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DYNAMIC STRUCTURAL ANALYSIS OF ENGINE CRANKSHAFT AT DIFFERENT ANGLE OF CRANK TURNS FOR THREE DIFFERENT MATERIALS

Authors:

Fida Hussain Jamali, Saifullah Samo, Intizar Ali Tunio, Abdul Fatah Abbasi, Qadir Bakhsh Jamali

DOI NO:

https://doi.org/10.26782/jmcms.2021.03.00007

Abstract:

For many years, engines have been one of the main power machinery of different kinds of applications, and the main part of power machinery is a crankshaft that converts the piston's reciprocating displacement with four-link mechanisms into rotary motion. . The major limitation of the engine crankshaft is fatigue failure due to repeated load caused by bending and torsional load. In this paper, the comparative dynamics structural analysis was carried out for three different materials such as forged steel, cast iron, and chromium-molybdenum steel with different angles of turns of cranks from 0° to 720° and to predict the stresses, deformation, and fatigue life of crankshaft without compromising its weight, strength and reliability. The 3D CAD model was simulated with FEA software. The simulated results show that by applying bending load and torsional load for three materials, the maximum stresses produced in the fillet area of the main bearing journal and in the fillet area of the crankpin journal at a crank angle of 360° respectively. The deformation results revealed that maximum deformation occurs at the mid-surface of the crankpin. From fatigue life prediction it was observed that forged steel and chromium-molybdenum steel shows better fatigue life as compared to cast iron. Moreover, in the comparative study, it was concluded that chromium-molybdenum steel shows fewer stresses and better fatigue life. Therefore it is suggested that chromium-molybdenum steel would be the better option for manufacturing crankshaft.

Keywords:

Dynamics Analysis,Engine Crankshaft,Finite Element Analysis,Fatigue Life,Stress Distribution,Deformation Distribution,

Refference:

I. Aldhaidhawi Mohanad, Muneer Naji, Abdel Nasser Ahmed. : EFFECT OF IGNITION TIMINGS ON THE SI ENGINE PERFORMANCE AND EMISSIONS FUELED WITH GASOLINE, ETHANOL AND LPG, J. Mech. Cont.& Math. Sci., Vol.-15, No.-6, June (2020) pp 390-401
II. Degefe, M., P. Paramasivam, and T. Dabasa, “Optimization and Finite Element Analysis of Single Cylinder Engine Crankshaft for Improving Fatigue Life”. American Journal of Mechanical and Materials Engineering, 2017. 1(3): p. 58-68.
II. Fonte, M., et al., Failure mode analysis of two crankshafts of a single cylinder diesel engine. Engineering Failure Analysis, 2015. 56: p. 185-193.
III. Gopal, G.; Kumar, L. S.; Reddy, K. V. B.; Rao, M. U. M. and Srinivasulu, G. Analysis of Piston, Connecting Rod and Crank Shaft Assembly. Materials Today: Proceedings 2017, 4, 7810-7819.

IV. Horváth, P. and Égert, J. Stress Analysis and Weight Reduction of a One-Cylinder Engine Crankshaft. Acta Technica Jaurinensis 2015, 8, 201-217.
V. Metkar, R.M., et al., “Evaluation of FEM based fracture mechanics technique to estimate life of an automotive forged steel crankshaft of a single cylinder diesel engine”. Procedia Engineering, 2013. 51: p. 567-572.
VI. Montazersadgh, F.H. and A. Fatemi, Dynamic load and stress analysis of a crankshaft. 2007, SAE Technical Paper.
VII. Pratiksha M. Nargolkar. “Analysis of Crankshaft”. International Journal of Scientific Engineering and Research, 2015.p.122-127.
VIII. R. Jagadeesh Kumar, K. Phaniteja, K. Sambasiva Rao. “Transient Structural Analysis Of A Single Cylinder 4 Stroke Petrol Engine Crankshaft,” international journal of advanced technology in engineering and science., 2017 vol .5, pp 559-612.
IX. Sandya, K.; Keerthi, M. and Srinivas, K. Modeling and Stress Analysis of Crankshaft Using Fem Package Ansys. International Research Journal of Engineering and Technology IRJET 2016, 3, 687-693.
X. Saurabh P. Jangam, Satish Kumar, Shruti Maheshwari.” Literature review on analysis of various components of IC engine”. Materials Today: Proceedings,2018.:p. 19027–19033.
XI. Thejasree, P., G.D. Kumar, and S.L.P. Lakshmi, “Modelling and Analysis of Crankshaft for passenger car using ANSYS”. Materials Today: Proceedings, 2017. 4(10): p. 11292-11299.
XII. Witek, L.; Sikora, M.; Stachowicz, F. and Trzepiecinski, T. Stress and Failure Analysis of the Crankshaft of Diesel Engine. Engineering Failure Analysis 2017, 82, 703-712.
XIII. Williams, J.R., F. Montazersadgh, and A. Fatemi, Fatigue Performance Comparison and Life Predictions of Forged Steel and Ductile Cast Iron Crankshafts. 2007, University of Toledo.

