Rasul Mohebbi

In this paper, a new double multi relaxation time (MRT) Lattice Boltzmann method (LBM) has been used to simulate magnetohydrodynamics (MHD) natural convection in a porous media. A new nanofluid named; multi-walled carbon nanotubes–iron oxide/water nanofluid (MWCNT–Fe3O4/water hybrid nanofluid) has been utilized to investigate the effect of nanoparticle on heat transfer. The thermo-physical properties of the nanofluid have been extracted from experimental results. D2Q9 and D2Q5 lattices are used to solve the flow and temperature fields respectively, and the effect of various parameters such as; Darcy number (Da) (10−2–10−1), Rayleigh number (103 ≤ Ra ≤ 105), porosity (0.4 ≤ ε ≤ 0.9), volume fraction of nanoparticles (0≤ Ø ≤ 0.003) and Hartmann number (0 ≤ Ha ≤ 50) have been investigated. Based on the present results, the new double MRT LBM is a proper method to solve the complex flows such as MHD natural convection in porous media. The results show that augmentation of Rayleigh number increases the heat transfer rate for all cases however by increasing the Hartmann number the effect of Rayleigh number decreases. Also, adding the nanoparticles enhances the average Nusselt number as increases 4.9% for Ra = 105, Da = 10−1, Ha = 50, and ε = 0.9 when the volume fraction of nanoparticles rises from 0 to 0.003. Results indicate that by enhancing Darcy number heat transfer rate increases and average Nusselt number improves by porosity. © 2018 Elsevier Ltd

This experimental study examines the impact of ultrasonic vibration on pressure drop and heat transfer enhancement of inlet turbulent flows. A stainless steel tube connected to an ultrasonic transducer and immersed in a constant temperature two-phase fluid was considered as the test section. Regarding the designed configuration, the ultrasonic transducer utilized had an acoustic frequency of 28 kHz and two different power levels of 75 W and 100 W. The experiments were conducted for different ultrasonic power levels, inlet temperatures, and flow rates. The accuracy of measurements was successfully validated via the existing empirical correlations. The results indicate that the effect of ultrasonic vibration on pressure drop and heat transfer enhancement diminishes with the growth of both Reynolds number and inlet temperature. Based on previously reported results on inlet flows with a laminar flow regime, the effect of ultrasonic vibration is very trivial in current turbulent inlet flows (up to 7.28% for heat convection enhancement). The results of the present study will be beneficial for future investigations on designing vibrating heat exchangers. © 2018 Elsevier B.V.

In this study, nanofluid natural convection in a baffled U-shaped enclosure in the presence of a magnetic field is investigated. Lattice Boltzmann method (LBM) is used to study present problems. KKL (Koo-Kleinstreuer-Li) correlation is applied to calculate the effective thermal conductivity and viscosity of nanofluid. The effect of the Brownian motion on the effective thermal conductivity is considered in this correlation. The combination of the four topics (nanofluid, U-shaped enclosure, baffle, magnetic field) is the main novelty of the present study. Effect of Rayleigh number, Hartmann number, nanoparticle volume fraction and cavity aspect ratio on the flow field and heat transfer characteristics have been investigated. The results demonstrate that the average Nusselt number increases by increments of the Rayleigh number, nanoparticle solid volume fraction and aspect ratio. However, the rate of heat transfer is suppressed by the magnetic field. The effect of magnetic field on heat transfer is more significant at higher Rayleigh number and the effect of Ra on the average Nusselt number is more noteworthy at lower Ha. Besides, the effect of Rayleigh number on heat transfer enhancement becomes more significant at higher aspect ratio. © 2018 Elsevier Ltd

