Journal Vol – 13 No -5, December 2018

Abstract:

As beam steering antennas are being an ideal solution for many satellite applications, this paper is concerned on the design of a 16-element linear array antenna, using an RT Duroid substrate at 20.2 GHz for Ka-Band satellite communications. The design is initiated with single element and thereby incremented in steps to 2, 4, 8 and 16 elements. An optimum inter element spacing of 0.73λ is considered for the purpose of fulfilling the desired scanning requirement. Performance analysis of the proposed antenna is analyzed mainly in terms of Relative Side Lobe level (RSLL) and Beam steering. To synthesize the antenna, weights of the antenna are considered according to Taylor’s amplitude distribution along the antenna aperture to attain a relative side lobe level of -25dB. The proposed 16-element linear array antenna achieved a maximum gain of 19.5dB and the main beam direction can be switched up to 50o (±25o) without introduction any grating lobes. In addition to, other relevant antenna parameters such as reflection coefficient, VSWR, gain and efficiency of single, 2, 4, 8 and 16 element antennas are compared. The proposed linear array antenna is designed using Ansoft HFSS.

Keywords:

Linear array antenna, Beam steering, Relative Side Lobe Level,Ka-Band,Satellite Communication Links, Taylor’s Amplitude distribution,

Refference:

I.A. Mehta, D.M. Syahkal, “Pattern steerable square loop antenna”. Electronics Letters., 43 (2007) 491-493.

II.Bondarik, Alexander, S. Daniel, “Pattern reconfigurable wideband stacked microstrip patch antenna for 60 GHz band”. International Journal of Antennas and Propagation., (2016).

III.Daly, P. Michael, T. B. Jennifer, “Beamsteering in pattern reconfigurable arrays using directional modulation”. IEEE Transactions on Antennas and Propagation., 58 (2010) 2259-2265.

IV.Li, Zhouyuan, A. Elsayed, E. Ahmed, M. Eltawil, B. A. Cetiner, “A beam-steering reconfigurable antenna for WLAN applications”. IEEE Transactions on Antennas and Propagation., 63 (2015) 24-32.

V.Nair, S. V. Shynu, M. J. Ammann, “Reconfigurable antenna with elevation and azimuth beam switching”. IEEE Antennas and Wireless Propagation Letters., 9 (2010) 367-370.

VI.Nor, M. Nuramirah, M. H. Jamaluddin, M. R. Kamarudin, M. Khalily, “Rectangular dielectric resonator antenna array for 28 GHz applications”. Progress In Electromagnetics Research., 63 (2016), 53-61.

VII.Pal, Arpan, A. Mehta, D. M. Syahkal, P. Deo, H. Nakano, “Dual-band low-profile capacitively coupled beam-steerable square-loop antenna”. IEEE Transactions on Antennas and Propagation., 62 (2014) 1204-1211.

VIII.Qin, Pei-Yuan, Y. J. Guo, C. Ding, “A beam switching quasi-Yagi dipole antenna”. IEEE Transactions on Antennas and Propagation., 61 (2013) 4891-4899.

IX.R. Guzmán-Quirós, A. R. Weily, J. L. Gómez-Tornero, Y. J. Guo, “A Fabry–Pérot antenna with two-dimensional electronic beam scanning”. IEEE Transactions on Antennasand Propagation., 64 (2016) 1536-1541.

X.Sabapathy, Thennarasan, F. Mohd, R. Jamlos, B. Ahmad, J. Muzammil, I. Mohd, M. R. Kamarudin, “Electronically reconfigurable beam steering antenna using embedded RF PIN based parasitic arrays (ERPPA)”. Progress In Electromagnetics Research., 140 (2013) 241-262.

XI.S. F. Maharimi, M. F. Abdul Malek, M. F. Jamlos, S. C. Neoh, M. Jusoh, “Impact of spacing and number of elements on array factor”. In PIERS Proceedings, Kuala Lumpur, MALAYSIA., (2012) 1550-1553.