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ON ASYMPTOTIC APPROXIMATIONS OF THE SOLUTION FOR TRANSLATING STRING UNDER EXTERNAL DAMPING

Authors:

Sindhu Jamali, Khalid H. Malak, Sanaullah Dehraj, Sajad H. Sandilo, Zubair A. Kalhoro

DOI NO:

https://doi.org/10.26782/jmcms.2021.03.00008

Abstract:

In this paper, a mathematical model for an externally damped axially moving string is studied. This mathematical model is a second order partial differential equation which is a wave-like equation. The String is assumed to be externally damped by the viscous medium such as oil, and there is no restriction on the parametric values of the damping parameter. From a physical point of view, a string is represented as a chain moving in oil in the  positive horizontal direction between pair of pulleys. The axial speed of the string is assumed to be constant, positive and small compared to wave-velocity. To approximate the exact solutions of the initial-boundary value problem, the straightforward expansion method has been used to obtain valid approximations. It will be shown that if the damping parameter is neglected then the method breaks down as expected, and if damping is present in the system then the amplitudes of the oscillations are damped out and, solutions are valid and uniform.

Keywords:

axially moving string,viscous damping,straightforward expansion method,

Refference:

I. A. A. Maitlo, S. H. Sandilo, A. H. Sheikh, R. A. Malookani, and S. Qureshi, On aspects of viscous damping for an axially transporting string, Sci. Int.(Lahore) Vol. 28, No. 4, 3721–3727(2016).
II. Darmawijoyo and W. T. Van Horssen, On the weakly damped vibrations of a string attached to a spring mass dashpot system, J. Vib. Control. Vol. 9, No. 11, 1231–1248(2003).
III. Darmawijoyo and W. T. Van Horssen, On boundary damping for a weakly nonlinear wave equation, Nonlinear Dyn. Vol. 30, No. 2, 179–191(2002).
IV. Darmawijoyo , W. T. Van Horssen, and P. H. Clément, On a rayleigh wave equation with boundary damping, Nonlinear Dyn. Vol. 33 , 399–429(2003).
V. J. W. Hijmissen, On aspects of boundary damping for cables and vertical beams, PhD Thesis (2008), Delf University of Technology, Delft, The Netherlands.
VI. K. Marynowski and T. Kapitaniak, Zener internal damping in modelling of axially moving viscoelastic beam with time-dependent tension, Int. J. Non. Linear. Mech. Vol. 42, No. 1, 118–131(2007).
VII. Khalid H. Malik , Sanaullah Dehraj, Sindhu Jamali, Sajad H. Sandilo, Asif Mehmood Awan. : On transversal vibrations of an axially moving Beam under influence of viscous damping. J. Mech. Cont.& Math. Sci., Vol.-15, No.-11, pp. 12-22 (2020).
VIII. M. A. Zarubinskaya and W. T. van Horssen, On aspects of boundary damping for a rectangular plate, J. Sound Vib. Vol. 292, No. 3–5, 844–853(2006).
IX. N. Jakšić and M. Boltežar, Viscously damped transverse vibrations of an axially moving string, Journal Mech. Eng. Vol. 51, No. 9, 560–569 (2005).
X. N. V. Gaiko and W. T. van Horssen, On the transverse, low frequency vibrations of a traveling string with boundary damping, J. Vib. Acoust. Vol. 137, No. 4, 041004-1041004-10(2015).
XI. R. A. Malookani and W. T. Van Horssen, On resonances and the applicability of Galerkin’s truncation method for an axially moving string with time-varying velocity, J. Sound Vib. Vol. 344, 1–17(2015).
XII. R. A. Malookani, S. Dehraj, and S. H. Sandilo, Asymptotic approximations of the solution for a traveling string under boundary damping, J. Appl. Comput. Mech. Vol. 5, No. 5, 918–925(2019).
XIII. R. Heberman, Applied partial differential equations, Pearson Prentice-Hall, New Jersey (2004).
XIV. S. Krenk, Vibrations of a taut cable with an external damper, J. Appl. Mech. Vol. 67, No. 4, 772–776(2000).
XV. S. M. Shahruz, Stability of a nonlinear axially moving string with the Kelvin-Voigt damping,J. Vib Acoust. Vol. 131 No. 1, 014501 (4 pages) (2009).