This problem deals with natural convective heat transfer of a magnetic nanofluid in a porous medium subjected to two variable magnetic sources. In many industrial processes, heat transfer is affected by magnetic sources. The equations governing the problem were solved, using the finite element method. The study results were compared to literature ones and a very good consistency was found. The effects of different parameters, namely the magnetic number (Mnf= 100–5000), the strength ratio of the two magnetic sources (γr= 0.2–5), Hartmann number (Ha = 0–50), and porosity coefficient (ε = 0.1–09), on natural convective heat transfer inside a porous cavity have been examined. At low Rayleigh numbers, the average Nusselt number was independent of the strength ratio of the two magnetic sources. At high Rayleigh numbers, the Nusselt number decreases first with increasing the strength ratio of the two magnetic sources and then remains constant. Results also showed that at Ra = 1e4, the Nusselt number increases with increasing the magnetic number; whereas, at Ra = 1e6, the magnetic number has an increasing impact on the Nusselt number only at high γr values. © 2018 Elsevier Ltd

In the current study, the effects of the ultrasonic vibration and nanoparticles on the pressure drop and heat transfer enhancement of inlet turbulent flow are experimentally investigated. Two important factors in the design of heat exchangers, namely, heat transfer improvement and pressure drop, have been considered at different nanoparticle volume fractions, ultrasonic power levels, and flow rates. Existing experiential correlations are utilized to ensure the accuracy of the measurement instruments. It is observed that the effects of ultrasound vibration are more pronounced on the lower Reynolds number as well as the higher nanoparticle volume fraction. The result indicates that the ultrasonic vibrations could reduce the negative effect of pressure drop and improve the positive effect of heat transfer enhancement caused by nanoparticles up to 15.27% and 11.37%, respectively. The effect of ultrasonic power level variation is also bolder in more concentrated nanofluids and lower flow rates. The results of this work will be useful for designing future-oriented vibrating heat exchangers that also have the ability to work with nanofluid. © 2018 Elsevier Ltd

Research on nanofluid for heat transfer enhancement of thermal systems has received great attention owing to the lack of energy sources. In this study, fluid flow and natural convection heat transfer of Al2O3–Water or TiO2–water nanofluid inside a U-shaped cavity consist of a hot obstacle has been investigated numerically by lattice Boltzmann method (LBM). In this paper, different parameters are investigated such as Rayleigh number, the solid volume fraction of the nanoparticles, the U-shaped cavity's aspect ratio and heating obstacle's height on the flow field and heat transfer in the enclosure. The results showed that the Rayleigh number (Ra), cavity aspect ratio (AR) and obstacle's height can be affected on isotherms, streamlines and local and average Nusselt number. The average Nusselt number of the obstacle sides increased by increasing the Ra number and solid volume fraction of nanoparticles (ϕ) regardless the AR. In addition, by increasing the AR, the average Nusselt number increased. At low Ra, the effect of nanoparticles on increment of heat transfer for narrow cavities was more than wide ones. © 2018 Taiwan Institute of Chemical Engineers

In this study, lattice Boltzmann method (LBM) simulation is performed to investigate laminar forced convection of nanofluids in a horizontal parallel-plate channel with three rectangular cavities. Two cavities are considered as located on the top wall of the channel and one on the bottom wall. The effects of the Reynolds number (100-400), the cavity aspect ratio (AR = 0.25, 0.5), the various distances of the cavities from each other (Xc′) at different solid volume fractions of nanofluids (•=0 '0.05) on the velocity and the temperature profiles of the nanofluids are studied. In addition, the flow patterns, i.e. the deflection and re-circulation zone inside the cavities, and the local and averaged Nusselt numbers on the channel walls are calculated. The results obtained are used to ascertain the validity of the written numerical code, which points to the excellent agreement across the results. The results show that, as the solid volume fraction of nanofluids is enhanced, the transfer of heat to working fluids increases significantly. Further, the results show that the maximum value of the averaged Nusselt number in the channel is obtained at Xc′=0.1204 for AR = 0.5 and Xc′=0.1024 for AR = 0.25. The interval [0.1224, 0.1304] is the best position for the second cavity. It is concluded that the results of this paper are very useful for designing optimized heat exchangers. © World Scientific Publishing Company.