XII.Suárez, Sara, G. L. Fernandez, M. Arrebola, L. F. H. Ontanon, F. L. H Andres, “Experimental validation of linear aperiodic array for grating lobe suppression”. Progress In Electromagnetics Research., 26 (2012) 193-203.

XIII.Tekkouk, Karim, H. Jiro, S. Ronan, E. Mauro, S. Makoto, A. Makoto, “Dual-layer ridged waveguide slot array fed by a Butler matrix with sidelobe control in the 60-GHz band”. IEEE Transactions on Antennas and Propagation., 63 (2015) 3857-3867.

XIV.Topak; Eray, Jürgen Hasch, Christoph Wagner, Thomas Zwick. “Anovel millimeter-wave dual-fed phased array for beam steering”. IEEE Transactions on Microwave Theory and Techniques., 61 (2013), 3140-3147.

XV.V. K. Kothapudi, V. Kumar, “Design of 0.73 λ inter-element spacing linear array for 0.43 GHz P/UHF-band tropospheric radar wind profiler”. In Synthetic Aperture Radar (APSAR), 2015 IEEE 5th Asia-Pacific Conference (2015) 277-282.

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Abstract:

In this paper, we explore the existence and uniqueness of positive solutions for the following nonlinear fourth order ordinary differential equation        (4) u t  f t,u t , t a, b , withthe following arbitrary two-point boundary conditions: ua  ub  ua  ub  0, where, a, b are two arbitrary constants satisfying b  0, a 1 b and f Ca,b0,,0,.Here we also demonstrate that under certain assumptions the above boundary value problem exist a unique symmetric positive solution. The analysis of this paper is based on a fixed point theorem in partially ordered metric spaces due to Amini-Harandi and Emami. The results of this paper generalize the results of several authors in literature. Finally, we provide some illustrative examples to support our analytic proof.

Keywords:

Arbitrary two-pointboundary conditions,Nonlinear fourthorder ordinary differential equation,Unique symmetric positive solutions,Fixed point theorem,

Refference:

I.A. Cabada, J.A. Cid, and L. Sanchez, Positivity andlower and upper solutions for fourth order boundary value problems,Nonl.Anal.67(5) (2007) 1599–1612.http://DOI: 10.1016/j.na.2006.08.002.

II.A. Amini-Harandi and H. Emami, A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations,Nonl.Anal.72(5) (2010) 2238–2242.http://DOI: 10.1016/j.na.2009.10.023.

III.C. Zhai, R. Song, Q. Han, The existence and the uniqueness of symmetric positive solutions for a fourth-order boundary value problem, Com. Math. Appl., 62 (2011) 2639-2647.https://doi.org/10.1016/j.camwa.2011.08.003.

IV.C. P. Gupta, Existence and uniqueness theorems for some fourth order fully quasilinearboundary value problems,Appl. Anal., 36(3-4) (1990) 157–169.

V.D.G. Zill, M.R. Cullen, Differential Equations with Boundary-Value Problems, 5thed., Brooks/Cole, (2001). ISBN10:0534380026, ISBN13:9780534380021.

VI.G. Bonanno, B. DiBella, D. O’Regan,Non-trivialsolutionsfornonlinearfourth-orderelasticbeamequations, Comp. Math. Appl.62(4) (2011) 1862-1869.https://doi.org/10.1016/j.camwa.2011.06.029

VII.H. Li, L. Wang, M. Pei, Solvability of a Fourth-Order Boundary Value Problem with Integral Boundary Conditions, J. Appl. Math., Hind. Publ. Corp., Volume 2013, Article ID 782363, 7 pages.http://dx.doi.org/10.1155/2013/782363.

VIII.J. Caballero, J. Harjani, K. Sadarangani, Uniqueness of Positive Solutions for a Class of Fourth-Order Boundary Value Problems, Abst. Appl. Anal, Hind. Publ. Corp.Vol. 2011, Art. ID 543035, 13 pages, http://doi:10.1155/2011/543035.

