Free convection in a square porous cavity filled with a nanofluid using thermal non equilibrium and Buongiorno models

2016 ◽  
Vol 26 (3/4) ◽  
pp. 671-693 ◽  
Author(s):  
Ioan Pop ◽  
Mohammad Ghalambaz ◽  
Mikhail Sheremet
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Brownian Motion ◽  
Base Fluid ◽  
Average Nusselt Number ◽  
Solid Phase ◽  
Porous Matrix ◽  
Governing Equations ◽  
Content Type ◽  
Brownian Motion And Thermophoresis

Purpose – The purpose of this paper is to theoretically analysis the steady-state natural convection flow and heat transfer of nanofluids in a square enclosure filled with a porous medium saturated with a nanofluid considering local thermal non-equilibrium (LTNE) effects. Different local temperatures for the solid phase of the nanoparticles, the solid phase of porous matrix and the liquid phase of the base fluid are taken into account. Design/methodology/approach – The Buongiorno’s model, incorporating the Brownian motion and thermophoresis effects, is utilized to take into account the migration of nanoparticles. Using appropriate non-dimensional variables, the governing equations are transformed into the non-dimensional form, and the finite element method is utilized to solve the governing equations. Findings – The results show that the increase of buoyancy ratio parameter (Nr) decreases the magnitude of average Nusselt number. The increase of the nanoparticles-fluid interface heat transfer parameter (Nhp) increases the average Nusselt number for nanoparticles and decreases the average Nusselt number for the base fluid. The nanofluid and porous matrix with large values of modified thermal capacity ratios (γ p and γ s ) are of interest for heat transfer applications. Originality/value – The three phases of nanoparticles, base fluid and the porous matrix are in the LTNE. The effect of mass transfer of nanoparticles due to the Brownian motion and thermophoresis effects are also taken into account.

Free convection in a tilted triangle porous cavity filled with Cu-water nanofluid with flush mounted heater on the wall

2013 ◽  
Vol 24 (1) ◽  
pp. 2-20 ◽  
Author(s):  
Qiang Sun ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Fluid Flow ◽  
Rayleigh Number ◽  
Free Convection ◽  
Average Nusselt Number ◽  
Governing Equations ◽  
Content Type ◽  
Tilted Angle ◽  
Industrial Sectors

Purpose – Steady-state free convection heat transfer and fluid flow of Cu-water nanofluid is investigated within a porous tilted right-angle triangular enclosure. The paper aims to discuss these issues. Design/methodology/approach – The flush mounted heater with finite size is placed on one right-angle wall. The temperature of the inclined wall is lower than the heater, and the rest of walls are adiabatic. The governing equations are obtained based on the Darcy's law, and the nanofluid model adopted is that by Tiwari and Das. The transformed dimensionless governing equations were solved numerically by finite difference method, and the solution for algebraic equations was obtained through successive under relaxation method. Findings – Investigations were made as the tilted angle of the cavity varies within under different values of Rayleigh number for a porous medium with and solid volume fraction parameter of Cu-water nanofluid with. It is found that the maximum value of the average Nusselt number is achieved with the highest Rayleigh number when the tilted angle of the cavity is 150°, while the minimum value of the average Nusselt number is obtained with the lowest Rayleigh number when the tilted angle of the cavity locates at 240°. As soon as the flow convection in the cavity is not significant, increasing can improve the value of, but opposite effects appear when flow convection becomes stronger. Originality/value – The present results are new and original for the heat transfer and fluid flow in a porous tilted triangle enclosure filled by Cu-water nanofluid. The results would benefit scientists and engineers to become familiar with the flow behaviour of such nanofluids, and the way to predict the properties of this flow for possibility of using nanofluids in advanced nuclear systems, in industrial sectors including transportation, power generation, chemical sectors, ventilation, air-conditioning, etc.