The aim of this work is to conduct numerical study of fluid flow and natural convection heat transfer by utilizing the nanofluid in a two-dimensional horizontal channel consisting of a sinusoidal obstacle by lattice Boltzmann method (LBM). The fluid in the channel is a water-based nanofluid containing Cuo nanoparticles. Thermal conductivity and nanofluid's viscosity are calculated by Patel and Brinkman models, respectively. A wide range of parameters such as the Reynolds number (Re=100-400) and the solid volume fraction ranging (φ=0-0.05) at different non-dimensional amplitude of the wavy wall of the sinusoidal obstacle (A=0-20) on the streamlines and temperature contours are investigated in the present study. In addition, the local and average Nusselt numbers are illustrated on lower wall of the channel. The sensitivity to the resolution and representation of the sinusoidal obstacle's shape on flow field and heat transfer by LBM simulations are the main interest and innovation of this study. The results showed that increasing the solid volume fraction φ and Reynolds number Re leads to increase the average Nusselt numbers. The maximum average Nusselt number occurs when the Reynolds number and solid volume fraction are maximum and amplitude of the wavy wall is minimum. Also, by decreasing the A, the vortex shedding forms up at higher Reynolds number in the wake region downstream of the obstacle. © 2018 World Scientific Publishing Company.

Purpose: The purpose of this paper is to consider natural convection of a nanofluid inside of a C-shaped cavity using Lattice Boltzmann method (LBM). Design/methodology/approach: Effects of some geometry and flow parameters consisting of the aspect ratio of the cavity, aspect ratio of the heat source; Rayleigh number (Ra = 103 − 106) have been investigated. The validity of the method is checked by comparing the present results with ones from the previously published work. Findings: The results demonstrate that for Ra = 103, the aspect ratio of the heat source has more influence on the average Nusselt number in contrast to the case of Ra = 106. Contrary to the fact that the average Nusselt number increases non-linearly more than twice because of the increase of the aspect ratio of the enclosure at Ra = 103, the average Nusselt number has a linear relation with the aspect ratio for of Ra = 106. Therefore, upon increasing the Rayleigh number, the efficiency of the aspect ratio of the cavity on the thermal convection, gradually diminishes. Originality/value: The authors believe that all the results, both numerical and asymptotic, are original and have not been published elsewhere. © 2018, Emerald Publishing Limited.

Lattice Boltzmann method (LBM) was carried out to investigate the effects of magnetic field and nanofluid on the natural convection heat transfer in a baffled U-shaped enclosure. The combination of different specifications of the baffle, LBM, nanofluid and magnetic field is the main innovation in the present study. In order to consider the effect of Brownian motion on the thermal conductivity, Koo–Kleinstreuer–Li model is used to define thermal conductivity and viscosity of nanofluid. Effects of Rayleigh number, Hartmann number, nanoparticle volume fraction, height and position of the baffle on the fluid flow and heat transfer characteristics have been examined. It was found that raising the Rayleigh number and nanoparticle solid volume fraction leads to increase the average Nusselt number irrespective of the position of the hot obstacle. However, the heat transfer rate is suppressed by the magnetic field. The heat transfer enhancement by introducing nanofluid decreases as increasing Rayleigh number, but it increases as increasing the Hartmann number. Moreover, the maximum heat transfer rate was observed when the enclosure equipped with a baffle with (s, h) = (0.2, 0.3) or (0.4, 0.3). © 2018 Akadémiai Kiadó, Budapest, Hungary

