Simulation of convection heat transfer of magnetic nanoparticles including entropy generation using CVFEM

International Journal of Heat and Mass Transfer 136 (2019) 146–156 Contents lists available at ScienceDirect International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt Simulation of convection heat transfer of magnetic nanoparticles including entropy generation using CVFEM Tawfeeq Abdullah Alkanhal a, M. Sheikholeslami b, A. Arabkoohsar c, Rizwan-ul Haq d, Ahmad Shafee e, Zhixiong Li f,g,⇑, I. Tlili h a Department of Mechatronics and System Engineering, College of Engineering, Majmaah University, Al-Majmaah 11952, Saudi Arabia Department of Mechanical Engineering, Babol Noshirvani University of Technology, Babol, Islamic Republic of Iran Department of Energy Technology, Aalborg University, Denmark d Department of Electrical Engineering, Bahria University Islamabad Campus, Islamabad, Pakistan e Public Authority of Applied Education & Training, College of Technological Studies, Applied Science Department, Shuwaikh, Kuwait f School of Engineering, Ocean University of China, Qingdao 266110, China g School of Mechanical, Materials, Mechatronic and Biomedical Engineering, University of Wollongong, Wollongong, NSW 2522, Australia h Department of Mechanical and Industrial Engineering, College of Engineering, Majmaah University, Al-Majmaah 11952, Saudi Arabia b c a r t i c l e i n f o Article history: Received 16 December 2018 Received in revised form 23 February 2019 Accepted 26 February 2019 Keywords: Numerical simulation MHD Convection Nanomaterial Entropy generation CVFEM a b s t r a c t An investigation has been conducted to study Lorentz effect on nanomaterial behavior within a permeable space including innovative numerical technique namely CVFEM. Iron oxide has been mixed with H2O and porous domain was filled with this nanomaterial. The impacts of the flow and geometric variables on entropy generation along with the heat transfer have been examined. The simulations have been carried out with wide ranges of the magnetic force, permeability and Rayleigh numbers. The outcomes indicate that the Darcy term has inverse relationship with temperature of hot surface. Stronger convection mode and lower exergy loss appear when buoyancy forces augment. Entropy generation goes up with growth of Hartmann number. Ó 2019 Elsevier Ltd. All rights reserved. 1. Introduction Nanomaterials have the proficiency to augment heat efficiency of carrier liquids. Base liquid have poor heat transport competence and should be modified. Various shape and type of nanoparticles can change the heat transfer rate. Nanomaterials have wide utilization in industrial and technological processes like power generator, cooling of papers, micro-reactors, etc. Xu et al. [1] developed their code for nanomaterial flow inside a duct. They considered microorganisms’ impact, too. Hybrid nanoparticles convection within an annulus with two wires has been simulated by Sheikholeslami et al. [2]. They employed COMSOL software. Triangular open cavity has been investigated by Bondareva et al. [3] to find the impact of Brownian diffusion. Roles of MHD on double diffusion micropolar flow were analyzed by Mishra et al. [4]. Utilization of CVFEM for second law analysis has been examined by Sheikholeslami [5]. ⇑ Corresponding author at: School of Engineering, Ocean University of China, Qingdao 266110, China. E-mail address: zhixiongli@cumt.edu.cn (Z. Li). https://doi.org/10.1016/j.ijheatmasstransfer.2019.02.095 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved. He assumed that domain is under the impact of magnetic forces. Nanomaterial entropy generation due to MHD with including variable heating was modeled by Malik and Nayak [6]. They also utilized porous medium to augment convection. Khan et al. [7] tried to present Dual solution for unsteady nanomaterial MHD flow. Enclosure with different permeable block was investigated by Gibanov et al. [8]. They employed MHD and examined entropy generation. Rayleigh-Bénard problem with nanomaterial has been solved by Yadav et al. [9]. They added magnetic force to eliminate thermal plume. Astanina et al. [10] carried out numerical examination for MHD effect on entropy generation. Qi et al. [11] extended their LBM code for two phase simulation of nanomaterial with buoyancy effect. CNT nanoparticles behavior in appearance of tilted magnetic field was demonstrated by Haq et al. [12]. They utilized two various carrier fluids along slip plate. These days, scientists try to discover new ways to augment thermal properties of carrier fluid [13–36]. This article aims to study impacts of permeability, buoyancy and Lorentz forces on the hydrothermal efficiency and entropy generation of nanomaterial inside a porous tank. Homogeneous 147 T.A. Alkanhal et al. / International Journal of Heat and Mass Transfer 136 (2019) 146–156 Nomenclature Ha Xd V B Da Nu T Be Ra Sgen CVFEM Hartmann number exergy loss vertical velocity magnetic field Darcy number Nusselt number temperature Bejan number Rayleigh number entropy generation control volume based finite element method Greek symbols dynamic viscosity b thermal expansion coefficient h temperature X vorticity r electrical conductivity l Subscripts f carrier fluid M due to Lorenz th thermal nf nanomaterial nanomaterial in appearance of magnetic force was simulated via CVFEM. Various cases have been reported. Based on the outcomes, good correlations in terms of permeability, buoyancy and Lorentz forces have been developed. 2. Explanation of geometry and formulation Here entropy generation and natural convection through a permeable geometry which is demonstrated in Fig. 1, has been modeled. Ferrofluid with properties of Table 1 was considered as carrier fluid. Viscosity of ferrofluid is function of B which is mentioned in below formulation [37]. Magnetic field is imposed in x direction. Buoyancy forces are estimated by Boussinesq model. Boundary condition for inner elliptic wall is uniform heat flux and outer sinusoidal kept in cold temperature. To enforce the porous space terms in governing equations, non-Darcy model was used. Considering two dimensional flow yields below formulation: @ v @u þ ¼0 @y @x ð1Þ
 Bx ; By ¼ Bo ðcosc; sincÞ;    h ¼ rnf By v Bx qnf @u v þ u @u @y @x qnf  @v @y k
nf qC p nf  v þ @@xv u lnf ¼ K v þ lnf þBx uBy rnf @2T @2T þ @x2 @y2 ! B2y rnf u @P @x  @2 v @x2 @P @y lnf K uþ  2 þ @@yv2 þ qnf g ðT B2x  @2 u @y2  i 2 þ @@x2u lnf ð2Þ T c Þbnf ð3Þ v rnf ;   @T @T ¼ u þv @x @y ð4Þ Ferrofluid properties can be found by using below six formulas: RR ¼ ks kf ;   þ2/RRþ2kf þks kf kn f ¼ /RRþ2k þks ð5Þ f   lnf ¼ 0:035B2 þ 3:1B 27886:4807/2 þ 4263:02/ þ 316:0629 e qnf ¼ þqs / þ ð1 /Þqf 1þ h