IX.J.P. Sun and X.Q. Wang, Monotone Positive Solutions for an Elastic Beam Equation with Nonlinear Boundary Conditions, Mathematical Problems in Engineering, Hind. Publ. Corp., Vol. 2011, Art. ID 609189, 9 pages. http://doi:10.1155/2011/609189.

X.J.R.L.Webb, G. Infante, and D. Franco, Positive solutions of nonlinear fourth-order boundary-value problems with local and non-local boundary conditions, Proc. Royal Soc.Edin.138(2) (2008) 427–446.http://doi: 10.1017/S0308210506001041.

XI.J. Liu1, W. Xu, Positive Solutions for Some Beam EquationBoundary Value Problems,Bound. V. Prob., Hind. Publ. Corp., Volume 2009, Article ID 393259, 9 pages.http://doi:10.1155/2009/393259.

XII.J. J. Nieto and R. Rodr ́ıguez-L ́opez, Contractive mapping theorems in partially ordered sets andapplications to ordinary differential equations, Order, 22(3) (2005) 223–239.

XIII.M. Feng, P. Li and S. Sun, Symmetric positive solutions for fourth-order n-dimensional m-Laplace systems,Bound. V.Probl.63 (2018).https://doi.org/10.1186/s13661-018-0981-3.

XIV.M. Pei and S. K. Chang, “Monotone iterative technique and symmetric positive solutions for a fourth order boundary value problem, Math. Comp. Model.51(9-10) (2010) 1260–1267.https://doi.org/10.1016/j.mcm.2010.01.009.

XV.R. Ma, J. Wang and D. Yan, The method of lower and upper solutionsfor fourth order equations with the Naviercondition, Bound. V. Probl. (2017) 2017:152 https://DOI: 10.1186/s13661-017-0887-5.

XVI.R. Ma, L. XuExistence of positive solutions of an onlinear fourth-order boundaryValue problem, Appl. Math.Lett. 23 (2010) 537–543.https://doi.org/10.1016/j.aml.2010.01.007

XVII.X. Lv, L. Wang and M. Pei, Monotone positive solution of a fourth-order BVP with integral boundary conditions, Bound. V.Probl.(2015) 2015:172.https://doi.org/10.1186/s13661-015-0441-2.

XVIII.X. L. Liu and W. T. Li, Existence and multiplicity of solutions for fourth-order boundary value problems with parameters,J. Math. Anal. Appl.327(1) (2007) 362–375.https://doi.org/10.1016/j.jmaa.2006.04.021.

XIX.Z. Bai, H. Wang, On positive solutions of some nonlinear fourth-order beam equations, J. Math. Anal. Appl. 270 (2002) 357–368.

XX.Z. Bai, The method of lower and upper solutions for abending of an elastic beam equation, J. Math. Anal. Appl.248(1) (2000) 195–202.http://doi:10.1006rjmaa.2000.688.

XXI.Z. Liu, S.M. Kang and J.S. Ume, Triple positive solutions of nonlinear third order boundary value problems, Taiw. J. Math., 13(3) (2009) 955-971. http://www.tjm.nsysu.edu.tw/.

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Abstract:

In the present internet world, Security is a prime vital concern and the secure hash function is one of the ideal alternative means to guarantee security. In this paper we made a study on different nonlinear dynamical systems – Chaotic maps and introduced a novel hash scheme based on integrated chaotic maps. The experimental outcomes shows that the proposed model satisfies all cryptographic properties of secure hash functions such as resistant to collisions, high level of sensitivity to initial conditions, high confusion and diffusion, high randomization etc. The suggested model is fast and accurate in terms of speed and security is concern. In this model, multiple chaotic maps are integrated as a single chaotic system to generate an n-bit digest value, where the length of digest is flexible in terms of security is concern.

Keywords:

Access Control,Authentication,Chaotic Maps,Complex Chaotic Maps,Integrity,

Refference:

I.A Kanso , H. Yahyaoui b, M. Almulla, “Keyed hash function based on a chaotic map”,Information Sciences 186 (2012) 249–264, Elsevier.

II.A Kanso, M. Ghebleh, “A fast and efficient chaos-based keyed hash function”, Commun Nonlinear Sci Numer Simulat 18 (2013) 109–123, Elsevier.