Using Buongiorno's model, the natural convection of Cu-water nanofluid flowing within a wavy wall porous enclosure at the presence of a cylindrical heater was numerically investigated. The problem is considered such that there is no local thermal equilibrium between two phases of porous media. The effects of Rayleigh number (103 ≤ Ra ≤ 106), the Lewis number (1 ≤ Le ≤ 50), Brownian motion parameter (0.1 ≤ Nb ≤ 0.5), the thermophoresis parameter (0.1 ≤ Nt ≤ 0.5), the buoyancy ratio (0.1 ≤ Nr ≤ 0.5), the Darcy number (10−5 ≤ Da ≤ 10−1), porosity (0.1 ≤ ε ≤ 0.9), the ratio of the thermal conductivity of the nanofluid to the solid phase (0.1 ≤ γs ≤ 10), coefficient of heat transfer at the interface (1 ≤ Nhs ≤ 1000) on hydrodynamic and thermal parameter have been studied. Streamlines, distribution of temperature and concentration of nanoparticles are presented and discussed. Increasing in the Rayleigh, the Darcy, the Lewis numbers, the thermal conductivity ratio and the Brownian parameter of the nanoparticle motions homogenizes the nanofluid. Meanwhile, the homogeneity is reduced as thermophoresis is increased. The results show that the thermal equilibrium model for porous media is applicable for the cases with large heat transfer coefficient at the interface between the solid matrix and the nanofluid. Moreover, the average Nusselt number of both porous phases' increases with the Brownian parameter, while the Nusselt number is reduced as the thermophoresis is increased. © 2018 Elsevier B.V.

A two-dimensional (2D) numerical simulation is performed to simulate the laminar forced convection of a nanofluid in a ribbed channel with apart heating (cooling) sources using lattice Boltzmann method (LBM). The multi-walled carbon nanotubes–iron oxide nanoparticles/water hybrid nanofluid (MWCNT–Fe3O4/water hybrid nanofluid) is used in this simulation. The velocity field, temperature distribution and heat transfer rate are numerically analyzed with the streamlines and isotherm patterns employing of a house code. In addition, the effect of Reynolds number (Re = 25, 50, 75 and 100), nanoparticle solid volume fraction (ϕ = 0, 0.001, 0.003) and ratio of the blocks height (A = 0.2, 0.3, 0.4) are measured. The results are validated against the results reported in the literature, and a good agreement is reported. The obtained results show a maximum value of 16.49% increase in the average heat transfer coefficient for all the considered cases relative to the base fluid. Moreover, the local Nusselt number proves that the use of blocks on the channel walls can increase the amount of heat transfer. Finally, the average Nusselt number shows a linear dependence on the increasing ratio of blocks height for constant solid volume fraction. The results of this study apply to the industrial equipment heating and cooling applications. © 2018 Akadémiai Kiadó, Budapest, Hungary

A numerical investigation is carried out to analyze the flow patterns, drag and lift coefficients, and vortex shedding around a square cylinder using a control circular bar upstream and downstream. Lattice Boltzmann method (LBM) was used to investigate flow over a square cylinder controlled by upstream and downstream circular bar, which is the main novelty of this study. Compared with those available results in the literature, the code for flow over a single square cylinder proves valid. The Reynolds number (Re) based on the width of the square cylinder (D) and diameter of circular bar (d) are 100 for square cylinder, 30 and 50 for different circular bars. Numerical simulations are performed in the ranges of 1≤L/D≤5 and 1≤G/D≤5, where L and G are the center-To-center distances between the bar and cylinder. Five distinct flow patterns are observed in the present study. It is found that the maximum percentage reduction in drag coefficient is 59.86% by upstream control bar, and the maximum percentage reduction in r.m.s. lift coefficient is 73.69% by downstream control bar. By varying the distance ratio for the downstream control bar, a critical value of distance ratio is found where there are two domain frequencies. © 2018 World Scientific Publishing Company.

In this paper, the laminar forced convection heat transfer of nanofluid through a bent channel was numerically investigated. The lattice Boltzmann method was used for solving the governing equations in the domain. The effect of different parameters such as Reynolds number (50 ≤ Re ≤ 150), vertical passage ratio (2.0 ≤ M ≤ 4.0), and nanoparticle solid volume fractions (Φ = 0, 0.01, 0.03, 0.05) are analyzed in terms of streamlines, isotherms, and local Nusselt numbers. It was concluded from this study that the local and average Nusselt number increased with increasing nanoparticle volume fraction regardless of Re and M. Moreover, the effect of the nanofluid concentration on the increment of heat transfer was more remarkable at higher values of the Reynolds number. Simulations show that by increasing the Reynolds number or decreasing the vertical passage ratio, the local and average Nusselt number increases. © 2018 Author(s).

