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Energy 162 (2018) 1052e1061

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Energy

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Effects of geometric parameters on the performance of solar chimneypower plants

Davood Toghraie a, Amir Karami a, Masoud Afrand b, *, Arash Karimipour b

a Department of Mechanical Engineering, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Iranb Department of Mechanical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran

a r t i c l e i n f o

Article history:Received 10 November 2017Received in revised form17 July 2018Accepted 11 August 2018Available online 12 August 2018

Keywords:Solar chimneyEfficiencyOutput powerNumerical simulationRenewable energy

* Corresponding author.E-mail address: masoud.afrand@pmc.iaun.ac.ir (M

https://doi.org/10.1016/j.energy.2018.08.0860360-5442/© 2018 Elsevier Ltd. All rights reserved.

a b s t r a c t

In this study, the influences of geometrical properties on a solar chimney were investigated numericallyby applying the k� ε turbulence model, continuity, momentum, and energy equations in the 3D finitevolume approach inside a solar chimney power plant. The following variables should be involved: col-lector radius (Rcl), collector height (Hcl), chimney height (Hch), chimney radius (Rch), and heat flux (q

00).

The effects of changes in these variables on temperature, velocity, pressure distributions, efficiency, andoutput power were investigated. The results indicated that output power and solar chimney efficiencyhave positive relationships with chimney height and collector radius but a negative one with collectorheight. In addition, it was found that the parameter of chimney radius has an optimum range which hasthe maximum values for efficiency and output power.

© 2018 Elsevier Ltd. All rights reserved.

1. Introduction

Two major problems, poverty and dependence on fossil fuels,are prevalent worldwide. Fossil fuels are non-renewable sources ofpollution, and poverty negatively affects the livelihood of millionsaround the world. The livelihoods of impoverished people can bedramatically improved with cheap energy. Energy can improve thesanitation of food andwater, makemany educational tools possible,allow students to study during the night, bolster the local economyby setting up and encouraging the location of businesses, andmuchmore. The most potent, dependable, and sustainable source of en-ergy in our solar system is the sun. There is great interest in har-nessing its power, both efficiently and economically. Solar energy isone affordable type of renewable energy. Other energy sourceshave several problems such as discontinuous availability [1]. Oneinnovative system that is receiving more and more attention is thesolar updraft tower, or solar chimney. The absence of contamina-tion by solar power plants is an interesting symbol of solar chimneyoperation to produce a large amount of solar powered electricity.The working properties of the solar chimney rely on the buoyantnature of air to turn a turbine that generates electricity. The system

. Afrand).

has 3 primary parts: the chimney, a collector, and a turbine. Thechimney is a large pressure tower typically made from adiabaticmaterials. The collector is made of a transparent material, such asglass, and functions similarly to a greenhouse. The turbine operatesas a low wind pressure generator to convert pressure into energyusing cased turbines.

During the day, solar radiation penetrates the transparent col-lector to warm the thermal storage layer. Some thermal energy ismaintained in the thermal reservoir layer, and some is moved on tothe air of the thermal reservoir surface. The warm airflow accel-erates along the solar collector to the bottom of the chimney, drivesthe turbine and then the generator to produce electricity, andfinally leaves the system through the top of the chimney. Outsideair flows over the system of the solar collector and is called acontinuous air current. Thermal energy is released from the ther-mal storage layer at night or on cloudy days, and the systemcontinuously produces electricity.

The basic fundamentals and descriptions of a solar chimneypower plant were reported by Cabanyes [2] and Gunther [3].Similar research was carried out by Schlaich in 1970 and in 1981 toconstruct a pilot solar chimney of 50 kW power [4]. After this plantwas established, many researchers proposed their solar chimneydesigns and buildings [5,6]. The prototype solar chimney with a50 kW power output was designed by Bergermann approximately150 km south of Madrid, Spain in 1981 [1]. The plant had a solar

Fig. 1. The solar chimney configuration.

D. Toghraie et al. / Energy 162 (2018) 1052e1061 1053

chimney measuring 194.6m in height, 5.08m in diameter, and a0.00125-m thick metallic wall; it also had a collector with a radiusof 122m. Krisst et al. [7] built four pilot solar chimney power plantsmeasuring 10m in height and 6m in diameter, which had a powercapacity of 10W.