qC p  1
f qC p  s ð6Þ ð7Þ i

 1 1 / ¼ qC p nf qC p f rnf 3ð@ 1Þ/ ¼ þ 1; rs =rf ¼ @ rf ð@ þ 2Þ þ ð1 @Þ/ ðqbÞnf ¼ /ðqbÞs þ ð1 0:01T ð8Þ ð9Þ /ÞðqbÞf ð10Þ By using Eq. (11), we could remove pressure terms and Eq. (12) help us to present equation in dimensionless forms: v¼ Fig. 1. Porous enclosure under the influence of imposed B. wx ; uy 1 v x ¼ x; DT ¼ kf Lq00 ; ðT ð11Þ T Þc ¼ HDT; u ¼ af U=L; ð12Þ ðx; yÞ ¼ LðX; Y Þ; v ¼ af V=L; Table 1 Details of Fe3O4 and H2O. Cp (J/kg K) b  105 (K 1) r (X
m) 1 k (W/m
K) q (kg/m3) u ¼ wy ; Fe3O4 H2O 670 1.3 25,000 6 5200 4179 21 0.05 0.613 997.1 Table 2 Obtained Nuav e for mesh analysis when at / ¼ 0:04,Da ¼ 100; Ha ¼ 40; and Ra ¼ 104 . 151  51 1.6889 181  61 1.6971 211  71 1.7076 241  81 1.7085 271  91 1.7094 148 T.A. Alkanhal et al. / International Journal of Heat and Mass Transfer 136 (2019) 146–156 Ra=104 0.0018 0.0016 0.0014 0.0012 0.001 0.0008 0.0006 0.0004 0.0002 0.0001 6E-05 5.94515E-05 1.5E-05 4.5E-06 2.5E-06 3 2.5 2 1.5 1 0.5 Sgen,f 0.5 0.4 0.3 0.2 0.1 0.01 0.00085 0.0008 0.00075 0.0007 0.00065 0.0006 0.00055 0.0005 0.00045 0.0004 0.00035 0.0003 0.00025 0.0002 0.00015 0.0001 5E-05 0.00038 0.00036 0.00034 0.00032 0.0003 0.00028 0.00026 0.00024 0.00022 0.0002 0.00018 0.00016 0.00014 0.00012 0.0001 8E-05 6E-05 4E-05 2E-05 0.04 0.038 0.036 0.034 0.032 0.03 0.028 0.026 0.024 0.022 0.02 0.018 0.016 0.014 0.012 0.01 0.008 0.006 0.004 0.002 Be 9.5E-06 9E-06 8.5E-06 8E-06 7.5E-06 7E-06 6.5E-06 6E-06 5.5E-06 5E-06 4.5E-06 4E-06 3.5E-06 3E-06 2.5E-06 2E-06 1.5E-06 1E-06 5E-07 0.65 0.6 0.55 0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 Sgen,th 0.7 0.65 0.6 0.55 0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0.7 0.65 0.6 0.5 0.45 0.4 0.3 0.2 0.1 0.05 0.01 Xd Sgen,p Sgen,M Isotherms Streamlines Ra=103 0.999 0.998 0.997 0.996 0.995 0.994 0.993 0.992 0.991 0.99 0.989 0.988 0.987 0.986 0.985 0.984 0.983 200 190 180 170 160 150 140 130 120 110 100 90 80 70 60 50 40 30 20 10 Fig. 2. Effect of Ra on first and second law analysis at Ha ¼ 1; / ¼ 0:04; Da ¼ 0:01. 0.12 0.1 0.08 0.06 0.04 0.03 0.02 0.01 0.007 0.003 0.002 0.0008 0.0002 5.2E-05 1E-05 0.7 0.65 0.6 0.55 0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0.03 0.02 0.01 0.005 0.98 0.96 0.94 0.92 0.9 0.88 0.86 0.84 0.8 0.76 0.72 0.68 0.64 0.56 0.52 0.48 0.44 200 190 180 170 160 150 140 130 120 110 100 90 80 70 60 50 40 30 20 10 149 T.A. Alkanhal et al. / International Journal of Heat and Mass Transfer 136 (2019) 146–156 Ra=103 Ra=104 0.06 0.05 0.04 0.03 0.02 0.01 0.7 0.6 0.5 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 1.3E-05 1.2E-05 1.1E-05 1E-05 9E-06 8E-06 7E-06 6E-06 5E-06 4E-06 3E-06 2E-06 1E-06 0.00115 0.00105 0.00095 0.00085 0.00075 0.0007 0.00065 0.0006 0.00055 0.0005 0.00045 0.0004 0.00035 0.0003 0.00025 0.0002 0.00015 0.0001 5E-05 Sgen,f Be 0.00022 0.0002 0.00018 0.00016 0.00014 0.00012 0.0001 8E-05 6E-05 4E-05 2E-05 1E-05 1E-06 0.021 0.02 0.019 0.018 0.017 0.016 0.015 0.014 0.013 0.012 0.011 0.01 0.009 0.008 0.007 0.006 0.005 0.004 0.003 0.002 0.001 Sgen,th 0.7 0.65 0.6 0.55 0.5 0.45 0.4 0.35 0.25 0.15 0.05 Xd Sgen,p Sgen,M Isotherms Streamlines 0.55 0.5 0.4 0.3 0.2 0.1 0.07 0.05 0.02 0.0001 9E-05 8E-05 7E-05 6E-05 5E-05 4E-05 3E-05 2.5E-05 2E-05 1.5E-05 1E-05 5E-06 9.5E-07 5.5E-07 2E-07 1.2E-07 3.5E-08 1.4E-08 0.75 0.7 0.65 0.6 0.55 0.5 0.45 0.4 0.35 0.25 0.15 0.1 0.05 0.025 0.9998 0.999737 0.9995 0.999 0.9985 0.998 0.9975 0.997 0.9965 200 190 180 160 140 120 110 100 80 60 40 20 10 Fig. 3. Effect of Ra on first and second law analysis at Ha ¼ 40; / ¼ 0:04; Da ¼ 0:01. 