III.B Madhuravani, Dr. D.S.R. Murthy, “An Efficient Authentication Protocol to amplify collision resistance using Dynamic Cryptographic Hash Function & LSB Hop based Image Steganographic Technique”, International Journal of Applied Engineering Research, Volume 11, Number 7 PgNos: 5293-5296.(2016), ISSN 0973-4562.

IV.B Madhuravani, Dr. D.S.R. Murthy, “A NOVEL NODE INTEGRITY BASED AUTHENTICATION MODEL FOR DYNAMIC WIRELESS COMMUNCATION NETWORKS”, Journal of Advanced Research in Dynamical and Control Systems, ISSN: 1943-023X Issue: 12-Special Issue, (2017), Pages: 1145-1169.

V.Dean RD. Formal Aspects of Mobile Code Security. PhD thesis, Princeton University; (1999).

VI.Di Xiao a,b,, Xiaofeng Liao a, Shaojiang Deng , “Parallel keyed hash function construction based on chaotic maps”, Physics Letters A 372 (2008) 4682–4688, Elsevier.

VII.Di Xiao a, Xiaofeng Liao a, Yong Wanga,‟Improving the security of a parallel keyed hash function based on chaotic maps”, Physics Letters A 373 (2009) 4346–4353, Elsevier.

VIII.Joux A. Multicollisions in iterated hash functions. In: CRYPTO‟04, LNCS, vol. 3152; (2004). p. 306–16.

IX.Meysam Asgari Chenaghlu ∗, Shahram Jamali, Narjes Nikzad Khasmakhi,” A novel keyed parallel hashing scheme based on a new chaotic system”, Chaos, Solitons and Fractals 87 (2016) 216–225.

X.N. Chandra Sekhar Reddy, Dr. Purna Chandra Rao Vemuri, Dr. A. Govardhan, Ch. Vijay, “An empirical study on feature extraction techniques for Intrusion Detection system”, Journal of Advanced Research in Dynamicaland Control Systems, ISSN: 1943-023X Issue: 12-Special Issue, (2017),Pages: 1118-1130.

XI.NIST, Secure hash standard (SHS), federal information processing standards 180; (1993).

XII.NIST, secure hash standard (SHS), federal information processing standards 180-1; (1995).

XIII.NIST, secure hash standard (SHS), federal information processing standards 180-2; (2002).

XIV.Rivest R. The MD4 message digest algorithm. In: CRYPTO‟90, LNCS, vol. 537; 1991. p. 303–11.

XV.Rivest R. The MD5 message digest algorithm, request for comments (RFC) 1321. Internet engineering task force; (1992).

XVI.Shaojiang Deng, Yantao Li *, Di Xiao, «Analysis and improvement of a chaos-based Hash function construction”, Commun Nonlinear Sci Numer Simulat 15 (2010) 1338–1347, Elsevier.

XVII.Tian-Fu Lee, Efficient three-party authenticated key agreements based on Chebyshev chaotic map-based Diffie–Hellman assumption, Nonlinear Dynamics ,2014, vol 10,pp 23-43.

XVIII.Yantao Li ,Di Xiao, Parallel chaotic Hash function construction based on cellular neural network, Neural Comput & Applic (2012) 21:1563–1573.

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Abstract:

Mathematical treatment for numbers and arrays in the field of functional analysis need special interest. In the present paper, we will focus on a new alternative approach of greedy summation approach of unordered numbers and arrays. A theoretical background is firstly presentedregarding the numbers and arrays and their importance in the field of functional analysis, then the alternative approach for the greedy summation based on absolute values is presented. Some theoretical proofs regarding the relation between theoretical greedy summation and the Dirichlet series is presented in brief details. At the end of the present paper, some important conclusions are listed due to their importance and their effect for the upcoming research works.

Keywords:

Numbers,Arrays,unordered sum,Numerical arrays,Greedy sum of numbers,Greedy sum of arrays,convergence of series,Dirichlet series of array,

Refference:

I.E. V. Shchepin, Summation of Unordered Arrays, Functional Analysis and Its Applications, Vol. 52, No. 1, pp. 35–44, 2018.