A demonstration power plant using a solar chimney was built in1997 [8], in which an intermediate absorber and an extendingcollector were applied to achieve greater efficiency [9]. In 2002, apilot solar chimney with a power capacity of 5W was set up byZhou et al. on the roof of a building in China [10,11]. The pilot plant,which had a height of 8m and a collector measuring 10m indiameter, was rebuilt several times for different purposes. In 2011,another pilot solar chimney was built by Kasaeian et al. [12] on thecampus of the University of Zanjan, Iran. This solar chimney wasconstructed with a covered collector measuring 10m in diameterand a chimney with a 12m polyethylene pipe. Based on the tem-perature and air velocity at various collector positions, themaximum air velocity and chimney temperature were obtained.Measurements showed that on hot and cold days, the air at thelower section of the chimney appeared after sunrise. Khanal and Leiperformed an experimental study on an inclined passive wall solarchimney [13]. The active wall of this model had uniform heat flux.The researchers observed that the air velocity in the air gap widthdepended significantly on the inclination angle.

Patel et al. [14] optimized the shape of important sections of thesolar chimney to numerically improve its performance. Their col-lector inlet and outlet, angle divergence, and chimney inlet openingwere changed as the diameter of the collector was adjusted. Hur-tado et al. [15] developed a numerical model under transient con-ditions based on the pilot one produced by Manzanares [6] toanalyze the efficiency and thermodynamic properties of an SCPPover a daily operation cycle while considering soil as the heatstorage material. Their results showed a significant increase inpower as the soil compression was increased.

Sangi et al. [16] investigated the simulation of a Manzanaresprototype configuration. They compared their results with theexperimental achievements of Schlaich [4] and Pastohr et al. [17].Their results showed that a 2-D axis symmetric model could beutilized. Pastohr et al. [17] solved the complicated Navier-Stokescorrelation at an upwind power plant. Koonsrisuk and Chitsom-boon [18] established a dynamic correspondence among the pro-totype and the models by combining eight primary variables intoone dimensionless variable. Moreover, three geometrical figures ofa plant were numerically tested in their work. A numerical inves-tigation of a solar chimney measuring 1 km in height and 2 km inradius and intended to create multi-climate conditions inside thecollector was reported from China [19]. Buonomo et al. [20] pre-sented a numerical study of a solar chimney in a south-facingbuilding. They analyzed the effects of the height and spacing of asolar chimney on increasing system energy efficiency.

Gholamalizadeh and Kim [21] studied the greenhouse effect onthe natural convection heat transfer characteristics in a solarchimney. They used an unsteady CFD model to analyze SCPP. Theyalso used the discrete ordinates method to solve the equations ofradiation heat transfer by Dehghani and Mohammadi [22], andthey carried out the multi-objective optimization of solar chimneydimensions. The researchers considered the capital cost and poweroutput of the system to be minimized and maximized, respectively.They found this optimization method to be effective and useful.

Hanna et al. [23] studied the distribution of temperature effectsin Egypt. Their results revealed that the temperature of the exit airof a solar collector depended on weather conditions and was alsorelated to differences in air temperature in the solar collector.

Gholamalizadeh and Kim [24] reported the optimization of asolar chimney power plant utilizing genetic algorithms. They

applied an inclined roof as the collector and showed that its shapeplayed a significant role in the setup optimization approach.

Attig Bahar et al. [25] developed a new numerical research for asolar chimney according to the well-known three-dimensional CFDmodels; they also validated the accuracy of the achieved resultsversus the experimental ones of Manzanares.

Nilesh et al. [26] reviewed the numerical simulation of a solarchimney by changing its radius and height. It was seen that thevarious tower domains changed the power plant flow rates andefficiency.

Sudprasert et al. [27] investigated the influence of using moistair through the solar chimney in a vertical position. They recom-mended a suitable aspect ratio to achieve more ventilation and lessbackward fluid in the inlet.

Karami and Toghraie [28] performed a computational fluid dy-namics analysis and geometric optimization of a solar chimneypower plant using genetic algorithms. They concluded that theoutput power of the plant could be increased considerably byincreasing the height of the solar chimney, but increasing the radiusof the collector could slightly reduce output power.

