dietary pattern (MDP) in Iran as a non-Mediterranean country are scarce. Thus, the aim of the study is to determine the adherence to the MDP in a sample of female adolescents who are residents of Tehran, Iran.Design/methodology/approachIn this cross-sectional study, 263 female adolescents aged 15-18 years were studied. Information on socio-demographic, lifestyle and anthropometric variables were obtained using a structured questionnaire. Also, dietary intakes were determined using a validated 168-item food frequency questionnaire. Adherence to MDP was characterized using Mediterranean-style dietary pattern score (MSDPS).FindingsTypically, the mean ± SD MSDPS was low in the present study (15.9 ± 5.6). The mean ± SD age and body mass index of the study population was 16.2 ± 0.9 years and 22.2 ± 4.1 kg/m2, respectively. In this study, the maximum MSDPS was 34.3, which was only one-third of maximum possible score (100). Multiple linear regression analyses showed that higher MSDPS scores were positively associated with age (standardizedβ= 0.1;p= 0.006), higher energy intake (standardizedβ= 0.2;p< 0.001) and marginally higher physical activity (standardizedβ= 0.1;p= 0.079).Originality/valueUnderstanding low adherence to MDP in Tehranian female adolescents can provide basic knowledge to launch systematic programmes for gravitation toward MDP.

Household food security through cooperative societies in northern Ethiopia

2015 ◽  
Vol 14 (1) ◽  
pp. 60-72
Author(s):  
Woldegebrial Zeweld ◽  
Guido Van Huylenbroeck ◽  
Jeroen Buysse
Keyword(s):  
Food Security ◽  
Poverty Reduction ◽  
Decision Makers ◽  
Household Food Security ◽  
Northern Ethiopia ◽  
Cross Sectional ◽  
Content Type ◽  
Heckman Model ◽  
Household Food ◽  
The Mean

Purpose – This paper aims to investigate the effect of cooperative societies on household food security in six villages of Northern Ethiopia. Cooperative societies have significant contribution to the food security and poverty reduction. However, limited empirical studies exist in the study areas about the roles of cooperative societies on food security. Design/methodology/approach – Primary cross-sectional data were collected from randomly selected 400 households. The study also gathered secondary data from the cooperative associations and government offices for comparison purposes. The paper applied Heckman two-stage model to capture the effect of cooperative societies on household food security. Findings – The probability of the households to join cooperative societies and also ensure food security depends on various determining factors like institutional factors, demographic variables and rural functions. The paired sample t-test shows that the mean income and expenditure of the cooperative member households were 70 and 40 per cent higher in 2010 and 2011, respectively, than in the baseline. The two-sample independent t-test indicates that the mean income and expenditure of the member households were 47 and 32 per cent higher than the counterpart households. The Heckman model explains that cooperative societies have statistically significant, positive and robust effects on household food security at 1 per cent level. Research limitations/implications – A few variables might suffer from endogeneity problem, although theoretically insignificant and have no sound justification. The study also considers only two indicators of food security (income and expenditure), but the findings of the study would have been good and sound with several and composite food security index. Practical implications – Such impact studies on cooperative societies are limited in the study areas. Thus, this study helps decision-makers, cooperative analysts and other concerned bodies to give priority for cooperative societies so as to curtail the food insecurity problem. It can also make meaningful contributions to bridge the gap in the cooperative literature. Social implications – The present study can improve the understanding of cooperative societies in the country. The finding of this paper can serve as an input for university students, decision-makers and cooperative analysts. The result can also strengthen the economic justification for policy intervention on cooperative societies. Originality/value – Most studies in the areas address the financial performance, historical movement and opportunities and challenges of cooperative societies. This implies that more work is necessary to obtain a clear picture and broad spectrum about cooperative societies, and thus, this study addresses the effect of cooperative societies on household food security.

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