Natural convection of multi-wall carbon nanotubes-Iron Oxide nanoparticles/water hybrid nanofluid (MWCNT-Fe3O4/water hybrid nanofluid) inside a ┴ shaped enclosure has been numerically investigated using Lattice Boltzmann Method. Numerical in-house code has been developed to study the effects of different parameters including the nanoparticles volume fraction, the Rayleigh number, the cavity obstruction ratio, the heat source position, and the heat source aspect ratio on the hydrodynamic and thermal characteristics. In order to validate the developed numerical code, the results have been compared with previous works and have shown a good concordance. The results indicate that Nusselt number degrades respect to the cavity obstruction ratio because of development of the thermal boundary layer thickness. In addition, an increment of the heat source aspect ratio results in better cooling condition due to decreasing in the boundary layer thickness. © 2018 Elsevier B.V.

The study of the forced convection in a channel has many practical applications. In this paper, the forced convection heat transfer from surface mounted blocks attached to the bottom wall of a horizontal channel with nanofluid is numerically studied by the second-order lattice Boltzmann method (LBM). The effects of Reynolds numbers and geometrical parameters of the blocks in different aspect ratios on the flow field and temperature distribution for various volume fractions of nanofluid (φ = 0, 0.01, 0.03 and 0.05) are analyzed. Also, the influence of these parameters is investigated on the local and average Nusselt numbers. It is concluded that heat transfer in channels can be enhanced by using the block on the walls and adding nanoparticles. There is a maximum value of 39.04% increase in average heat transfer coefficient for all the examined cases compared to the base fluid (i.e., water). © 2017 Elsevier Ltd

Research on nanofluids for heat transfer augmentation has received a great attention from many researchers. Recently, many numerical works have been conducted to examine their applicability in predicting heat transfer with nanofluids. In the present study, a two-dimensional (2D) lattice Boltzmann method (LBM) was applied for numerical simulation of forced convection in a channel with extended surface using three different nanofluids. The predicted were carried out for the laminar nanofluid flow at low Reynolds number (10 ⩽ Re ⩽ 70), nanofluid concentration (0.00 ⩽ φ ⩽ 0.050), different geometric parameter (0.2 ⩽ A = l/H ⩽ 0.8) and relative height of the extended surfaces (0.05 ⩽ B = h/H ⩽ 0.35). The results indicated that the average Nusselt number increases when the nanofluid concentration increased from 0% to 5%. Moreover, the effect of the nanofluid concentration on the increasing of heat transfer is more noticeable at higher values of the Reynolds number. It is concluded that the use of extended surfaces can enhance the rate of heat transfer for certain arrangements. We also found that the nanofluid with CuO nanoparticles performed better enhancement on heat transfer compared Al2O3/water and TiO2/water nanofluids. © 2017 Elsevier Ltd

In the present paper, the effect of nanofluid and the hot obstacle in a Π-shaped cavity is investigated. Lattice Boltzmann method is used to simulate the fluid flow and heat transfer. The effects of the parameters such as the nanoparticle solid volume fraction, the Rayleigh number, aspect ratio of cavity and hot obstacle position on the flow pattern and heat transfer parameters are studied. The numerical results are compared with previous results for validation, and a good agreement obtained. It is found that the average Nusselt number is increased by increasing the nanoparticle solid volume fraction, the Rayleigh number and the aspect ratio of cavity. Moreover, the effect of Rayleigh number on the average Nusselt number at high Rayleigh numbers (105–106) is more pronounced than that at low Rayleigh numbers (103–104) due to the different heat transfer mechanisms. The position of the hot obstacle affects the heat transfer significantly. When the hot obstacle is located on the center, the heat transfer is more effective. © 2018, Akadémiai Kiadó, Budapest, Hungary.