In this study, by keeping the characteristics of the grids fixed,the influence of physical and geometric variables such as the col-lector radius (Rcl), collector height (Hcl), chimney height (Hch),chimney radius (Rch), and heat flux (q

00) on the solar chimney output

power was investigated numerically using a three-dimensionalcompressible CFD method [see Fig. 1]. The effects of changes intemperature, velocity, pressure distributions, efficiency, and outputpower were investigated. To the best of the authors' knowledge,there has been no comprehensive and thorough investigation ofthe influence of physical and geometric variables on the perfor-mance of solar chimney power plants to date.

2. Mathematical modeling

The fundamental governing equations were summarized andimportant assumptions were explained. The viscous effect was notincluded as a variable. The cited study had concluded and proventhat flow in a solar tower, with a low ratio of tower height to radius,could be approximated as an inviscid flowwithout sacrificingmuchin accuracy. Therefore, the current study investigated only inviscidflow. Turbineworkwas also not included because it was beyond thescope of this study, inwhich determining the amount of no-load airkinetic energy was the main aim. The numerical approach to solarchimney treatment was provided by applying the well-knownclassic transport NaviereStokes equations for the thermo-physicalproperties of air. Moreover, the equations for energy and k� ε forinvestigating the flow movements should be involved. The

D. Toghraie et al. / Energy 162 (2018) 1052e10611054

governing equations are as follows:The conservation of mass is:

v

vxiðr uiÞ ¼ 0 (1)

The conservation of momentum is:

v

vxj

�r ui uj

� ¼ �vPvxi

þ v

vxj

"m

vuivxj

þ vujvxi

!#þ v

vxj

�� r u=i u

=j

�

(2)

The conservation of energy equation is:

v

vxiðuiðErþ PÞÞ ¼ v

vxj

"ðkÞ vT

vxj

#(3)

E ¼ h� Prþ u2

2(4)

The standard k� εturbulence model was used throughout thisstudy, and it was assumed that the flow is turbulent so that theinfluence of viscosity can be neglected. In the k� ε turbulenceapproach, the kinetic energy of turbulence (k) beside its dissipationrate are calculated from the governing equations:

v

vxiðr k uiÞ ¼

v

vxj

�mþ mt

sk

�vk

vxj

!þ Gk � r ε (5)

v

vxiðr ε uiÞ ¼

v

vxj

�mþ mt

sε

�vε

vxj

!þ C1 ε

ε

kGk � C2ε

ε2

kr

Gk ¼�� r u=i u

=j

�vujvxi

(6)

where sk and sε indicate turbulent Prandtl numbers for the vari-ables of k and ε; C1ε, C2εare also the constant ones.

Now, the kinetic energy of turbulence (Gk) is expressed in thisway:

Gk ¼ mtS2 (7)

where S and mtshow the average rate-of-strain tensor modulus andturbulent viscosity, respectively:

S ¼ffiffiffiffiffiffiffiffiffiffiffiffiffi2SijSij

q(8)

mt ¼ Cmrk2

ε

(9)

Table 1Dimensions of modeled power plant.

Parameter ChimneyHeight

ChimneyRadius

CollectorRadius

CollectorHeight

Value 100m 4m 100m 2m

Table 2Relative errors of power and efficiency at different mesh sizes against to [18].

Parameter Grid 1(26192 elements) Grid 2 (54960 elements) Grid 3

Power 65% 28% 12%Efficiency 71% 30% 14%

where, Cm is based on the mean rate of strain. The parameters inEquations (5) and (6) are defined as C1ε ¼ 1.44, C2ε ¼1.92, sk ¼1.0,and sε ¼ 1.3. The pressure drop in a solar chimney is defined byRef. [28]:

Dp ¼ 12rV2

t;max (10)

where Vch;maxis the maximum air velocity in a chimney without aturbine. The output power is given by Ref. [28]:

Ptot ¼ _mgHDTT0

(11)

where _m represents the air flow rate, g is the gravity acceleration, His the height of the chimney, DT is the temperature difference, andT0 illustrates the inlet temperature. The efficiency of the solarchimney was calculated from:

h ¼_mgH DT

T0Qin

(12)

where Qin is the input thermal power [28],

Qin ¼ _mcpðT2 � T1Þ ¼ _mcpDT (13)

and

_m ¼ rapDCollHCollvColl ¼ rap

4D21VColl (14)

3. Numerical solution

Basic equations were simplified to axisymmetric and steadystate equations. The governing equations were solved using apressure-based solver with a finite volume method. With thepressure-based solver for the incompressible flow, pressurebecame a primitive variable. The SIMPLE algorithm was chosen tocouple the pressure and velocity equations. It uses a momentumequation to estimate the pressure and then corrects both the

(78842 elements) Grid 4 (98730 elements) Grid 5 (126314 elements)

4.8% 4.6%4.4% 4.3%

Fig. 2. The numerical grids of object.

