2017
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4
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Multiboiling Heat Transfer Analysis of a Convective Straight Fin with TemperatureDependent Thermal Properties and Internal Heat Generation
2
2
In this study, by using the finite volume method, the heat transfer in a convective straight fin with temperaturedependent thermal properties and an internal heat generation under multiboiling heat transfer modes are analyzed. In this regard, the local heat transfer coefficient is considered to vary within a powerlaw function of temperature. In the present study, the coexistence of all the boiling modes is taken into consideration. The developed heat transfer models and the corresponding numerical solutions are used to investigate the effects of various thermogeometric parameters on the thermal performance of the longitudinal rectangular fin. The results shows that the fin temperature distribution, the total heat transfer, and the fin efficiency are significantly affected by the thermogeometric parameters of the fin and the internal heat generation within the fin. The obtained results can provide a platform for improvements in the design of the fin in the heat transfer equipment.
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229
239


Gbeminiyi
Sobamowo
Department of Mechanical Engineering, University of Lagos, Akoka, Lagos, Nigeria
Department of Mechanical Engineering, University
Iran
mikegbeminiyi@gmail.com


Ola
Kamiyo
Department of Mechanical Engineering, University of Lagos, Akoka, Lagos, Nigeria
Department of Mechanical Engineering, University
Iran
okamiyo@unilag.edu.ng
Multiboiling heat transfer
Convective straight fin
Finite volume method
Temperaturedependent properties
Internal heat generation
[Khani, F., Aziz, A. Thermal analysis of a longitudinal trapezoidal fin with temperature dependent thermal conductivity and heat transfer coefficient, Communications in Nonlinear Science and Numerical Simulation,15, 2010, pp. 590601. ##Partner Ndlovu L., Raseelo Moitsheki J. Analytical Solutions for Steady Heat Transfer in Longitudinal Fins with TemperatureDependent Properties, Mathematical Problems in Engineering, 2013, 14 pages. ##Aziz, A. EnamulHuq, S.M. Perturbation solution for convecting fin with temperature dependent thermal conductivity, Journal of Heat Transfer, 97, 1973, pp. 300301. ##Aziz, A. Perturbation solution for convecting fin with internal heat generation and temperature dependent thermal conductivity, International Journal of Heat and Mass Transfer, 20, 1977, pp. 12535. ##Campo, A., Spaulding, R.J. Coupling of the methods of successive approximations and undetermined coefficients for the prediction of the thermal behaviour of uniform circumferential fins, Heat and Mass Transfer, 34(6), 1999, pp. 461468. ##ChingHuang, C., Cha’oKuang, C. A decomposition method for solving the convective longitudinal fins with variable thermal conductivity, International Journal of Heat and Mass Transfer, 45, 2002, pp. 20672075. ##Arslanturk, A. A decomposition method for fin efficiency of convective straight fin with temperature dependent thermal conductivity, International Communications in Heat and Mass Transfer, 32, 2005, pp. 831841. ##Ganji, D.D. The application of He’s homotopy perturbation method to nonlinear equations arising in heat transfer, Physics Letters A,355, 2006, pp. 337–341. ##He, J.H. Homotopy perturbation method, Computer Methods in Applied Mechanics and Engineering, 178, 1999, pp. 257–262. ##Chowdhury, M.S.H., Hashim, I. Analytical solutions to heat transfer equations by homotopyperturbation method revisited, Physical Letters A, 372, 2008, pp. 12401243. ##Rajabi, A. Homotopy perturbation method for fin efficiency of convective straight fins with temperature dependent thermal conductivity, Physics Letters A, 364, 2007, pp. 3337. ##Inc, M. Application of Homotopy analysis method for fin efficiency of convective straight fin with temperature dependent thermal conductivity, Mathematics and Computers Simulation, 79, 2008, pp. 189200. ##Coskun, S.B., Atay M.T. Analysis of Convective Straight and Radial Fins with Temperature Dependent Thermal Conductivity Using Variational Iteration Method with Comparision with respect to finite Element Analysis. Mathematical problem in Engineering, 2007, pp. 42072. ##Languri, E.M., Ganji, D.D, Jamshidi, N. Variational Iteration and Homotopy perturbation methods for fin efficiency of convective straight fins with temperature dependent thermal conductivity, 5th WSEAS Int. Conf. On FLUID MECHANICS (fluids 08) Acapulco, Mexico January 25 27, 2008. ##Coskun, S.B., Atay, M.T. Fin efficiency analysis of convective straight fin with temperature dependent thermal conductivity using variational iteration method, Applied Thermal Engineering, 28, 2008, pp. 2345–2352. ##Atay, M. T. and Coskun, S. B. Comparative Analysis of PowerLaw FinType Problems Using Variational Iteration Method and Finite Element Method, Mathematical Problems in Engineering, 2008, 9 pages. ##Domairry, G., Fazeli, M. Homotopy analysis method to determine the fin efficiency of convective straight fins with temperature dependent thermal conductivity, Communication in Nonlinear Science and Numerical Simulation, 14, 2009, pp. 489499. ##Chowdhury, M.S.H., Hashim, I., Abdulaziz, O. Comparison of homotopy analysis method and homotopypermutation method for purely nonlinear fintype problems, Communications in Nonlinear Science and Numerical Simulation, 14, 2009,pp. 371378. ##Khani, F., Ahmadzadeh Raji, M., Hamedi Nejad, H. Analytical solutions and efficiency of the nonlinear fin problem with temperaturedependent thermal conductivity and heat transfer coefficient, Communications in Nonlinear Science and Numerical Simulation, 14, 2009, pp. 33273338. ##Moitheki, R.J., Hayat, T., Malik, M.Y. Some exact solutions of the fin problem with a power law temperature dependent thermal conductivity, Nonlinear Analysis real world Application, 11, 2010, pp. 32873294. ##Hosseini, K, Daneshian, B., Amanifard, N., Ansari, R. Homotopy Analysis Method for a Fin with Temperature Dependent Internal Heat Generation and Thermal Conductivity, International Journal of Nonlinear Science, 14(2), 2012, pp. 201210. ##Joneidi, A.A., Ganji, D.D., Babaelahi, M. Differential Transformation Method to determine fin efficiency of convective straight fins with temperature dependent thermal conductivity, International communication in Heat and Mass transfer, 36, 2012, pp.757762. ##Moradi, A., Ahmadikia, H. Analytical Solution for different profiles of fin with temperature dependent thermal conductivity, Mathematical Problem in Engineering, 2010, pp. 568263. ##Mosayebidorcheh, S., Ganji, D.D., Farzinpoor, M. Approximate Solution of the nonlinear heat transfer equation of a fin with the powerlaw temperaturedependent thermal conductivity and heat transfer coefficient, Propulsion and Power Reasearch, 3(1), 2014, pp. 4147. ##Moradi, A., Ahmadikia, H. Investigation of effect thermal conductivity on straight fin performance with DTM, International Journal of Engineering and Applied Sciences, 1, 2011, pp. 4254. ##Ghasemi, S.E., Hatami, M., Ganji, D.D. Thermal analysis of convective fin with temperaturedependent thermal conductivity and heat generation, Cases Studies in Thermal Engineering, 4, 2014, pp. 18. ##Ganji, D.D., Dogonchi, A.S. Analytical investigation of convective heat transfer of a longitudinal fin with temperaturedependent thermal conductivity, heat transfer coefficient and heat generation, International Journal of Physical Sciences, 9(21), 2014, pp. 466474. ##Fernandez, A. On some approximate methods for nonlinear models, Applied Mathematics and Computation, 215, 2009, pp. 16874. ##Aziz, A., Bouaziz, A. A least squares method for a longitudinal fin with temperature dependent internal heat generation and thermal conductivity, Energy Conversion and Management, 52, 2011, pp. 28762882. ##]
Effect of Variable Thermal Expansion Coefficient and Nanofluid Properties on Steady Natural Convection in an Enclosure
2
2
Steady state natural convection is numerically investigated in an enclosure using variable thermal conductivity, viscosity and thermal expansion coefficient of Al2O3–water nanofluid. This study has been conducted for a wide range of Rayleigh numbers (103≤ Ra ≤ 106), concentrations of nanoparticles (0% ≤ Φ ≤ 7%), enclosure aspect ratios (0.5 ≤ AR ≤ 2) and temperature differences between the cold and the hot walls (1≤ ∆T≤ 30). The main idea in this study is about the effect of temperature on natural convection pattern of nanofluid by changing nanoparticles concentration. Also, changing thermal expansion coefficient with temperature is considerd in this study which will have significant effects on natural convection and has not been considerd before. In low Rayleigh numbers (Ra= 103) and for cavities with AR≥1, the pattern shown in the average Nusselt number versus volume fraction of nanoparticles diagram deteriorates by increasing ∆T. However, for other cases, increasing ∆T has a positive effect on NuΦ diagram. The actual Nuselt number curve depicts that dispersing nanoparticles in base fluid deteriorate natural convection heat transfer which is in a good agreement with experimental works.
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240
250