Effectiveness in incorporating Brownian and thermophoresis effects in modelling convective flow of water-Al2O3 nanoparticles

2018 ◽  
Vol 28 (1) ◽  
pp. 47-63 ◽  
Author(s):  
M. Ziad Saghir ◽  
Abdulmajeed Mohamed
Keyword(s):  
Heat Transfer ◽  
Mass Transfer ◽  
Brownian Motion ◽  
Transfer Equation ◽  
Base Fluid ◽  
Heat Removal ◽  
Al2o3 Nanoparticles ◽  
Content Type ◽  
Thermophoresis Effect ◽  
Brownian Motion And Thermophoresis

Purpose Nanofluids are widely used in heat transfer phenomena owing to the higher rate of heat removal as compared to their base fluids. Nanoparticle’s motion in nanofluids is analysed by slip mechanisms that consider physical properties, which can be found in literature. It is assumed that among few, only Brownian motion and thermophoresis affect the slip mechanism to produce a relative velocity between the nanoparticles and the base fluid. The purpose of this paper is to study the effects of Brownian motion and thermophoresis in a square cavity by considering it pure fluid as well as porous cavity. Design/methodology/approach A finite element method is used to solve the flow porous equations together with the heat transfer equation and the mass transfer equation numerically. The heat and mass transfer equations were modified to take into consideration the Brownian motion as well as the thermophoresis effect. Findings A negligible amount of Brownian motion and thermophoresis effect has been found by considering 1 to 3 Vol.% of aluminium oxide as nanoparticles suspended in base fluid of water. Practical implications This study has provided an interesting insight into the importance of Brownian motion as well as the thermophoresis effect in heat enhancement. Originality/value The present study is believed to be an interesting and original contribution on nanofluid thermal behaviours.

Investigating the effect of nanoparticles diameter on turbulent flow and heat transfer properties of non-Newtonian carboxymethyl cellulose/CuO fluid in a microtube

2019 ◽  
Vol 29 (5) ◽  
pp. 1699-1723 ◽  
Author(s):  
Ali Rahimi Gheynani ◽  
Omid Ali Akbari ◽  
Majid Zarringhalam ◽  
Gholamreza Ahmadi Sheikh Shabani ◽  
Abdulwahab A. Alnaqi ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Average Nusselt Number ◽  
Electronic Devices ◽  
Convection Heat Transfer ◽  
Reynolds Numbers ◽  
Vlsi Circuits ◽  
Convection Heat Transfer Coefficient ◽  
Content Type ◽  
Competing Interests

Purpose Although many studies have been conducted on the nanofluid flow in microtubes, this paper, for the first time, aims to investigate the effects of nanoparticle diameter and concentration on the velocity and temperature fields of turbulent non-Newtonian Carboxymethylcellulose (CMC)/copper oxide (CuO) nanofluid in a three-dimensional microtube. Modeling has been done using low- and high-Reynolds turbulent models. CMC/CuO was modeled using power law non-Newtonian model. The authors obtained interesting results, which can be helpful for engineers and researchers that work on cooling of electronic devices such as LED, VLSI circuits and MEMS, as well as similar devices. Design/methodology/approach Present numerical simulation was performed with finite volume method. For obtaining higher accuracy in the numerical solving procedure, second-order upwind discretization and SIMPLEC algorithm were used. For all Reynolds numbers and volume fractions, a maximum residual of 10−6 is considered for saving computer memory usage and the time for the numerical solving procedure. Findings In constant Reynolds number and by decreasing the diameter of nanoparticles, the convection heat transfer coefficient increases. In Reynolds numbers of 2,500, 4,500 and 6,000, using nanoparticles with the diameter of 25 nm compared with 50 nm causes 0.34 per cent enhancement of convection heat transfer coefficient and Nusselt number. Also, in Reynolds number of 2,500, by increasing the concentration of nanoparticles with the diameter of 25 nm from 0.5 to 1 per cent, the average Nusselt number increases by almost 0.1 per cent. Similarly, In Reynolds numbers of 4,500 and 6,000, the average Nusselt number increases by 1.8 per cent. Research limitations/implications The numerical simulation was carried out for three nanoparticle diameters of 25, 50 and 100 nm with three Reynolds numbers of 2,500, 4,500 and 6,000. Constant heat flux is on the channel, and the inlet fluid becomes heated and exists from it. Practical implications The authors obtained interesting results, which can be helpful for engineers and researchers that work on cooling of electronic devices such as LED, VLSI circuits and MEMS, as well as similar devices. Originality/value This manuscript is an original work, has not been published and is not under consideration for publication elsewhere. About the competing interests, the authors declare that they have no competing interests.