D. Toghraie et al. / Energy 162 (2018) 1052e1061 1055

pressure and velocity until the conservation of mass equation issatisfied with the second order upwind scheme. The operationprinciple of solar chimney is presented in Fig. 1. Air enters the spaceat a low circular transparent that is open at the periphery and

Table 3Explaintion about the 4 models.

Specifications Boundarycondition

Locatiob Boundary

Pressure¼ 0PaT ¼ 308K Pressure inlet A Inlet

q00 ¼ 0

Wm2

Wall B Surface of Earth

q00 ¼ 600

Wm2

Wall C Collector ceiling

q00 ¼ 800

Wm2

e Wall D Chimney surface

e Symmetry E Collector'ssurroundings

Pressure¼ 0PaT ¼ 308K Pressure outlet F Chimney outlet

Fig. 3. Compared obtained results for (a) Power, (b) Efficiency with [18].

receives heat from solar radiation. The solar air collector consists ofa roof and the ground under it. The height of the collector roofvaries from the inlet to the junction with the chimney in accor-dance with the law of meridian flow theory. Table 1 illustrates thedimensions of the modeled power plant.

The selected variables, including the main geometric parame-ters of the SCPP, were collector radius (Rcl), collector height (Hcl),chimney height (Hch), chimney radius (Rch), and heat flux (q

00). Each

variable was generally required to be within a reasonable range asfollows:25m � Hch � 500m1m � Rch � 10m25m � Rcl � 500m1m � Hcl � 10m600W

.m2 � q

00 � 800W.m2

(15)

Fig. 4. Contours of temperature magnitude in the base case for a) 600W/m2, b)800W/m.2.

D. Toghraie et al. / Energy 162 (2018) 1052e10611056

The present work used the unstructured tetrahedral grids atdifferent mesh sizes which led to 98,730 grid points in the gridindependent study, as shown in Table 2.

Those plants in which the tower centerline is the axis wereconsidered to be axisymmetric. A five-degree part of the plant wascut out from the periphery to investigate the 3-D setting (see Fig. 2).

Governing equations were solved numerically with thefollowing boundary conditions at each one of all 4 models. In eachmodel, one of the geometric parameters of the chimney was vari-able and the rest were fixed.

� Model 1: Variable chimney height, constant chimney radius,constant collector radius, and constant collector height.

� Model 2. Variable chimney radius, constant chimney height,constant collector radius, and constant collector height.

� Model 3: Variable collector height, constant chimney radius,constant chimney height, and constant collector height.

� Model 4. Variable collector radius, constant chimney height,constant chimney radius, and constant collector height.

Fig. 5. Velocity contours for base case at a) 600W/m2, b) 800W/m.2.

The temperature and pressure at the inlet of the roof wereknown, while zero pressure was considered at the outlet of thechimney with a symmetry condition along 2 walls of the sector.Moreover, the insulated no-slip conditionwalls were supposed andillustrate the frictionless flow on the boundaries. The suitably ac-curate residual coefficients for mass and other equations werechosen to achieve the convergence situation (See Table 3).

4. Results and discussion

4.1. Validation

A CFD model was used to simulate a solar chimney for thegeneration of power; the results were compared with those of [18]in Fig. 3. The average relative error rates between the obtainedresults and the data obtained by Koonsrisuk and Chitsomboon [18]are less than 5.0% and 4.7% for power and efficiency, respectively. Itis clear that the model predicts the output power and efficiency of a

Fig. 6. Effect of collector height on a) temperature, b) pressure.

D. Toghraie et al. / Energy 162 (2018) 1052e1061 1057

Manzanares power plant with good agreement [18]. The results ofthe solar chimney power plant from the present work can be pro-vided for different elements such as chimney and collector heights,chimney and collector radiuses, and heat flux.

4.2. Investigation of heat flux

The air velocity and temperature distributionswere analyzed fordifferent heat fluxes, and the results are presented in Figs. 4 and 5.The velocity magnitude increased with a rise in the heat flux, andits maximum value was located near the walls of the chimney. Thevelocity contours showed an appreciable increase in the flow. Thismeans that the transfer was done primarily by convection andpredominated the conduction.