Esmaeil
Ghahremani
Department of Energy Engineering and Physics, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Islamic Republic of Iran
Department of Energy Engineering and Physics,
Iran
eghahremani86@gmail.com


Reihaneh
Ghaffari
University of Calgary, Canada
University of Calgary, Canada
Iran
reihaneh.ghaffari@ucalgary.ca


Hossein
Ghadjari
Department of Energy Engineering and Physics, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Islamic Republic of Iran
Department of Energy Engineering and Physics,
Iran


Javad
Mokhtari
Department of Mathematics, Isfahan (Khorasgan) Branch, Islamic Azad University, Isfahan, Iran
Department of Mathematics, Isfahan (Khorasgan)
Iran
javadmokhtari67@gmail.com
Nanofluid
Natural convection
variable property
[[1] Vahl Davis, G.D. Natural convection of air in a square cavity, a benchmark numerical solution, Int. J. Numer. Methods Fluids, 3, 1962, pp. 249–264. ##[2] Fusegi, T., Hyun, J.M., Kuwahara, K. Farouk, B. A numerical study of threedimensional natural convection in a differentially heated cubical enclosure, Int. J. Heat Mass Transfer, 34, 1991, pp. 1543–1557. ##[3] Barakos, G. Mitsoulis, E. Natural convection flow in a square cavity revisited: laminar and turbulent models with wall functions, Int. J. Numer. Methods Fluids, 18, 1994, pp. 695–719. ##[4] Choi, U.S. Enhancing thermal conductivity of fluids with nanoparticles, ASME Fluids Engineering Division, 231, 1995, pp. 99–103. ##[5] Xuan, Y., Roetzel, W. Conceptions for heat transfer correlation of nanofluids, Int. J. Heat Mass Transfer, 43, 2000, pp.3701–3707. ##[6] Khanafer, K., Vafai, K. Lightstone, M. Buoyancydriven heat transfer enhancement in a twodimensional enclosure utilizing nanofluids, Int. J. Heat Mass Transfer, 46, 2003, pp. 3639–3653. ##[7] Gosselin, L. da Silva, A.K. Combined heat transfer and power dissipation optimization of nanofluid flows, Appl. Phys. Lett., 85, 2004, pp.4160–4162. ##[8] Brinkman, H.C. The viscosity of concentrated suspensions and solutions, J. Chem. Phys., 20, 1952, pp.571–581. ##[9] Polidori, G., Fohanno, S. Nguyen, C.T. A note on heat transfer modeling of Newtonian nanofluids in laminar free convection, Int. J. Thermal Sciences, 46, 2007, pp. 739–744. ##[10] Ho, C.J., Chen, M.W. Li, Z. W. Numerical simulation of natural convection of nanofluid in a square enclosure: Effects due to uncertainties of viscosity and thermal conductivity, Int. J. Heat and Mass Transfer, 51, 2008, pp. 4506–4516. ##[11] Maiga, S.E.B., Nguyen, C.T., Galanis, N., Roy, G. Heat transfer behaviors of nanofluids in a uniformly heated tube, Superlattices and Microstructures, 35, 2004, pp. 543–557. ##[12] Aminossadati, S.M. Ghasemi, B. Natural convection of water–CuO nanofluid in a cavity with two pairs of heat source–sink, Int. Comm. in Heat and Mass Transfer, 38, 2011, pp. 672678. ##[13] Koo, J. Kleinstreuer, C. A new thermal conductivity model for nanofluids, J. Nanoparticle Research, 6(6), 2004, pp. 577–588. ##[14] Koo, J. Kleinstreuer, C. Laminar nanofluid flow in micro heatsinks, Int. J. Heat and Mass Transfer, 48(13), 2005, pp. 2652–2661. ##[15] AbuNada, E., Masoud, Z., Oztop, H.F. Campo, A. Effect of nanofluid variable properties on natural convection in enclosures, Int. J. Thermal Sciences, 49, 2010, pp. 479–491. ##[16] Nnanna, A.G.A., Fistrovich, T., Malinski, K. Choi, S.U.S. Thermal transport phenomena in buoyancydriven nanofluids, Proc. ASME Int. Mech. Eng. Congress RDD Expo., IMECE200462059, Anaheim, CA, 2004, pp. 18. ##[17] Nnanna, A.G.A. Routhu, M. Transport phenomena in buoyancy driven nanofluids Part II, Proc. ASME Summer Heat Transfer Conf., SHTC— 72782, San Francisco, CA, 2005, pp. 1–8. ##[18] Putra, N., Roetzel, W. Das, S.K. Natural convection of nanofluids, Heat Mass Transfer, 39, 2003, pp. 775–784. ##[19] Wen, D. Ding, Y. Formulation of nanofluids for natural convective heat transfer applications, Int. J. Heat and Fluid Flow, 26, 2005, pp. 855–864. ##[20] Wen, D. Ding, Y. Natural convection heat transfer of suspensions of titanium dioxide nanoparticles (nanofluids), IEEE Trans. Nanotechnol., 5(3), 2006, pp. 220–227. ##[21] Li, C.H. Peterson, G.P. Experimental studies of natural convection heat transfer of Al2O3/DI water nanoparticle suspensions (nanofluids), Advances in Mechanical Engineering, 2010, Article ID 742739. ##[22] Hu, Y., He, Y., Wang, S., Wang, Q. Schlaberg, H.I. Experimental and numerical investigation on natural convection heat transfer of Tio2–Water nanofluids in a square enclosure, ASME Journal of Heat Transfer, 136, 2014, Article ID 022502. ##[23] Nnanna, A.G.A. Experimental model of temperaturedriven nanofluid, ASME Journal of Heat Transfer, 129, 2007, pp.697–704. ##[24] Ho, C.J., Liu, W.K., Chang, Y.S. Lin, C.C. Natural convection heat transfer of aluminawater nanofluid in vertical square enclosures: An experimental study, Int. J. Thermal Sciences, 49, 2010, pp.1345–1353. ##[25] Corcione, M. Heat transfer features of buoyancydriven nanofluids inside rectangular enclosures differentially heated at the sidewalls, Int. J. Thermal Sciences, 49, 2010, pp.1536–1546. ##[26] Kestin, J., Sokolov, M. Wakeham, W.A. Viscosity of liquid water in the range 8 °C to 150 °C., J. Phys. Ref. Data, 7(3), 1978, pp. 941–948. ##[27] Sharqawy, M.H. New correlations for seawater and pure water thermal conductivity at different temperatures and salinities, Desalination, 313, 2013, pp. 97–104. ##[28] Patankar, S.V. Numerical Heat Transfer and Fluid Flow, Hemisphere Publishing Corporation, Taylor and Francis Group, New York, 1980. ##[29] Versteeg, H.K. Malalasekera, W. An Introduction to Computational Fluid Dynamic: The Finite Volume Method, John Wiley Sons Inc., New York, 1995. ##[30] Fusegi, T. Hyun, J.M. Laminar, Transitional natural convection in an enclosure with complex, realistic conditions, Int. J. Heat Fluid Flow, 15, 1994, pp. 258–268. ##[31] AbuNada, E. Effects of variable viscosity and thermal conductivity of Al2o3–water nanofluid on heat transfer enhancement in natural convection, Int. J. Heat and Fluid Flow, 30, 2009, pp. 679–690. ##[32] AbuNada, E. Chamkha, A.J. Effect of nanofluid variable properties on natural convection in enclosures filled with a CuOEGWater nanofluid, Int. J. Thermal Sciences, 49, 2010, pp. 2339–2352.##]
Investigation on the Ultrasonic Tube Hydroforming in the Bulging Process Using Finite Element Method
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2
In ultrasonic tube hydroforming, the tube is hydro formed while the ultrasonic vibration is applied to the die. Prior studies provide experimental proof that ultrasonic tube hydroforming reduces corner radius, improves lubrication and uniform thickness. Use of ultrasonic vibration can decrease friction at the tubedie interface. Few attempts have been made to analyze the wire drawing while the ultrasonic vibrations were also applied during the processes. A detailed analysis and understanding of the mechanism of improvement is not possible with conventional experimental observation because the ultrasonic vibration processing phenomenon occurs at high speed. Therefore, we attempt to understand the processing mechanism of ultrasonic tube hydroforming using the finite element method (FEM).ABAQUS was used for the FEM. Forming force and formability in tube hydroforming analyzed. From these studies, we quantitatively clarified the mechanism of improved formability characteristics, such as decreased forming load and increasing bulging diameter.
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251
257


Mehdi
Zarei
Department of Mechanical Engineering, Tarbiat Modares University (TMU),
Tehran 14115143, Iran
Department of Mechanical Engineering, Tarbiat
Iran
mehdi.zarei@modares.ac.ir


Gholam
Faghani
Department of Mechanical Engineering, Khatam Al Anbia Air Defense University,Tehran, Iran,178183513, Iran
Department of Mechanical Engineering, Khatam
Iran
g.r.faghani@stud.nit.ac.ir


Mahmood
Farzin
Department of Mechanical Engineering, Isfahan University of Technology
, Isfahan 8415683111, Iran
Department of Mechanical Engineering, Isfahan
Iran
farzin@cc.iut.ac.ir