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.

Heat Transfer in Cavities Having a Fixed Amount of Solid Material

2005 ◽  
Author(s):  
Edimilson J. Braga ◽  
Marcelo J. S. de Lemos
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Continuum Model ◽  
Average Nusselt Number ◽  
Numerical Solutions ◽  
Solid Phase ◽  
Transfer Problem ◽  
Void Space ◽  
Fixed Amount ◽  
The Continuum

This work compares two different approaches for obtaining numerical solutions for laminar natural convection within a square cavity, which is filled by a fixed amount of a solid conducting material. The first model considered, namely, porous-continuum model, is based on the assumption that the solid and the fluid phases are seen as the same medium, over which volume-averaged transport equations apply. Secondly, a continuum model is considered to solve the momentum equations for the fluid phase that would resemble a conjugate heat transfer problem in both the solid and the void space. In the continuum model, the solid phase is composed of square obstacles, equally spaced within the cavity. In both models, governing equations are numerically solved using the finite volume method. The average Nusselt number at the hot wall, obtained from the porous-continuum model, for several Darcy numbers, are compared with those obtained with the second approach, namely the continuum model, with different number of obstacles. When comparing the two methodologies, this study shows that the average Nusselt number calculated for each approach for the same Ram differs between each other and that this discrepancy increases as the Darcy number decreases, in the porous-continuum model, or the number of blocks increases and their size decreases, in the continuum model. A correlation is suggested to modify the macroscopic thermal expansion coefficient in order to match the average Nusselt numbers calculated by the two models for Ram = const = 104 and Da ranging from 1.2060×10−4 to 1.

Unsteady convective heat and mass transfer of a nanofluid in Howarth’s stagnation point by Buongiorno’s model

2015 ◽  
Vol 25 (5) ◽  
pp. 1176-1197 ◽  
Author(s):  
Saeed Dinarvand ◽  
Reza Hosseini ◽  
Ioan Pop
Keyword(s):  
Mass Transfer ◽  
Nusselt Number ◽  
Brownian Motion ◽  
Heat And Mass Transfer ◽  
Stagnation Point ◽  
Three Dimensional ◽  
Stagnation Point Flow ◽  
Content Type ◽  
Buongiorno’S Model ◽  
Brownian Motion And Thermophoresis

Purpose – The purpose of this paper is to do a comprehensive study on the unsteady general three-dimensional stagnation-point flow and heat transfer of a nanofluid by Buongiorno’s model. Design/methodology/approach – In this study, the convective transport equations include the effects of Brownian motion and thermophoresis. By introducing new similarity transformations for velocity, temperature and nanoparticle volume fraction, the basic equations governing the flow, heat and mass transfer are reduced into highly non-linear ordinary differential equations. The resulting non-linear system has been solved both analytically and numerically. Findings – The analysis shows that velocity, temperature and nanoparticle concentration profiles in the respective boundary layers depend on five parameters, namely unsteadiness parameter A, Brownian motion parameter Nb, thermophoresis parameter Nt, Prandtl number Pr and Lewis number Le. It is found that the thermal boundary layer thickens with a rise in both of the Brownian motion and the thermophoresis effects. Therefore, similar to the earlier reported results, the Nusselt number decreases as the Brownian motion and thermophoresis effects become stronger. A correlation for the Nusselt number has been developed based on a regression analysis of the data. This correlation predicts the numerical results with a maximum error of 9 percent for a usual domain of the physical parameters. Originality/value – The stagnation point flow toward a wavy cylinder (with nodal and saddle stagnation points) that a little attention has been given to it up to now. The examination of unsteadiness effect on the general three-dimensional stagnation-point flow. The application of an interesting and global model (Boungiorno’s model) for the nanofluid that incorporates the effects of Brownian motion and thermophoresis. The study of the effects of Brownian motion and thermophoresis on the nanofluid flow, heat and mass transfer characteristics. The prediction of correlation for the Nusselt number based on a regression analysis of the data. General speaking, we can tell the problem with this geometry, characteristics, the applied model, and comprehensive results, was Not studied and analyzed in literature up to now.