0.01 0.008 0.006 0.004 0.003 0.002 0.001 9E-05 4.5E-05 1.8E-05 1E-05 6E-06 3.5E-06 1.5E-06 0.7 0.65 0.6 0.55 0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0.02 0.999283 0.994379 0.98 0.96 0.94 0.92 0.9 0.88 0.86 0.84 0.82 0.8 0.76 0.72 0.68 0.64 0.6 200 190 180 170 150 130 120 110 90 70 60 50 40 30 10 150 T.A. Alkanhal et al. / International Journal of Heat and Mass Transfer 136 (2019) 146–156 Sgen,p 0.000115 0.00011 0.000105 0.0001 9.5E-05 9E-05 8.5E-05 8E-05 7.5E-05 7E-05 6.5E-05 6E-05 5.5E-05 5E-05 4E-05 3E-05 2E-05 1.5E-05 1E-05 5E-06 1.05E-06 1E-06 9.5E-07 9E-07 8.5E-07 8E-07 7.5E-07 7E-07 6.5E-07 6E-07 5.5E-07 5E-07 4.5E-07 4E-07 3.5E-07 3E-07 2.5E-07 2E-07 1.5E-07 1E-07 5E-08 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0.0025 0.0023 0.0021 0.0019 0.0015 0.0013 0.0011 0.001 0.0009 0.0008 0.0007 0.0006 0.0005 0.0004 0.0003 0.0002 0.0001 2.2E-05 2.1E-05 2E-05 1.9E-05 1.8E-05 1.7E-05 1.6E-05 1.5E-05 1.4E-05 1.3E-05 1.2E-05 1.1E-05 1E-05 9E-06 8E-06 7E-06 6E-06 5E-06 4E-06 3E-06 2E-06 1E-06 Sgen,th 0.65 0.6 0.55 0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 7 6 5 4 3 2 1 Be Sgen,M Isotherms Streamlines 2.2 2 1.5 1 0.5 0.1 Sgen,f Ra=104 Xd Ra=103 0.008 0.007 0.006 0.005 0.004 0.0035 0.003 0.0025 0.002 0.0015 0.001 0.0005 0.0003 0.0001 5.6E-05 0.7 0.65 0.6 0.55 0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0.03 0.995 0.99 0.985 0.98 0.975 0.97 0.965 0.96 0.955 0.95 0.945 0.94 0.935 0.93 0.925 0.92 0.915 0.91 200 190 180 170 160 150 140 130 120 110 100 90 80 70 60 50 40 30 20 10 Fig. 4. Effect of Ra on first and second law analysis at / ¼ 0:04; Ha ¼ 1; Da ¼ 100. 0.28 0.26 0.24 0.22 0.2 0.18 0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0.006 0.0027 0.001 0.0004 0.65 0.6 0.55 0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0.01 0.005 0.003 0.95 0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.55 0.5 0.45 0.4 0.35 0.3 0.25 0.2 200 190 180 170 160 150 140 130 120 110 100 90 80 70 60 50 40 30 20 10 151 T.A. Alkanhal et al. / International Journal of Heat and Mass Transfer 136 (2019) 146–156 0.00026 0.00024 0.00022 0.0002 0.00018 0.00016 0.00014 0.00012 0.0001 8E-05 6E-05 4E-05 2E-05 1.5E-09 1.4E-09 1.3E-09 1.2E-09 1.1E-09 1E-09 9E-10 8E-10 7E-10 6E-10 5E-10 4E-10 3E-10 2E-10 1E-10 0.7 0.55 0.45 0.35 0.25 0.2 0.15 0.1 0.05 0.023 0.021 0.019 0.017 0.015 0.013 0.012 0.011 0.01 0.009 0.008 0.007 0.006 0.005 0.004 0.003 0.002 0.001 1.3E-07 1.2E-07 1.1E-07 1E-07 9E-08 8E-08 7.5E-08 6.5E-08 6E-08 5.5E-08 5E-08 4.5E-08 4E-08 3.5E-08 3E-08 2.5E-08 2E-08 1.5E-08 1E-08 5E-09 Sgen,th 0.7 0.65 0.6 0.55 0.5 0.45 0.35 0.25 0.15 0.05 0.6 0.5 0.4 0.3 0.2 0.1 0.05 Be 0.065 0.06 0.05 0.04 0.03 0.02 0.01 0.005 0.001 Sgen,f Ra=104 Xd Sgen,p Sgen,M Isotherms Streamlines Ra=103 0.00011 9E-05 7E-05 5E-05 4E-05 3E-05 2E-05 1E-05 1.1E-06 6E-07 2E-07 6E-08 3.2E-08 0.75 0.7 0.65 0.6 0.55 0.5 0.45 0.4 0.35 0.3 0.25 0.15 0.05 0.01 0.9998 0.9995 0.999 0.9985 0.998 0.9975 0.997 0.9965 0.996 0.9955 0.9945 0.9925 0.9915 200 180 160 140 130 120 110 100 90 80 70 60 50 40 30 20 10 Fig. 5. Effect of Ra on first and second law analysis at Ha ¼ 40; / ¼ 0:04; Da ¼ 100. 