Mohammad
Mashayekhi
Department of Mechanical Engineering, Isfahan University of Technology
, Isfahan 8415683111, Iran
Department of Mechanical Engineering, Isfahan
Iran
mashayekhi@cc.iut.ac.ir
tube hydroforming
ultrasonic oscillation
Finite Element Method
bulging process
[[1] Ngaile, G., Gariety, M., Altan, T. Enhancing tribological conditions in tube hydroforming by using textured tubes, Journal of Tribology, 128, 2006, pp. 674676. ##[2] Siegert, K., Haussermann, M., Losch, B., Rieger, R. Recent developments in hydroforming technology, Journal of Materials Processing Technology, 98, 2000, pp. 251258. ##[3] Ahmetoglu, M., Altan, T. Tube hydroforming: stateoftheart and future trends, Journal of Materials Processing Technology, 98, 2000, pp. 2533 ##[4] Ahmetoglu, M., Sutter, K., Li, X.J., Altan, T. Tube hydroforming: current research, applications and need for training, Journal of Materials Processing Technology, 98, 2000, pp. 224231. ##[5] Jirathearanat, S., Hartl, C., Altan, T. Hydroforming of Yshapes –product and process design using FEA simulation and experiments, Journal of Materials Processing Technology, 146, 2004, pp. 124129. ##[6] Liu, G., Yuan, S., Teng, B., Analysis of thinning at the transition corner in tube hydroforming, Journal of Materials Processing Technology, 177, 2006, pp. 688691. ##[7] Kridli, G.T., Bao, L., Mallick, P.K., Tian, Y. Investigation of thickness variation and corner filling in tube hydroforming, Journal of Materials Processing Technology, 133, 2003, pp. 287296. ##[8] Plancak, M., Vollertsen, F., Woitschig, J. Analysis, finite element simulation and experimental investigation of friction in tube hydroforming, Journal of Materials Processing Technology, 170, 2005, pp. 220228. ##[9] Jain, N., Wang, J. Plastic instability in dualpressure tube hydroforming process, International Journal of Mechanical Sciences, 47, 2005, pp. 18271837. ##[10] Mori, K., Maeno, T., Maki, S. Mechanism of improvement of formability in pulsating hydroforming of tubes, International Journal of Machine Tools & Manufacture, 47, 2007, pp. 978984. ##[11] Smith, L.M., Ganeshmurthy, S., Alladi, K. Doublesided high pressure tubular hydroforming, Journal of Materials Processing Technology, 142, 2003, pp. 599608. ##[12] Bunget, C., Ngaile, G. Microforming and Ultrasonic Forming, Report MFMAENG06R1, Department of Mechanical and Aerospace Engineering, North Carolina State University, 2006. ##[13] Murakawa, M., Jin, M. The utility of radially and ultrasonically vibrated dies in the wire drawing process, J. Mater. Process. Technol., 113, 2001, pp. 8186. ##[14] Hayashi, M., Jin, M., Thipprakmas, S., Murakawa, M., Hung, J.C., Tsai, Y.C., Hung, C.H. Simulation of ultrasonicvibration drawing using the finite element method (FEM), J. Mater. Process. Thecnol., 140, 2003, pp. 3035. ##[15] Siegert, K., Ulmer, J. Superimposing Ultrasonic Waves on the Dies in Tube and Wire Drawing, J. Eng. Mater. Technol., 123, 2001, pp. 517523. ##[16] Huang, Z., Lucas, M., Adams, M.J. Modeling wall boundary conditions in an elastoviscoplastic material forming process, J. Mater. Process. Technol., 107, 2000, pp. 267275. ##[17] Huang, Z., Lucas, M., Adams, M.J. Influence of ultrasonic on upsetting of a model paste, Ultrasonic, 40, 2002, pp. 4348 ##[18] LohMousavi, M., Mori, K., Hayashi, K., Maki, S., Bakhshi, M. 3D finite element simulation of pulsating Tshape hydroforming of tubes, Key Engng. Mater., 340, 2007, pp. 353–358. ##[19] Hama, T., Asakawa, M., Fukiharu, H., Makinouchi, A. Simulation of hammering hydroforming by static explicit FEM, ISIJ Int., 44(1), 2004, pp. 123–128. ##[20] Zarei, M., Farzin, M., Mashayekhi, M. Investigations on the ultrasonic assistance in the tube hydroforming process, Journal of Applied and Computational Mechanics, DOI: 10.22055/jacm.2017.21474.1102 ##[21] Bunget, C., Mechanics of Ultrasonic Tube Hydroforming, Ph.D. Dissertation, North Carolina State University, 2008.##]
Flow and Heat Transfer Analysis of the Sodium Alginate Conveying Copper Nanoparticles between Two Parallel Plates
2
2
In this study, the steady incompressible flow of a nonNewtonian sodium alginate (SA) fluid conveying copper nanoparticles (Cu) which flow within two vertical parallel plates is investigated by using the homotopy perturbation analytical scheme to solve the coupled nonlinear ordinary equations arising from the mechanics of the fluid. The developed analytical solutions are used to investigate the effect of the fluid flow and heat transfer parameters such as the nanoparticle concentration, the nonNewtonian parameter and the viscosity variation parameter. The obtained analytical results as compared to existing works in literature are in satisfactory agreements. Moreover, the results obtained from the present study can be used for further analysis of the behavior of the sodium alginate in applications such as food processing and chemical and pharmaceutical industries.
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258
266


Akin T.
Akinshilo
Mechanical Engineering Department; University of Lagos, AkokaYaba, 100001, Nigeria
Mechanical Engineering Department; University
Iran
ta.akinshilo@gmail.com


Joseph O.
Olofinkua
Mechanical Engineering Department; University of Lagos, AkokaYaba, 100001, Nigeria
Mechanical Engineering Department; University
Iran
josepholofinkua@yahoo.com