4.3. Investigation of collector height

Changes in the temperature and pressure of the air at the end of

Fig. 7. Influence of collector height on the solar chimney performance.

the collector were analyzed for different collector inlet heights. Theoutput data at collector heights of 1me10m were simulated, andthe results are shown in Fig. 6. The inlet temperature in all nu-merical simulations was 308 K. According to Fig. 6a, the maximumdifference in air temperature was 12.1 K at a collector height of 1m,and the minimum temperature difference was 4.7 K at a collectorheight of 10m for q

00 ¼ 800W/m2. Moreover, it became clear thatwhen the heat flux decreased, the temperature difference at allheights had less magnitude. At the first state shown in Fig. 6b, thecollector flow rate was in its smallest value; hence, the greatestnumber of air temperature variations was seen. With increases inthe radius of the collector, the air pressure in the solar chimneydecreased. For a thermal flux of 800W/m2, the amount of pressurein the radius of 25m was �157 Pa. In a radius of 500m, the airpressure was �1607 Pa, which is 90% less than that of the 25-mradius, and for the thermal flux of 600W/m2at radii of 25 and500m, the pressure was�133.64Pa and�1365.9Pa. As can be seen,

Fig. 8. Influence of collector radius on a) temperature, b)pressure.

D. Toghraie et al. / Energy 162 (2018) 1052e10611058

the pressure in the thermal flux 800W/m2was less than the ther-mal flux of 600W/m2, which has a greater effect on the outputpower, but the variation process is similar for both thermal quan-tities; this reduction in pressure had a positive effect on tensilestrength. Fig. 6b shows that the maximum output power was ob-tained at a radius of 500m. By comparing the output power chartwith a measurable pressure variation of 500m radius, the pressureis found to be at the minimum limit. In other words, the outputpower was increased by decreasing pressure.

Fig. 7 shows the influence of changes in collector height Hcl from1m to 10m on the power and efficiency of the solar chimney powerplant. Numerical results revealed that the output power decreasedfrom 82.5 kW to 52.5 kW when the collector height was increasedfrom 1m to 10m at a heat flux of 800W/m2. This trend was alsoseen for a heat flux of 600W/m2. Increasing the collector heightcaused pressure to increase and, due to the ideal gas law, thetemperature and output power both decreased. Efficiency curves

Fig. 9. Influence of collector radius on solar chimney plant performance.

for different heat fluxes had similar behaviors and were decreasedwith increments in collector height. In Fig. 8a and b, the variationsin air pressure and temperature versus different collector heightsare shown. The fluid temperature difference rose and the fluidpressure declined in the solar chimney when collector height wasincreased.

4.4. Investigation of collector radius

In Fig. 9, changes to output power and solar chimney efficiencyare indicated where the value of Rcl varies from 25m to 200m,which means that flow power would be greater at more Rcl whilethe inverse process is confirmed for efficiency.

As seen in Fig. 9, for q00 ¼ 800W/m2, the output power and ef-

ficiency were 14.25 kW and 0.003 at the collector radius of 25m,respectively. At a collector radius of 500m, output power and ef-ficiency both had different behavior. The output power increased to

Fig. 10. Influence of chimney height on a) mass flow rate, b) pressure.

D. Toghraie et al. / Energy 162 (2018) 1052e1061 1059

1415 kW, and efficiency decreased to 0.00195. The main reason forthe augmentation in output power can be the reduction in pressurecaused by the increase in collector radius (as shown in Fig. 8b),which caused the air mass flow rate and temperature to increase.However, by increasing the collector radius, the area of heattransfer increased, and with respect to the constant heat flux, ef-ficiency decreased.