Natural convection of nanofluids in a cavity: criteria for enhancement of nanofluids

2017 ◽  
Vol 27 (7) ◽  
pp. 1504-1534 ◽  
Author(s):  
M. Sabour ◽  
Mohammad Ghalambaz ◽  
Ali Chamkha
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Dynamic Viscosity ◽  
Base Fluid ◽  
Convection Heat Transfer ◽  
Governing Equations ◽  
Content Type ◽  
Separation Line ◽  
Working Temperature ◽  
Dimensional Parameters

Purpose The purpose of this study is to theoretically analyze the laminar free convection heat transfer of nanofluids in a square cavity. The sidewalls of the cavity are subject to temperature difference, whereas the bottom and top are insulated. Based on the available experimental results in the literature, two new non-dimensional parameters, namely, the thermal conductivity parameter (Nc) and dynamic viscosity parameter (Nv) are introduced. These parameters indicate the augmentation of the thermal conductivity and dynamic viscosity of the nanofluid by dispersing nanoparticles. Design/methodology/approach The governing equations are transformed into non-dimensional form using the thermo-physical properties of the base fluid. The obtained governing equations are solved numerically using the finite element method. The results are reported for the general non-dimensional form of the problem as well as case studies in the form of isotherms, streamlines and the graphs of the average Nusselt number. Using the concept of Nc and Nv, some criteria for convective enhancement of nanofluids are proposed. As practical cases, the effect of the size of nanoparticles, the shape of nanoparticles, the type of nanoparticles, the type of base fluids and working temperature on the enhancement of heat transfer are analyzed. Findings The results show that the increase of the magnitude of the Rayleigh number increases of the efficiency of using nanofluids. The type of nanoparticles and the type of the base fluid significantly affects the enhancement of using nanofluids. Some practical cases are found, in which utilizing nanoparticles in the base fluid results in deterioration of the heat transfer. The working temperature of the nanofluid is very crucial issue. The increase of the working temperature of the nanofluid decreases the convective heat transfer, which limits the capability of nanofluids in decreasing the size of the thermal systems. Originality/value In the present study, a separation line based on two non-dimensional parameters (i.e. Nc and Nv) are introduced. The separation line demonstrates a boundary between augmentation and deterioration of heat transfer by using nanoparticles. Indeed, by utilizing the separation lines, the convective enhancement of using nanofluid with a specified Nc and Nv can be simply estimated.

scholarly journals Mixed convection heat transfer from a heated circular cylinder

2019 ◽  
Vol 54 (1) ◽  
pp. 83-88
Author(s):  
H Laidoudi ◽  
M Bouzit
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Drag Coefficient ◽  
Average Nusselt Number ◽  
Convection Heat Transfer ◽  
Circular Cylinders ◽  
Governing Equations ◽  
Thermal Buoyancy ◽  
Flow And Heat Transfer ◽  
Mixed Convection Heat Transfer

This paper performs the effects of thermal buoyancy and the triangular arrangement of circular cylinders on fluid flow and heat transfer within a horizontal channel, the governing equations involving continuity; momentum and energy are solved in two-dimensional, laminar and steady flow regime. The average Nusselt number and drag coefficient are computed for the range of these conditions: Ri = 0 to 2 at fixed value of Pr = 1, Reynolds number Re = 30 and geometrical configurations (blockage ratio of β = 0.1). In order to observe the flow structure and temperature field under the gradual effect of thermal buoyancy, the streamlines and isotherm contours are illustrated. It is found that, a gradual increase in the value of buoyancy strength creates an asymmetrical flow around the cylinders. Interesting variations of drag coefficient and average Nusselt number are plotted with respect to Richardson number for each cylinder. Bangladesh J. Sci. Ind. Res.54(1), 83-88, 2019

scholarly journals Evaluation of Multiple Semi-Twisted Tape Inserts in a Heat Exchanger Pipe Using Al2O3 Nanofluid