0.0115 0.0095 0.0075 0.0055 0.005 0.0045 0.004 0.0035 0.003 0.0025 0.002 0.0015 0.001 0.0005 0.0001 6E-05 3E-05 9E-06 0.7 0.6 0.55 0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0.98 0.96 0.94 0.92 0.9 0.88 0.86 0.84 0.82 0.8 0.78 0.76 0.74 0.72 0.68 0.64 0.6 0.56 200 190 180 170 160 150 140 130 120 110 100 90 80 70 50 30 10 152 T.A. Alkanhal et al. / International Journal of Heat and Mass Transfer 136 (2019) 146–156 Fig. 6. Changes of Nuav e respect to Ha; Ra; Da at / ¼ 0:04. T.A. Alkanhal et al. / International Journal of Heat and Mass Transfer 136 (2019) 146–156 Fig. 7. Changes of Be respect to Ha; Ra; Da at / ¼ 0:04. 153 154 T.A. Alkanhal et al. / International Journal of Heat and Mass Transfer 136 (2019) 146–156 Fig. 8. Changes of X d respect to Ha; Ra; Da at / ¼ 0:04. 155 T.A. Alkanhal et al. / International Journal of Heat and Mass Transfer 136 (2019) 146–156 Therefore, last formulations are obtained as below: V @2H @H @H þU ¼ @Y @X @Y 2 þ ! @2H @X 2 ð13Þ WXX þ WYY ¼ X ð14Þ    2 Pr A5 A2 þ @@XX2 X Da A1 A4 h i  2 2 A A þHa2 Pr A61 A24 V Y ðsincÞðcoscÞ þ ðcoscÞU X ðsincÞ þ ðsincÞ U Y V X ðcoscÞ
A A2  þRa Pr @@XH A3 A22 ¼ U @@XX þ @@YX V Pr  4. Results and discussion A5 A2 A1 A4  @2 X @Y 2 1 4 ð15Þ The above three equations, following parameters have been employed: Da ¼ LK2 ; Ra ¼ gbf q} L4 =ðkf tf af Þ; qffiffiffiffiffiffiffiffiffiffiffiffiffi ðq C Þ A2 ¼ ðqCPP Þnf ; Ha ¼ LB0 rf =lf ; f ðqbÞnf ðqbÞf A1 ¼ qnf qf ; A4 ¼ knf kf ; A6 ¼ rnf f A3 ¼ ð16Þ l ; A5 ¼ lnf ; Pr ¼ tf =af ; f r Based on Fig. 1, boundary conditions can be summarized as: W ¼ 0:0 @H @n on every surfaces ¼ 1:0 on elliptic wall H ¼ 0:0 ð17Þ Nuav e ¼ 1:99 þ 0:14Da þ 0:25logðRaÞ þ0:079Da logðRaÞ on outer wall Nuloc and Nuav e are determined from: In current paper, we calculated entropy generation, Bejan number, Nusselt number and exergy loss: Sgen;total In current manuscript, insertions of permeable medium and dispersing magnetic nanoparticles into carrier fluid have been applied to help the convection in appearance of magnetic force. Characteristics of nanomaterial were predicted with assumption of single phase model and final equations were solved via new numerical technique. Simulations based of CVFEM were conduct to demonstrate the roles of permeability, Hartmann and buoyancy forces. Not only the heat transfer but also entropy generation and exergy drops are our goal factors in current paper. Outputs of exergy drop, entropy generation, w and temperature contours were reported in Figs. 2–5. As buoyancy force is augmented vertical velocity of nanomaterial enhances (jwmax j augments) and more heat is transmitted to upper side of domain. Presence of thermal plume can prove this fact, too. Obtaining greater heat transfer cause exergy loss to decline. Imposing magnetic field yields reduction in velocity. Therefore, entropy generation augments with growth of Ha. Sgen,p, Sgen,f and Sgen,M act as same as each other while their behavior has inverse relationship with Sgen,th. The contours show that when permeability has been enhanced, although the convection augments, reduction of exergy loss has been observed. Nuav e ; Be and X d as functions of the Da, Ra and Ha were demonstrated in Figs. 6–8. Besides, below formulas can make sense for relationship of variables and outputs. "    2 #  2 2 @v @u @ v @u ¼þ 2 2 þ þ2 þ @y @x @x @y T |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} lnf X d ¼ 45:62 0:14Da Ha 1:86Da 0:3Ha ð22Þ 0:23logðRaÞHa 2:89logðRaÞ þ 4:3Ha ð23Þ 0:65Da logðRaÞ þ 1:83Da Ha þ 2:73logðRaÞHa Be ¼ 0:041 logðRaÞHa þ 0:94 7:8  10 3 logðRaÞDa 0:0581 logðRaÞ 3 0:01 Da þ 9:4  10 Da Ha þ 0:044Ha ð24Þ Sgen;f 2 1 B2 2 0 lnf