II.G. H. Hardy, M. RieszThe general theory of Dirichlet’s series, Cambridge University Press, London, 1915.

III.M. Ruzhansky and D. Suragan, Adv. Math., Vol. 308, pp.483–528; http://arxiv.org/abs/1512.02547, 2017.

IV.M. Ruzhansky and D. Suragan, Proc. Amer. Math. Soc., Vol. 144, No. 2, pp. 709–721, 2016.

V.M. Ruzhansky and V. Turunen, Pseudo-Differential Operators and Symmetries, Background Analysis and Advanced Topics, Pseudo-Differential Operators, Theory and Applications, vol. 2, Basel, 2010.

VI.R. Graham, D. Knuth, and O. Patashnik, Concrete Mathematics: A Foundation of Computer Science, Addison-Wesley, Boston, 1994.

VII.S. V. Konyagin and V. N. Temlyakov, Convergence of greedy approximations I. General systems, Studia Math., Vol. 159, No.1, pp. 143-160, 2003.

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Abstract:

Portable water is a gift of God, which is used by human beings both for domestic and industrial purposes, but when it is polluted by certain reasons it become useless and adversely effects human health, aquatic life and threats the ground water. There are many sources of water pollution and Industrial pollution is one major source and concern for today’s world because toxic substances and chemicals used as raw products in industries is being discharged as residual to the water bodies if not treated. The HIE is no exception, where different industries are indiscriminately releasing their untreated effluents to open nallah, which ultimately makes its way into river Kabul while passing through urban and rural areas of Peshawar. The river Kabul water is widely used for irrigation purposes and is affecting the human and marine life because of the untreated toxic effluents. The study deals with the estimation and characterization of pollutions load discharged by the HIE and possible solutions to control these effluents at source i.e. at individual industrial level or at a Combined Effluent Treatment Plant (CETP). The study concluded that toxic effluents with high BOD, COD and TSS along with number of other heavy metals are released untreated. These effluents cannot be treated at source due to high cost and non-availability of land in existing developed industries. Also it is not advisable to install individual treatment plants due to lack of technical knowhow and high maintenance costs. The solution for this is to install a CETP at a suitable location on common benefit and maintenance cost mechanism.

Keywords:

Industrial estate, Combined Effluent Treatment Plant,Human health,Healthy Environment,

Refference:

I.Anonymous. 2001: The NEWS International, 2001.Water Quality Assessment.

II.Ali, A., H.N. Hashmi, I.A. Querashi and S. Athar, 2009: „Treatment feasibilityof NSSC pulpingeffluent using UASB reactor,‟ HYDRO Nepal: Journal ofWater, Energy and Environment(Kathmandu) 5:57-60.

III.Chillers, J. and A. Henrik. 1996: Effect of contaminated water. Global WaterHazards. Pp 25:25-27.

IV.IUCN. 1996: Sarhad Provincial ConservationStrategy Document: A report ofIUCN.

V.Industrial Estate Peshawar. Pakistan Journalof Agriculture Sciences 2: 457461.VI.Khan, S. and M. Noor. 2002: Investigationof pollutants in wastewater ofHayatabad

VII. Pak-EPA, 1999: EnvironmentalTechnology Programme for Industries (DraftEnvironmental Report), Islamabad: Environmental Protection Agency,Pakistan.

VIII. Panayotou, Theodore, 1994:Economic Instruments for EnvironmentalManagement andSustainableDevelopment, UNEP Environmental EconomicsSeries Paper No.16, Nairobi: UNEnvironment Program, Environment andEconomicsUnit.

IX. Shivkumar, K. and G. Biksham. 1995: Statistical approach for the assessmentof water pollutionaround industrial area. Environ Monitoringand Assessment36: 229-249.