Forced convection heat transfer of multi-wall carbon nanotubes–iron oxide nanoparticles/water hybrid nanofluid (MWCNT–Fe3O4/water hybrid nanofluid) inside a partially heated τ-shaped channel has been numerically investigated. The effect of magnetic field is taken into account. The governing equations are solved by the lattice Boltzmann method in the domain, and the results were compared with other numerical methods by an excellent agreement between them. The effects of parameters such as Hartmann number (0 ≤ Ha ≤ 60), volume fraction of nanoparticles (0 ≤ ϕ ≤ 0.003) and different location of two heaters on the fluid flow and heat transfer are studied. The results indicate that for all cases, the average Nusselt number of each heater increases as the volume fraction of nanoparticles increases. The heat transfer characteristics were significantly affected by the arrangement of the two heaters. The heaters located on the left half of the top wall is convection-dominant mechanism, and the conduction heat transfer is the primary mechanism when the heater is on the right half of the top wall. The average Nusselt number increases as Ha increases for the heater of dominating convection mechanism but decreases for the heater of dominating conduction mechanism. © 2018, Akadémiai Kiadó, Budapest, Hungary.

Purpose: This paper aims to numerically investigate the natural convection heat transfer of multi-wall carbon nanotubes (MWCNTs)-water nanofluid in U-shaped enclosure equipped with a hot obstacle by using the lattice Boltzmann method. Design/methodology/approach: The combination of the three topics (U-shaped enclosure, different positions of the hot obstacle and MWCNTs-water nanofluid) is innovative in the present study. In total, 15 different positions of the hot obstacle have been arranged, and the effects of pertinent parameters such as Rayleigh numbers, the solid volume fraction of the MWCNTs nanoparticles on the flow field, temperature distribution and the rate of heat transfer inside the enclosure are also investigated. Findings: It is found that the average Nusselt number increased by raising the Rayleigh number, and so did the nanoparticle solid volume fraction regardless the position of the hot obstacle. Moreover, enclosures where the hot obstacle is located at the bottom region proved to provide a better rate of heat transfer at high Rayleigh number (106). It is concluded that at a low Ra number (103-105), the higher heat transfer rate and Nu number will be obtained when the hot obstacle is located in the left or right channel. Originality/value: In the literature, no trace of studying the natural convection of nanofluids in U-shaped enclosures with heating obstacles was found. Also, MWCNTs were less used as nanoparticles. As the natural convection of nanofluids in thermal engineering applications would expand the existing knowledge, the current researchers conducted a numerical study of the natural convection of Maxwell nanofluid with MWCNTs in U-shaped enclosure equipped with a hot obstacle by using lattice Boltzmann method. © 2018, Emerald Publishing Limited.

In this work, the effect of the presence of a heat source and its location on natural convection in a C-shaped enclosure saturated by a nanofluid is investigated numerically using the lattice Boltzmann method. Fifteen cases consisting of different heat source locations attached to an isolated wall of the enclosure have been considered to achieve the best configuration at different Rayleigh numbers (103-106) and various solid volume fractions of the nanofluid (0-0.05). Results are shown in terms of the streamlines, isothermal lines, velocity profiles, and the local and average Nusselt numbers. The numerical solution is benchmarked against published results from previous studies for validation, and a good agreement is demonstrated. According to the results, at Ra = 103, the maximum Nusselt number is achieved when the heat source is located within the upper horizontal cavity. Moreover, at higher Rayleigh numbers (Ra = 106) and locations of the heat source within the vertical cavity yield the best Nusselt numbers. Compared to the base fluid and at low Rayleigh numbers, the increase in the Nusselt number of the nanofluid is not found to be dependent on the location of the heat source. However, for high Rayleigh numbers, the maximum increase is obtained when the heat source is located in the upper part of the vertical. © 2017 Author(s).