Osamudiamen
Olaye
Mechanical Engineering Department; University of Benin, Benin City, 300271, Nigeria
Mechanical Engineering Department; University
Iran
osamudiamen.olaye@uniben.edu
Sodium alginate
copper
parallel plates
perturbation
Nano fluid
NonNewtonian
[[1] Hatami, M., Ganji, D.D. Heat transfer and fluid flow analysis of SATiO2 nonNewtonian Nano fluid passing through porous media between two coaxial cylinder, Journal of Molecular Liquids, 188, 2013, pp. 155161. ##[2] Hatami, M., Ganji, D.D. Natural convection of sodium alginate (SA) nonNewtonian Nano fluid flow between two vertical flat plates by analytical and numerical methods, Thermal Engineering, 2, 2014, pp. 1422. ##[3] Ganji, D.D., Hashemi Kachapi, S.H. Analysis of nonlinear equations in fluids, Asian Academic Publisher Ltd, Hong Kong, 2011. ##[4] Hatami, M., Jing, D. Differential transformation method for Newtonian and nonNewtonian Nano fluid flow analysis: compared to numerical solution, Alexander Engineering Journal, 55, 2015, pp. 731739. ##[5] Ziabakhsh, Z., Domairry, G. Analytic solution of natural convection flow of a nonNewtonian fluid between two vertical flat plates using homotopy analysis method, Communication nonlinear Science Numerical Simulation, 14, 2009, pp. 18681880. ##[6] Ahmadi, A.R., Zahmatkesh, A., Hatami, M., Ganji D.D. A comprehensive analysis of the flow and heat transfer for nanofluid over an unsteady stretching flat plate, Powder Technology, 258, 2014, pp.125133. ##[7] Sheihol Eslami, M., Ganji, D.D., Ashorynejad, H.R. Investigation of squeezing unsteady Nano fluid flow using ADM, Powder Technology, 239, 2013, pp.259265. ##[8] Sheihol Eslami, M., Rashidi, M.M., Alsaad, D.M., Rokni, H.B. Steady Nano fluid flow between parallel plates considering thermophoresis and Brownian effects, Journal of King Saud University Science, 28(4), 2016, pp. 380389. ##[9] Pourmehran, O., RahimiGorji, M., GorjiBandpy, M., Ganji, D.D. Analytical investigation of squeezing unsteady Nano fluid flow between parallel plates by LSM and CM, Alexandria Engineering Journal, 54, 2015, pp.1726. ##[10] Mandy, A. Unsteady mixed convection boundary layer flow and heat transfer of Nano fluid due to stretching sheet, Nuclear Engineering, 249, 2012, pp.248255. ##[11] Hamad, M.A.A., Pop, I., Ismail, M.A.I. Magnetic field effects on free convection flow of a Nano fluid past a vertical semiinfinite plate, Nonlinear Analysis Real World Application, 12, 2011, pp.13381346. ##[12] Mustafa, M., Hayat, T., Obadiat, S. On heat and mass transfer in an unsteady squeezing flow between parallel plates, Mechanica, 47, 2012, pp. 15811589. ##[13] Siddiqui, A.M., Irium, S., Ansari, A.R. Unsteady squeezing flow of viscous MHD fluid between parallel plates, Mathematical Modeling Analysis, 13, 2008, pp. 565576. ##[14] Domairry, G., Hatami, M. Squeezing Cuwater Nano fluid flow analysis between parallel plates by DTMPade Method, Journal of Molecular Liquids, 188, 2014, pp.155161. ##[15] Afify, A.A., AbdelAzizi, M. Lie group analysis of flow and heat transfer of nonNewtonian Nano fluid, Pramana Journal of Physics, 31, 2017, pp. 88104. ##[16] Sheikholeslami, M., Abelman, S. Two phase simulation of Nano fluid flow and heat transfer in an annulus in the presence of an axial magnetic field, IEEE transaction on nanotechnology, 14, 2015, pp.561566. ##[17] Madaki, A.G., Roslan, R., Mohamed, M., Kamardan, M.G. Analytical solutions of squeezing unsteady nanofluid flow in the presence of thermal radiation, Journal of Computer Science and Computational Mathematics, 6, 2016, pp. 451463. ##[18] Adesanya, S.O., Falade, J.A. Thermodynamic analysis of hydro magnetic third grade fluid flow through a channel filled with porous medium, Alexandria Engineering Journal, 14, 2015, pp. 615622. ##[19] Hoshyar, H.A., Ganji, D.D., Borran, A.R., Falahatid, M. Flow behavior of unsteady incompressible Newtonian fluid flow between two parallel plates via homotopy analysis method, Latin American Journal of Solids and Structures, 12, 2015, pp. 18591869. ##[20] Myers, T.G., Charprin, J.P.F., Tshehia, M.S. Flow of a variable viscosity fluid between parallel plates with shear heating, Applied Mathematical Modeling, 30, 2006, pp.799815. ##[21] Kargar, A., Akbarzade, M. Analytical solution of Natural convection Flow of a nonNewtonian between two vertical parallel plates u,sing the Homotopy Perturbation Method, World Applied Sciences Journal, 20, 2012, pp. 14591465.##]
A Method for Determination of the Fundamental Period of Layered Soil Profiles
2
2
In this study, a method is proposed to determine the fundamental period of layered soil profiles. A model considering the layered soil as shear type structure is used. At first, the soil profile is divided into substructures. Then, the stiffness matrices of the substructures considered as the equivalent shear structures are assembled according to the Finite Element Method. Thereinafter, the stiffness matrices of the substructures are transformed into the Modified Finite Element Transfer Matrices, which take part in the literature. Finally, the system matrix is assembled using matrices of the substructures. The proposed method provides reduction in the size of the matrix. Therefore, analysis time is remarkably reduced. At the end of the study, the accuracy of the method is presented by the examples. Consequently, the proposed method offers a practical method for determination of the fundamental period of the soil.
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267
273


Duygu
Ozturk
Department of Civil Engineering., Faculty of Engineering, University of Ege, Bornova, Izmir, Turkey
Department of Civil Engineering., Faculty
Iran
duygu.ozturk@ege.edu.tr