X. Steel, E.W., 1995:Water Supply and Sewerage (6th ed.), London: McGraw Hill

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Abstract:

Nanotechnology has enticed a good attention in boosting base fluid such as crude oil. A mathematical model is investigated to study MHD Carreau crude oil based nanofluids. Analysis over stretching sheet surface is illustrated that include consideration of nanoparticles shape with high (E1=5.0) and low (E1=0.0) electric field. Depending on nanoparticle shape, deferent expects of nanofluids flow such that the shapes as (sphere, cylinder, lamina) to boost the heat and mass transfer. Employing convenient self-similar transformation, the set of partial differential equation converted to dimensionless system. These equations has numerically solution by apply Runge-Kutta Fehlberg form plus so-called shooting technique and solving algebraically in Maple 18. Effect of relevant parameters on all concerned profile are incurred to examine the heat and mass transfer properties. For thermal radiation and heat generation parameters the profiles are on negative worth of temperature, is seen in the out of boundary region all these physical behaviours are due to the combined effects of the viscosity and density of the crude oil. The result obtained that heat generation, Brownian motion and magnetic field hit a dominant role on  Al₂ O₃ Crude Oil. The investigation revealed that there is no important role for nanoparticle shapes on Al₂ O₃ Crude Oil.

Keywords:

MHD Carreau mode,crude oil-AL2O3,nanoparticle shapes,

Refference:

I.B. M’hamed,N. A. C. Sidik, M. N. A. W. M. Yazid, R. Mamat, G. Najafi, and G. H. R. Kefayati, ―A review on why researchers apply external magnetic field on nanofluids,‖ Int. Commun. Heat Mass Transf., vol. 78, pp. 60–67, 2016.

II.B. A. Suleimanov, F. S. Ismailov, and E. F. Veliyev, ―Nanofluid for enhanced oil recovery,‖ J. Pet. Sci. Eng., vol. 78, no. 2, pp. 431–437, 2011.

III.C. Negin, S. Ali, and Q. Xie, ―Application of nanotechnology for enhancing oil recovery–A review,‖ Petroleum, vol. 2, no. 4, pp. 324–333, 2016.

IV.D. Han, W. F. He, and F. Z. Asif, ―Experimental study of heat transfer enhancement using nanofluid in double tube heat exchanger,‖ Energy Procedia, vol. 142, pp. 2547–2553, 2017.

V.E. A. Taborda, C. A. Franco, S. H. Lopera, V. Alvarado, and F. B. Cortés, ―Effect of nanoparticles/nanofluids on the rheology of heavy crude oil and its mobility on porous media at reservoir conditions,‖ Fuel, vol. 184, pp. 222–232, 2016.

VI.J. Taheri-Shakib, A. Shekarifard, and H. Naderi, ―Heavy crude oil upgrading using nanoparticlesby applying electromagnetic technique,‖ Fuel, vol. 232, pp. 704–711, 2018.

VII.J. Y. Jang, M. M. Khonsari, and S. Bair, ―On the elastohydrodynamic analysis of shear-thinning fluids,‖ in Proceedings of the Royal Society of London A: Mathematical, Physical andEngineering Sciences, 2007, vol. 463, no. 2088, pp. 3271–3290.

VIII.M. Khan and A. Hafeez, ―A review on slip-flow and heat transfer performance of nanofluids from a permeable shrinking surface with thermal radiation: dual solutions,‖ Chem. Eng. Sci., vol. 173, pp. 1–11, 2017.

IX.M. Khan, ―A revised model to analyze the heat and mass transfer mechanisms in the flow of Carreau nanofluids,‖ Int. J. Heat Mass Transf., vol. 103, pp. 291–297, 2016.

X.M. Khan, M. Y. Malik, T. Salahuddin, and I. Khan, ―Numerical modelingof Carreau fluid due to variable thicked surface,‖ Results Phys., vol. 7, pp. 2384–2390, 2017.

XI.M. Azam, M. Khan, and A. S. Alshomrani, ―Effects of magnetic field and partial slip on unsteady axisymmetric flow of Carreau nanofluid over a radially stretching surface,‖ Results Phys., vol. 7, pp. 2671–2682, 2017.