The aim of this paper is investigating the forced convection heat transfer in a channel with transverse rectangular cavities using the lattice Boltzmann method (LBM) which is not available in the literature yet. The effects of the Reynolds number (100-400), cavity aspect ratio (AR=0.25, 0.5, 1.0), distance of cavities from each other (S′=0,2,4,6) in fixed depth of cavity (A′=0.5) on the velocity and temperature profiles are studied. Moreover, the flow patterns such as deflection and re-circulation zone inside the cavities are obtained. The local and averaged Nusselt numbers on the channel walls are achieved. The results show that the channel with cavities achieves heat transfer enhancements relative to the smooth channel. For the constant cavity aspect ratio, the maximum value of averaged Nusselt number in the channel is obtained in the case of S′=2. Heat transfer to the working fluids increases significantly by increasing the aspect ratio. The existed results are used to ascertain the validity of the numerical code and excellent agreement between results was found. © 2017 World Scientific Publishing Company.

The natural convection heat transfer in an L-shaped enclosure being filled with Al2O3/water nanofluid and having an internal heating obstacle is presented in this paper by LBM. The combination of the three topics (L-shaped cavity, hot obstacle and nanofluid) is the main novelty of the present study. The statistics focused specifically on the effects of different key parameters same as Ra number (103–106), aspect ratio of the channel (0.2–0.6), nano-particle volume fraction of (0–0.05), position and height of the hot obstacle and nanoparticle diameter (20–80 nm) on the heat transfer inside the L-shaped enclosure. The average Nusselt numbers were also calculated for the obstacle sides. The obtained results showed that the streamlines and isotherm lines had different patterns at different Ra numbers, aspect ratio and the height of obstacle. The heat transfer phenomena were highly affected by the heating obstacle position. With the nanofluid and the reducing AR, the increasing Ra number, the decreasing nanoparticle diameter and the increasing height of the obstacle, an increase in the heat transfer and the individual Nusselt number appeared. Moreover, the maximum Nusselt number was observed when the heating obstacle was located in the lower position inside the left wall. © 2017 Taiwan Institute of Chemical Engineers

A detailed comparison between the lattice Boltzmann method and the finite element method is presented for an incompressible steady laminar flow and heat transfer of a power-law fluid past a square cylinder between two parallel plates. Computations are performed for three different blockage ratios (ratios of the square side length to the channel width) and different values of the power-law index n covering both pseudo-plastic fluids (n < 1) and dilatant fluids (n > 1). The methodology is validated against the exact solution. The local and averaged Nusselt numbers are also presented. The results show that the relatively simple lattice Boltzmann method is a good alternative to the finite element method for analyzing non-Newtonian fluids. © 2016, Pleiades Publishing, Ltd.

The lattice Boltzmann method (LBM) has been established as an efficient technique for solving a fluid dynamics problem in a complex porous medium. In this paper, the power-law fluid flow and heat transfer are studied numerically in a channel partially filled with an anisotropic porous block for three power-law indices, n=0.8, 1 and 1.2. Combined pore level simulations of flow and heat transfer are performed for a 2D channel that is partially filled with square obstacles in both ordered and random arrangements. A step by step verification procedure is taken to ensure the accuracy and the physical correctness of the numerical simulation. The effects of the different arrangements of obstacles, Reynolds number, power index n, blockage ratio and porosity on the velocity and temperature profiles are studied. The local and averaged Nusselt numbers are also calculated on the channel walls. It is found that pseudo plastic fluids generate the highest heat transfer rate for all configurations of obstacles. For constant porosity and block size, the increase is noticeable when the arrangement of square obstacles is random. Also by decreasing the porosity, the value of averaged Nusselt number is increased. Two correlations for regular and random obstacle arrangements between the Nusselt number, Reynolds number, power index n, blockage ratio and porosity are presented. The values of averaged Nusselt number with the respective confidence interval are also reported in the case of random arrangement of obstacles. © 2013 Elsevier B.V.