4.5. Investigation of chimney height

Variations in air pressure and mass flow rate were simulated atdifferent chimney heights. Results for the heights of 25me500mare shown in Fig. 10a and b, respectively. Then the influence of thechimney height, Hch, was investigated. The Hch was changed from25m to 500m. The higher Hch corresponded with a higher level ofefficiency and power (see Fig. 11). Fig. 11 (a) shows the power of thesolar chimney variation against chimney height for different heat

Fig. 11. Influence of chimney height on plant.

fluxes. It can be seen that for q00 ¼ 800W/m2 the output power

increased from 24 kW for a chimney height of 25me313.5 kW for achimney height of 500m. Also, for q

00 ¼ 600W/m2, the output po-wer was 16 kW and 209 kW for chimney heights of 25m and500m, respectively. However, a higher chimney height led to lowerair pressure and larger velocity and mass flow rate. Augmentationin the flow rate caused increased output power. In Fig. 11 (b), theefficiency of the solar chimney for heat fluxes of 600W/m2 and800W/m2 are shown. Similar to the variation in output power,efficiency increased from 0.00063 at a chimney height of 25m to0.0083 at a chimney height of 500m.

4.6. Investigation of chimney radius

The numerical investigation of the chimney radius was per-formed for 1me10m values. Fig. 12a and b indicate the mass flowrate and pressure magnitude distribution of air for different

Fig. 12. Influence of chimney radius on a) mass flow rate, b) pressure.

Fig. 13. Effect of chimney radius on solar chimney plant performance.

D. Toghraie et al. / Energy 162 (2018) 1052e10611060

chimney radii. As seen in Fig. 12, the maximum mass flow rate ofworking fluid for a chimney radius of 5m at q

00 ¼ 800W/m2 was45.29 kg/s, which is 70% and 30.8% higher than the mass flow ratefor chimney radii of 1m and 10m, respectively. It is worthy to notethat the main n for this behavior can be that this radius had theminimum pressure value, according to Fig. 12b.

Effects of chimney radius, Rch, variations are displayed in Fig. 13,where Rch was varied from 1m to 10m. Fig. 13 (a) shows thatoutput power increased when chimney radius was increased from1m to 5m, and its maximum value equaled 85.5 kW forq

00 ¼ 800W/m2. One possible explanation for this could be thegreater mass flow inlet due to less chimney pressure. Then, byincreasing the chimney radius from 5m to 10m, the output powerdecreased 28%. This trend was also seen in the output power curvefor q

00 ¼ 600W/m2. It can be seen in Fig. 13 (b) that for the chimneyradius of 5m, the maximum efficiency was 0.00334; however, at10m, the efficiency decreased 28% for q

00 ¼ 800W/m2.

5. Conclusion

The present study demonstrated the capabilities of the CFDtechnique as a powerful research and engineering tool for theanalysis of complex aerodynamic and thermal systems like solarchimney power plants. The CFD approach might enable the con-version of an experimental work on this subject to a simpler andmore economical one. Thus, this approach can be further developedand upgraded for a more detailed analysis. In this study, three-dimensional numerical simulations were performed to investi-gate the influences of geometrical parameters on the performanceof the solar chimney. A three-dimensional region supposed withk� ε turbulencemodel was simulated. Firstly, the numerical resultsfor the base case were validated with [18]. Furthermore, the effectsof geometric characterizations of the solar chimney power plant onflow and performance were investigated. The profiles of tempera-ture, pressure, and mass flow rate are presented in variousgeometrical parameters. It is seen that output power can beincreased considerably by increasing solar chimney height, whileincreasing the collector radius can increase output power slightly.Through the analysis, it was found that the chimney radiusparameter had an optimum range with maximum values for effi-ciency and output power. The extension of this paper for CFDsimulation according to our previous works [28e56]affords engi-neers a good option for CFD simulation.

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[31] Akbari OA, Karimipour A, Toghraie D, Karimipour A. Impact of ribs on flowparameters and laminar heat transfer of Water/Alumina nanofluid withdifferent nanoparticle volume fractions in a three-dimensional rectangularmicrochannel. Adv Mech Eng 2016;7:1e11.

[32] Akbari OA, Karimipour A, Toghraie D, Safaei MR, Alipour M, Goodarzi H,Dahari M. Investigation of rib's height effect on heat transfer and flow pa-rameters of laminar water- Al2O3 nanofluid in a two dimensional rib-microchannel. Appl Math Comput 2016;290:135e53.

[33] Akbari OA, Toghraie D, Karimipour A. Numerical simulation of heat transferand turbulent flow of Water nanofluids CuO in rectangular microchannel withsemi attached rib. Adv Mech Eng 2016;8:1e25.

[34] Alipour H, Karimipour A, Safaei MR, Semiromi DT, Akbari OA. Influence of T-semi attached rib on turbulent flow and heat transfer parameters of a silver-Water nanofluid with different volume fractions in a three-dimensionaltrapezoidal microchannel. Physica E 2016;88:60e76.