XII.M. Khan, M. Y. Malik, and T. Salahuddin, ―Heat generation and solar radiation effects on Carreau nanofluid over a stretching sheet with variable thickness: Using coefficients improved by Cash and Carp,‖ Results Phys., vol. 7, pp. 2512–2519, 2017.

XIII.N. A. Ogolo, O. A. Olafuyi, and M. O. Onyekonwu, ―Enhanced oil recovery using nanoparticles,‖ in SPE Saudi Arabia section technical symposium and exhibition, 2012.

XIV.N. S. Akbar, S. Nadeem, R. U. Haq, and Z.H. Khan, ―Numerical solutions of Magnetohydrodynamic boundary layer flow of tangent hyperbolic fluid towards a stretching sheet,‖ Indian J. Phys., vol. 87, no. 11, pp. 1121–1124, 2013.

XV.N. Krishnan and B. S. Kumar, ―INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY REVIEW ON SHELL AND TUBE HEAT EXCHANGER USING NANOFLUIDS.‖

XVI.N. S. Akbar, S. Nadeem, R. U. Haq, and Z. H. Khan, ―Radiation effects on MHD stagnation point flow of nano fluid towards a stretching surface with convective boundary condition,‖ chinese J. Aeronaut., vol. 26, no. 6, pp. 1389–1397, 2013.

XVII.R. Tao and X. Xu, ―Reducing the viscosity of crude oil by pulsed electric or magnetic field,‖ Energy & fuels, vol. 20, no. 5, pp. 2046–2051, 2006.

XVIII.R. Kandasamy, N. A. bt Adnan, and R. Mohammad, ―Nanoparticle shape effects on squeezed MHD flow of water based Cu, Al2O3 and SWCNTs over a porous sensor surface,‖ Alexandria Eng. J., 2017.

XIX.R. Mohammad and R. Kandasamy, ―Nanoparticle shapes on electric and magnetic force in water, ethylene glycol and engine oil based Cu, Al2O3 and SWCNTs,‖ J. Mol. Liq., vol. 237, pp. 54–64, 2017.

XX.R. Dharmalingam, R. Kandasamy, and K. K. Sivagnana Prabhu, ―Lorentz forces and nanoparticle shape on water based Cu, Al2O3 and SWCNTs,‖ J. Mol. Liq., vol. 231, pp.663–672, 2017.

XXI.S. K. Das, S. U. S. Choi, and H. E. Patel, ―Heat transfer in nanofluids—a review,‖ Heat Transf. Eng., vol. 27, no. 10, pp. 3–19, 2006.

XXII.S. Z. Heris, M. N. Esfahany, and S. G. Etemad, ―Experimental investigation of convective heat transfer of Al2O3/water nanofluid in circular tube,‖ Int. J. Heat Fluid Flow, vol. 28, no. 2, pp. 203–210, 2007.

XXIII.T. Hayat, S. Asad, M. Mustafa, and A. Alsaedi, ―Boundary layer flow of Carreau fluid over a convectively heated stretching sheet,‖ Appl. Math. Comput.,vol. 246, pp. 12–22, 2014.

XXIV.T. Hayat, M. Z. Kiyani, I. Ahmad, and B. Ahmad, ―On analysis of magneto Maxwell nano-material by surface with variable thickness,‖ Int. J. Mech. Sci., vol. 131, pp. 1016–1025, 2017.

XXV.T. Fang, J. Zhang, and Y. Zhong, ―Boundary layer flow over a stretching sheet with variable thickness,‖ Appl. Math. Comput., vol. 218, no. 13, pp. 7241–7252, 2012.

XXVI.W. A. Khan and I. Pop, ―Boundary-layer flow of a nanofluid past a stretching sheet,‖ Int. J. Heat Mass Transf., vol. 53, no. 11–12, pp.2477–2483, 2010.

XXVII.W. Ibrahim, ―Magnetohydrodynamic (MHD) boundary layer stagnation point flow and heat transfer of a nanofluid past a stretching sheet with melting,‖ Propuls. Power Res., vol. 6, no. 3, pp. 214–222, 2017.

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