Nanomaterials ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 1570
Author(s):  
Yongfeng Ju ◽  
Tiezhu Zhu ◽  
Ramin Mashayekhi ◽  
Hayder I. Mohammed ◽  
Afrasyab Khan ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Heat Exchanger ◽  
Friction Factor ◽  
Base Fluid ◽  
Average Nusselt Number ◽  
Three Dimensions ◽  
Twisted Tape ◽  
Twisted Tapes

The hydrothermal performance of multiple semi-twisted tape inserts inside a heat exchanger pipe is numerically examined in three-dimensions. This study aims to find the optimum case for having the highest heat transfer enhancement with the lowest friction factor using nanofluid (Al2O3/water). A performance evaluation criterion (PEC) is defined to characterize the performance based on both friction factor and heat transfer. It was found that increasing the number of semi-twisted tapes increases the number of swirl flow streams and leads to an enhancement in the local Nusselt number as well as the friction factor. The average Nusselt number increases from 15.13 to 28.42 and the average friction factor enhances from 0.022 to 0.052 by increasing the number of the semi-twisted tapes from 0 to 4 for the Reynolds number of 1000 for the base fluid. By using four semi-twisted tapes, the average Nusselt number increases from 12.5 to 28.5, while the friction factor reduces from 0.155 to 0.052 when the Reynolds number increases from 250 to 1000 for the base fluid. For the Reynolds number of 1000, the increase in nanofluid concentration from 0 to 3% improves the average Nusselt number and friction factor by 6.41% and 2.29%, respectively. The highest PEC is equal to 1.66 and belongs to the Reynolds number of 750 using four semi-twisted tape inserts with 3% nanoparticles. This work offers instructions to model an advanced design of twisted tape integrated with tubes using multiple semi-twisted tapes, which helps to provide a higher amount of energy demand for solar applications.

Heat transfer hybrid nanofluid (1-Butanol/MoS2–Fe3O4) through a wavy porous cavity and its optimization

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Kh. Hosseinzadeh ◽  
Elham Montazer ◽  
Mohammad Behshad Shafii ◽  
D.D. Ganji
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Shape Factor ◽  
Average Nusselt Number ◽  
Heat Transfer Performance ◽  
Taguchi Methods ◽  
Hybrid Nanofluid ◽  
Transfer Performance ◽  
Content Type ◽  
Nanoparticle Shape

Purpose The purpose of this paper is to investigate natural convection in a porous wavy-walled enclosure that is including a cylinder cavity in the middle of it and filled with a hybrid nanofluid contains 1-Butanol as the base fluid and MoS2–Fe3O4 hybrid nanoparticles. Design/methodology/approach The domain of interest is bounded by constant temperature horizontal corrugated surfaces and isothermal vertical flat surfaces. The numerical outputs are explained in the type of isotherms, streamline and average Nusselt number with variations of the Rayleigh number, Hartmann number, nanoparticle shape factor and porosity of the porous medium. For solving the governing equations, the finite element method has been used. Findings The results show that Nuave is proportional to Rayleigh and nanoparticle shape factor directly as well as it has an inverse relation with Hartmann and porosity. The obtained results reveal that the shape factor parameter has a significant effect on the heat transfer performance, which shows a 55.44% contribution on the average Nusselt number. Originality/value As a novelty, to maximize the heat transfer performance in a corrugated walls enclosure, the optimal parameters have intended by using the response surface and Taguchi methods. Additionally, an accurate correlation for the average Nusselt number is developed with sensibly great precision.

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