2 2  þ rnf v þ v þu KT T ffl} |fflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflffl{zfflfflfflfflfflfflffl Sgen;M h 1 Sgen;th ¼ Be Sgen;total Nuav e ¼ 1 S Z
2 i þ ðT x Þ þ T y knf T 2 |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} 2 Sgen;th s Nuloc ds; Nuloc ¼ 0 Sgen;P ð18Þ ð19Þ   1!   knf 4 1 knf 1 þ Rd 3 h kf kf X d ¼ T 0 Sgen;total ð20Þ ð21Þ 3. Method, validation and mesh In recent eight years, Sheikholeslami [37] developed innovate numerical technique (CVFEM) in which lower computational cost needs for solving heat transfer problems. He employed this method for various fields. He published his experiences as nice reference book [37]. Each numerical code needs to be verified. In order to do not write repeated text about validation, we refer the reader to previous published article [38] which is done via current code. Accordingly, developed code has high accuracy. Besides, to make sure independence of outputs to mesh size, different configurations have been taken into account and one example exists in Table 2. Hot surface temperature declines with rise of permeability. So, rate of heat transfer enhances and Bejan number declines with rise of Da. An increase in Ha causes to decline in convection flow of nanomaterial and help to augmentation of exergy drop. Thus, Be is in direct relationship with Hartmann number. Greater Be has been obtained in lower Ra when conduction is more pronounced. 5. Conclusions In current article, results of thermal behavior, exergy drop and entropy generation of nanomaterial within a porous domain have been demonstrated. Domain is affected by horizontal magnetic field and inner elliptic is hot source. Changing of Darcy, Hartmann and Rayleigh numbers has been simulated via CVFEM. Outputs were reported as contours and good correlations. Outcomes prove that Be goes up with rise of Hartmann but it declines with augment of Ra and Da. Conflict of interest The author declares that there is no conflict of interest. Acknowledgment Dr. Tawfeeq Abdullah Alkanhal would like to thank Deanship of Scientific Research at Majmaah University for supporting this work under the Project Number No. 1440-49. 156 T.A. Alkanhal et al. / International Journal of Heat and Mass Transfer 136 (2019) 146–156 Author Contributions Dr. Tawfeeq Abdullah Alkanhal preside the actual team works start and generate the idea from the beginning till publication, he establish the mathematical formulation, modeled the problem. After modeling with his team he checked the result and wrote the related section. Other authors thoroughly checked the mathematical modeling and English corrections. All authors finalized the manuscript after its internal evaluation. References [1] Xu. Hang, Ji-Feng Cui, Mixed convection flow in a channel with slip in a porous medium saturated with a nanofluid containing both nanoparticles and microorganisms, Int. J. Heat Mass Transf. 125 (2018) 1043–1053. [2] M. Sheikholeslami, S.A.M. 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