[35] Nazari S. Toghraie D. Numerical simulation of heat transfer and fluid flow ofWater-CuO Nanofluid in a sinusoidal channel with a porous medium. PhysicaE, 123; 87: 134-140

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[37] Aghanajafi A, Toghraie D, Mehmandoust B. Numerical simulation of laminarforced convection of Water-CuO nanofluid inside a triangular duct. Physica E2017;85:103e8.

[38] Afrand M, Toghraie D, Karimipour A, Wongwises SA. Numerical study ofnatural convection in a vertical annulus filled with gallium in the presence ofmagnetic field. J Magn Magn Mater 2017;430:22e8.

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[41] Gravndyan Qumars, Ali Akbari Omid, Toghraie Davood, Ali Marzban,Mashayekhi Ramin, Karimi Reza, Pourfattah Farzad. The effect of aspect ratiosof rib on the heat transfer and laminar water/TiO2 nanofluid flow in a two-dimensional rectangular microchannel. J Mol Liq 2017;236:254e65.

[42] Akbari OA, Afrouzi HH, Marzban A, Toghraie D, Malekzade H, Arabpour A.Investigation of volume fraction of nanoparticles effect and aspect ratio of thetwisted tape in the tube. J Therm Anal Calorim 2017;129(3):1911e22.

[43] Shamsi MR, Akbari OA, Marzban A, Toghraie D, Mashayekhi R. Increasing heattransfer of non-Newtonian nanofluid in rectangular microchannel withtriangular ribs. Phys E Low-dimens Syst Nanostruct 2017;93:167e78.

[44] Rezaei O, Akbari OA, Marzban A, Toghraie D, Pourfattah F, Mashayekhi R. Thenumerical investigation of heat transfer and pressure drop of turbulent flowin a triangular microchannel. Phys E Low-dimens Syst Nanostruct 2017;93:179e89.

[45] Heydari M, Toghraie D, Akbari OA. The effect of semi-attached and offset mid-truncated ribs and Water/TiO2 nanofluid on flow and heat transfer propertiesin a triangular microchannel. Thermal Science and Engineering Progress2017;2:140e50.

[46] Ahmadi GR, Toghraie D. Energy and exergy analysis of Montazeri steam po-wer plant in Iran. Renew Sustain Energy Rev 2016;56:454e63.

[47] Afrand M, Farahat S, Nezhad AH, Sheikhzadeh GA, Sarhaddi F. 3-D numericalinvestigation of natural convection in a tilted cylindrical annulus containingmolten potassium and controlling it using various magnetic fields. Int J ApplElectromagn Mech 2014;46:809e21.

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[50] Ahmadi G, Toghraie D, Akbari OA. Efficiency improvement of a steam powerplant through solar repowering. Int J Exergy 2017;22(2):158e82.

[51] Afrand M, Rostami S, Akbari M, Wongwises S, Esfe MH, Karimipour A. Effect ofinduced electric field on magneto-natural convection in a vertical cylindricalannulus filled with liquid potassium. Int J Heat Mass Tran 2015;90:418e26.

[52] Afrand M, Farahat S, Nezhad AH, Sheikhzadeh GA, Sarhaddi F. Numericalsimulation of electrically conducting fluid flow and free convective heattransfer in an annulus on applying a magnetic field. Heat Tran Res 2014;45:749e66.

[53] Ahmadi G, Toghraie D, Azimian A, Akbari OA. Evaluation of synchronousexecution of full repowering and solar assisting in a 200 MW steam powerplant, a case study. Appl Therm Eng 2017;112:111e23.

[54] Moraveji A, Toghraie D. Computational fluid dynamics simulation of heattransfer and fluid flow characteristics in a vortex tube by considering thevarious parameters. Int J Heat Mass Tran 2017;113:432e43.

[55] Ahmadi G, Toghraie D, Akbari OA. Solar parallel feed water heating repow-ering of a steam power plant: a case study in Iran. Renew Sustain Energy Rev2017;77:474e85.

[56] Keshavarz E, Toghraie D, Haratian M. Modeling industrial scale reactionfurnace using computational fluid dynamics: a case study in Ilam gas treatingplant. Appl Therm Eng 2017;123:277e89.