K. Burak
Bozdogan
Department of Civil Engineering., Faculty of Engineering, University of Canakkale Onsekiz Mart, Canakkale, Turkey.
Department of Civil Engineering., Faculty
Iran
kbbozdogan@comu.edu.tr
Finite element
Soil profile
fundamental period
Transformation
Transfer matrix
[[1] Dobry, R.I., Oweis, I., Urzua, A. Simplified procedures for estimating the fundamental period of a soil profile, Bulletin of the Seismological Society of America, 66, 1976, pp. 12931321. ##[2] Gazetas, G. Vibrational characteristics of soil deposits with variable wave velocity, International Journal for Numerical and Analytical Methods in Geomechanics, 6, 1982, pp. 120. ##[3] Medina, F. Modeling of layered soilstructure interaction by infinite elements, Earthquake Engineering, Teneth World Conference, Balkema, Roterdam, 1992. ##[4] Singh, Y., Nagpal, A.K. Estimatıng fundamental period of soil profiles, Geotechnical Engineering, 24(2), 1977, pp. 167174. ##[5] Sarma, S.K. Analytical solution to the seismic response of viscoelastic soil layers, Géotechnique, 44(2), 1993, pp. 265275. ##[6] Hadjian, A.H. Fundamental period and mode shape of layered soil profiles, Soil Dynamics and Earthquake Engineering, 22, 2002, pp. 885891. ##[7] Sawada, S. A simplified equation to approximate natural period of layered ground on the elastic bedrock for seismic design of structures, 13th World Conference on Earthquake Engineering Vancouver, B.C., Canada, 2004. ##[8] Deb, K., Dey, A., Chandra, S. Modeling of layered soil system, 1st Indian Young Geotechnical Engineers Conference, Hyderabad, India, 23rd March, 5055, 2007. ##[9] Ruiz, S., Saragoni, S.R. Free vibration of soils during large earthquakes, Soil Dynamics and Earthquake Engineering, 29, 2009, pp. 116. ##[10] Vijayendra, K.V., Prasad, S.K., Nayak, S. Computation of Fundamental Period of Soil Deposit: A Comparative Study, Oxford, UK, second edition, Indian Geotechnical Conference, December 1618, 2010. ##[11] Choi, M.S. Free Vibration Analysis of Plate Structures Using Finite ElementTransfer Stiffness Coefficient Method, Journal of Mechanical Science and Technology, 17(6), 2003, pp. 805815. ##[12] Rong, B., Rui, X.T., Wang, G.P. Modified Finite Element Transfer Matrix Method for Eigenvalue Problem of Flexible Structures, Journal of Applied Mechanics, 78(2), 2011, 021016. ##[13] Ozturk, D., Bozdogan, K., Nuhoglu, A. Modified finite elementtransfer matrix method for the static analysis of structures, Structural Engineering and Mechanics, 43(6), 2012, pp. 761769. ##[14] Iyisan, R., Hatipoglu, M., Ozudogru, T.Y. Determination of shear wave velocity by suspension ps logging method, 16th National Congress of Soil Mechanics and Geotechnical Engineering, Erzurum, Turkey, 2016.##]
Bending, Buckling and Vibration of a Functionally Graded Porous Beam Using Finite Elements
2
2
This study presents the effect of porosity on mechanical behaviors of a power distribution functionally graded beam. The EulerBernoulli beam is assumed to describe the kinematic relations and constitutive equations. Because of technical problems, particle size shapes and microvoids are created during the fabrication which should be taken into consideration. Two porosity models are proposed. The first one describes properties in the explicit form as linear functions of the porosity parameter. The second is a modified model which presents porosity and Young’s modulus in an implicit form where the density is assumed as a function of the porosity parameter and Young’s modulus as a ratio of mass with porosity to the mass without porosity. The modified proposed model is more applicable than the first model. The finite element model is developed to solve the problem by using the MATLAB software. Numerical results are presented to show the effects of porosity on mechanical behaviors of functionally graded beams.
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274
282


Noha
Fouda
Production Engineering and mechanical Design Dept, Mansoura University
Al Mansurah, Egypt
Production Engineering and mechanical Design
Iran
nfooda@gmail.com


Tawfik
Elmidany
Production Engineering and mechanical Design Dept, Mansoura University
Al Mansurah, Egypt
Production Engineering and mechanical Design
Iran
tawfikm@gmail.com


A. M.
Sadoun
Mechanical Engineering Dept, King Abdulaziz University, Jeddah, Saudi Arabia
AND
Mechanical Design and Production Eng. Dept., Zagazig University,
Al Zagazig, Egypt
Mechanical Engineering Dept, King Abdulaziz
Iran
aymansadoun76@gmail.com
Mechanical Behaviors
Porous material
Functionally graded material
Beam Analysis
Finite Element Method
[[1] Eltaher, M.A., Khairy, A., Sadoun, A.M., Omar, F.A. Static and buckling analysis of functionally graded Timoshenko nanobeams, Applied Mathematics and Computation, 229, 2014, pp. 283295. ##[2] Zhu, J., Lai, Z., Yin, Z., Jeon, J., Lee, S. Fabrication of ZrO 2–NiCr functionally graded material by powder metallurgy, Materials Chemistry and Physics, 68(1), 2001, pp. 130135. ##[3] Aqida, S.N., Ghazali, M.I., Hashim, J. Effects of porosity on mechanical properties of metal matrix composite: an overview, Jurnal Teknologi, 40, 2004, pp. 1732. ##[4] Kim, H.S., Yang, Y., Koh, J.T., Lee, K.K., Lee, D.J., Lee, K.M., Park, S.W. Fabrication and characterization of functionally graded nano‐micro porous titanium surface by anodizing, Journal of Biomedical Materials Research Part B: Applied Biomaterials, 88B, 2009, pp. 427435. ##[5] Wattanasakulpong, N., Prusty, B.G., Kelly, D.W., Hoffman, M. Free vibration analysis of layered functionally graded beams with experimental validation, Materials & Design, 36, 2012, pp. 182190. ##[6] Ji, S., Gu, Q., Xia, B. Porosity dependence of mechanical properties of solid materials, Journal of Materials Science, 41, 2006, pp. 17571768. ##[7] Wattanasakulpong, N., Ungbhakorn, V. Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities, Aerospace Science and Technology, 32, 2014, pp. 111120. ##[8] Wattanasakulpong, N., Chaikittiratana, A. Flexural vibration of imperfect functionally graded beams based on Timoshenko beam theory, Chebyshev collocation method, Meccanica, 50(5), 2015, pp. 13311342. ##[9] Atmane, H.A., Tounsi, A., Bernard, F. Effect of thickness stretching and porosity on mechanical response of a functionally graded beams resting on elastic foundations, International Journal of Mechanics and Materials in Design, 13, 2015, pp. 7184. ##[10] Ebrahimi, F., Mokhtari, M. Transverse vibration analysis of rotating porous beam with functionally graded microstructure using the differential transform method, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 37, 2015, pp. 14351444. ##[11] Ebrahimi, F., Jafari, A. A fourvariable refined sheardeformation beam theory for thermomechanical vibration analysis of temperaturedependent FGM beams with porosities, Mechanics of Advanced Materials and Structures, 23, 2016, pp. 113. ##[12] Ebrahimi, F., Ghasemi, F., Salari, E. Investigating thermal effects on vibration behavior of temperaturedependent compositionally graded Euler beams with porosities, Meccanica, 51, 2016, pp. 223249. ##[13] Shafiei, N., Mousavi, A., Ghadiri, M. On sizedependent nonlinear vibration of porous and imperfect functionally graded tapered microbeams, International Journal of Engineering Science, 106, 2016, pp. 4256. ##[14] Ebrahimi, F., Barati, M.R. Sizedependent vibration analysis of viscoelastic nanocrystalline silicon nanobeams with porosities based on a higher order refined beam theory, Composite Structures, 166, 2017, pp. 256267. ##[15] Magnucki, K., Stasiewicz, P. Elastic buckling of a porous beam, Journal of Theoretical and Applied Mechanics, 42(4), 2004, pp. 859868. ##[16] Jabbari, M., Mojahedin, A., Joubaneh, E.F. Thermal Buckling Analysis of Circular Plates Made of Piezoelectric and Saturated Porous Functionally Graded Material Layers, Journal of Engineering Mechanics, 141(4), 2015, pp. 112. ##[17] Xue, L., Dui, G., Liu, B., Xin, L. A phenomenological constitutive model for functionally graded porous shape memory alloy, International Journal of Engineering Science, 78, 2014, pp. 103113. ##[18] Chen, D., Yang, J., Kitipornchai, S. Elastic buckling and static bending of shear deformable functionally graded porous beam, Composite Structures, 133, 2015, pp. 5461. ##[19] Kitipornchai, S., Chen, D., Yang, J., Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets, Materials & Design, 116, 2017, pp. 656665. ##[20] Hamed, M.A., Eltaher, M.A., Sadoun, A.M., Almitani, K.H. Free vibration of symmetric and sigmoid functionally graded nanobeams, Applied Physics A, 122(9), 2016, pp. 829839. ##[21] Ebrahimi, F., Zia, M., Large amplitude nonlinear vibration analysis of functionally graded Timoshenko beams with porosities, Acta Astronautica, 116, 2015, pp. 117125. ##[22] Sarkar, B.K., Mukherjee, M. K., Natarajan, A. A modification of the rule of mixture in estimating strengths of a composite, Materialwissenschaft und Werkstofftechnik, 13(8), 1982, pp. 269273. ##[23] Bert, C.W. Prediction of elastic moduli of solids with oriented porosity, Journal of Materials Science, 20(6), 1985, pp. 22202224. ##[24] Hardin, R.A., Beckermann, C. Effect of porosity on the stiffness of cast steel, Metallurgical and Materials Transactions A, 38(12), 2007, pp. 29923006. ##[25] Wachtman, J.B., Cannon, W.R., Matthewson, M.J. Mechanical properties of ceramics, John Wiley & Sons, New York, 2009. ##[26] Sabree, I., Gough, J.E., Derby, B. Mechanical properties of porous ceramic scaffolds: influence of internal dimensions, Ceramics International, 41(7), 2015, pp. 84258432. ##[27] Zok, F.W., Levi, C.G. Mechanical properties of porousmatrix ceramic composites, Advanced Engineering Materials, 3(12), 2001, pp. 1523. ##[28] Revel, G.M. Measurement of the apparent density of green ceramic tiles by a noncontact ultrasonic method, Experimental Mechanics, 47(5), 2007, pp. 637648. ##[29] Eltaher, M.A., Hamed, M.A., Sadoun, A.M., Mansour, A. Mechanical analysis of higher order gradient nanobeams, Applied Mathematics and Computation, 229, 2014, pp. 260272. ##[30] Alshorbagy A.E., Eltaher M.A., Mahmoud F.F. Free vibration characteristics of a functionally graded beam by finite element method, Applied Mathematical Modelling, 35(1), 2011, pp. 412–425. ##[31] Eltaher, M.A., ElBorgi, S., Reddy, J.N. Nonlinear analysis of sizedependent and materialdependent nonlocal CNTs, Composite Structures, 153, 2016, pp. 902913.##]
Finite Element Analysis for CFST Columns under Blast Loading
2
2
The columns of frame structures are the key loadbearing components and the exterior columns are susceptible to attack in terrorist blasts. When subjected to blast loads, the columns would suffer a loss of bearing capacity to a certain extent due to the damage imparted which may lead to their collapse and even cause the progressive collapse of the whole structure . The concretefilled steel columns have been extensively used in the world due to the existence of all suitable characteristics of concrete and steel, more ductility, increasing concrete confinement using the steel wall, the large energyabsorption capacity and the appropriate fire behavior. In the present study, the concretefilled steel square columns have been simulated under the influence of the blast load using the ABAQUS software. These responses have been compared for scaled distances based on the distance to the source and the weight of the explosive material. As a result, it can be seen that although concrete deformation has been restricted using the steel tube, the inner layer of concrete has been seriously damaged and the column displacement has been decreased by increasing the scaled distance. We also concluded that the concretefilled steel columns have the high ductility and the blast resistance.
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283
292


Peyman
Beiranvand
Department of Civil Engineering, Lorestan University, Khorram abad, Iran
Department of Civil Engineering, Lorestan
Iran
peyman51471366@gmail.com


Fereydoon
Omidinasab
Department of Civil Engineering, Lorestan University, Khorram abad, Iran
Department of Civil Engineering, Lorestan
Iran
omidinasab@gmail.com


Marziye
Sadate Moayeri
Lecturer, Civil Engineering faculty, Borujerd Branch, Islamic Azad University, Iran
Lecturer, Civil Engineering faculty, Borujerd
Iran
a.moayeri1990@yahoo.com


Shahpoor
Mehdipour
Department of Civil Engineering
Arak Branch, Islamic Azad University, Iran
Department of Civil Engineering
Arak Branch,
Iran
mehdipoor1349@gmail.com


Mohammad
Zarei
Department of Civil engineering, Imam Khomeini international university, Qazvin, Iran
Department of Civil engineering, Imam Khomeini
Iran
mohammadzarei959@yahoo.com
Blast Load
ConcreteFilled Steel Columns
Finite Element Analysis
[[1] Choi, Y.H., Foutch, D.A., LaFave, J.M. New approach to AISC PM interaction curve for square concrete filled tube (CFT) beam–columns,Engineering Structures, 28(11), 2006, pp. 1586–1598. ##[2] Choi, Y.H., Kim, K.S., Choi, S.M. Simplified PM interaction curve for square steel tube filled with highstrength concrete, ThinWalled Structures, 465, 2008, pp. 506–515. ##[3] Krauthammer, T. Modern Protective Structures, Taylor & Francis Group, New York, NY, USA, 2008. ##[4] Fujikura, S.C., Bruneau, M., LopezGarcia, D. Experimental investigation of blast performance of seismically resistant concretefilled steel tube bridge piers, Tech. Rep. MCEER07 0005, University at Buffalo, Buffalo, NY, USA, 2007. ##[5] Fujikura, S., Bruneau, M., LopezGarcia, D. Experimental investigation of multihazard resistant bridge piers having concretefilled steel tube under blast loading, Journal of Bridge Engineering, 13(6), 2008, pp. 586–594. ##[6] Li, G., Qu, H., Yang, T., Lu, Y., Chen, S. Experimental study of concretefilled steel tubular columns under blast loading, Journal of Building Structures, 34(12), 2013, pp. 69–76. ##[7] Remennikov, A.M., Uy, B. Explosive testing and modelling of square tubular steel columns for nearfield detonations, Journal of Constructional Steel Research, 101, 2014, pp. 290–303. ##[8] Ngo, T., Mohotti, D., Remennikov, A., Uy, B. Numerical simulations of response of tubular steel beams to closerange explosions, Journal of Constructional Steel Research, 105, 2015, pp. 151–163. ##[9] Zhang, F.R., Wu, C.Q., Wang, H.W., Zhou, Y. Numerical simulation of concrete filled steel tube columns against BLAST loads, ThinWalled Structures, 92, 2015, pp. 82–92. ##[10] Zhang, F., Wu, C., Zhao, X., Li, Z., Heidarpour, A., Wang, H. Numerical modeling of concretefilled doubleskin steel square tubular columns under blast loading, Journal of Performance of Constructed Facilities, 29(5), 2015, B4015002. ##[11] BS EN 199312, “Euro code 3: design of steel structures, Part 1.2: General rules structural fire design”, London, British Standards Institution, 2005. ##[12] BS EN 1994–1–2, “Euro code 4: design of composite steel and concrete structures. Part 1.2: general rules–structural fire design”, London, British Standards Institution, 2005. ##[13] ABAQUS standard user’s manual, 1–3. USA: Hibbitt, Karlsson and Sorensen, Inc; 2008. version 6.81. ##[14] TM51300, Structures to resist the effects of accidental explosions, US Army, USA, 1990. ##[15] Bing, L., TsoChien, P., Anand, N. A case study of the effect of cladding panels on the response of reinforced concrete frames subjected to distant blast loadings, Nuclear Engineering and Design, 239(3), 2009, pp. 455469. ##[16] Brode, H.L. Numerical solutions of spherical blast waves, Journal of Applied Physics, 26, 1955, pp.766766. ##[17] Newmark, N.M. Protective Construction Review Guidehardening, Defense Technical Information Center, 1961, pp. 324.##]
Modified USlot Stacked MicroStrip Patch Antenna for UltraWideband Applications in S Band, C Band and X Band
2
2
The Uslot microstrip patch antennas were originally developed for bandwidth broadening applications. This study presents a transmission line feed to modify the Uslot stacked rectangular microstrip patch antenna for UltraWide Band (UWB) communications. The modified antenna has a Ucut loaded with parallel slits and corner slots and is printed on a dielectric substrate of FR4 with relative permittivity (εr) of 4.4, the thickness of 1.59 mm and the tangent loss of 0.025. The results show that the proposed antenna achieves an impedance bandwidth of 11.55 GHz (2.1 – 13.65 GHz) with the return loss < (10) dB. This antenna can be employed for ultrawideband applications in S Band, C Band and X Band. The proposed patch antenna is designed and simulated by using IE3D 14.0 software. Simulation results are presented in terms of the resonant frequency, the return loss, VSWR, the impedance bandwidth and the impedance matching.
1

293
301


Monika
Surana
Poorima College of Engineering, Jaipur, Rajasthan, India
Poorima College of Engineering, Jaipur, Rajasthan,
Iran
suranamonika@gmail.com


Amit
Jain
Poornima College Of Engineering, Jaipur
Poornima College Of Engineering, Jaipur
Iran
jain.2102@gmail.com
UWB antenna
VSWR
IE3D & Return Loss
[[1] Kahrizi, M., Sarkar, T.K., Maricevic, Z.A. Analysis of a wide radiating slot in the ground plane of a microstrip line, IEEE Trans. Microw. Theory Tech., 41(1), 1993, pp. 29–37. ##[2] Chiou, J.Y., Sze, J.Y., Wong, K.L. A broadband CPWFed strip loaded square slot antenna, IEEE Trans. Antennas Propag., 51(4), 2003, pp. 719–721. ##[3] Chen, H.D. Broadband CPWFed square slot antennas with a widened tuning stub, IEEE Trans. Antennas Propagation, 51(4), 2003, pp. 1982–1986. ##[4] Gupta, N., Gupta, V. Gain and Bandwidth Enhancement in Compact Microstrip Antenna, Birla Institute of Technology, Mesra, Ranchi835215, INDIA, 2005. ##[5] Yoharaaj, D., Azmir, R.S., Ismail, A. A new approach for bandwidth enhancement technique in microstrip antenna for wireless applications, International RF and Microwave Conference, Putrajaya, Malaysia, 1214 September, 2006. ##[6] Pozar, D.M. A review of bandwidth enhancement techniques for microstrip antennas, Microstrip Antennas: Analysis and Design of Microstrip Antennas and Arrays, D. H. Schaubert (ed.), 157–166, IEEE Press, New York, 1995 ##[7] Tang, C.L., Chiou, J.Y., Waong, K.L. Beamwidth enhancement of circularly polarized microstrip antenna mounted on a three – dimensional ground structure, Microwave Opt. Technol. Lett., 32(2), 2002, pp. 149–154 ##[8] Mandal, K., Sarkar, S., Sarkar, P.P. Bandwidth enhancement of microstrip antennas by staggering effect, Microwave Opt. Technol. Lett., 53(10), 2011, pp. 2446–2447. ##[9] Wu, C.K., Wong, K.L. Broadband microstrip antenna with directly coupled and parasitic patches, Microwave Opt. Technol. Lett., 22(5), 1999, pp. 348–349. ##[10] Surana, M., Sharma, O.P. Analysis of Triple Band Rectangular Patch Antenna Loaded With Pairs of L Shaped Slots, International Journal of Computer Applications, 111(12), 2015, pp. 3641. ##[11] Kumar, R., Vijay, R. A Compact Multiband Frequency Agile Microstrip Slot Antenna, International Conference on Advanced Computing & Communication Technologies, 5, 2015, pp. 811. ##[12] Nornikman, H., Malek, F., Saudin, N., Shukor, M., Zainuddin, N.A., Abd Aziz, M.Z.A., Ahmad, B.H., Othman, M.A. Design of Rectangular Stacked Patch Antenna with Four LShape Slots and CPWFed for WiMAX Application, 3rd International Conference on Instrumentation, Communications, Information Technology and Biomedical Engineering, Bandung, 78 November, 2013. ##[13] Colles, D., Arakaki, D. Multi Technique Broadband Microstrip Patch Antenna Design, IEEE Transactions on Antennas and Propagations, Memphis, TN, USA, 2014, pp. 18791880. ##[14] Balanis, C.A. Antenna theory analysis and design, John Wiley & Sons, Inc., Hoboken, New Jersey, 2005.##]