XVI. S. V. Ponomareva and W. T. Van Horssen, On transversal vibrations of an axially moving string with a time-varying velocity, Nonlinear Dyn. Vol. 50, No. 1–2, 315–323(2007).
XVII. S. H. Sandilo, R. A. Malookani and A. H. Sheikh, On oscillations of an axially translating tensioned beam under viscous damping, Sci. Int. (Lahore) Vol. 28, No. 4, 4123–4127(2016).
XVIII. S. H. Sandilo and W. T. Van Horssen, On variable length induced vibrations of a vertical string, J. Sound Vib. Vol. 333, No. 11, 2432–2449(2014).
XIX. S. Dehraj, S. H. Sandilo, and R. A. Malookani, On applicability of truncation method for damped axially moving string, J. Vibroengineering. Vol. 22, No. 2 337–352(2020).
XX. Sidra Saleem, Imran Aziz and M. Z Hussain, Numerical solution of vibration equation using Haar Wavelet, Punjab Univ. J. Math. Vol. 51 No.3, 89-100(2019).
XXI. S. Dehraj, R. A. Malookani, and S. H. Sandilo, On Laplace transform and (In) stability of externally damped axially moving string, J. Mech. Cont. & Math. Sci., Vol.-15, No.-8, pp. 282-298(2020).
XXII. T. Akkaya and W. T. Van Horssen, On the transverse vibrations of strings and beams on semi-infinite domains, Procedia IUTAM. Vol. 19, 266–273(2016).
XXIII. T. Akkaya and W. T. van Horssen, On constructing a Green’s function for a semi-infinite beam with boundary damping, Meccanica. Vol. 52, No.10, 2251–2263(2017).
XXIV. W. T. Van Horssen and S. V. Ponomareva, On the construction of the solution of an equation describing an axially moving string, J. Sound Vib. Vol. 287, No. 1–2, 359–366(2005).

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DILEMMAS IN CONSTRUCTION PROJECT DUE TO SCARCE RISK ANALYSIS

Authors:

Fazal E Rahim Afridi, Muhammad Zeeshan Ahad

DOI NO:

https://doi.org/10.26782/jmcms.2021.03.00009

Abstract:

In this study, the authors try to compute the importance of risk management in construction industries and try to validate that risk management is a vital tool to manage the project for this purpose about 150 questionnaires were distributed to stakeholders a response rate of 66% thereby achieved acceptable for the construction industry. 86 % of respondents were over 30 years of age. While 67 % of respondents were having experience of over 10 years in construction. Maximum of the respondents were at the key positions in their organizations. Results of the survey have vividly shown that the construction industry faces many challenges and uncertainties. The trends are that as the business environment grows more complex and dynamic, the risks and uncertainties which construction organizations face also get complex and significant.   

Keywords:

risk management,construction industries,uncertainties,

Refference:

I. Acar, E., Göç, Y., 2011. Prediction of risk perception by owners’ psychological traits in small building contractors. Construction Management and Economics. 29, 841–852. doi:10.1080/01446193.2011.611521
II. Adeed Khan, Asif Subhan, Muhammad Hasnain, Mohammad Adil, Muhammad Amar Rafiq, Mehre Munir. : Identification of Risk Management in Bus Rapid Transit (BRT) Project Peshawar. J. Mech. Cont. & Math. Sci., Vol.-14, No.2, March-April (2019) pp 87-99
III. Akintoye, A.S., MacLeod, M.J., 1997. Risk analysis and management in construction. International Journal of Project Management. 15, 31–38. doi:10.1016/S0263-7863(96)00035-X
IV. Cagliano, A.C., Grimaldi, S., Rafele, C., 2015. Choosing project risk management techniques. A theoretical framework. Journal of Risk Research. 18, 232– 248. doi:10.1080/13669877.2014.896398
V. Hwang, B.-G., Zhao, X., Toh, L.P., 2014. Risk management in small construction projects in Singapore: Status, barriers and impact. Int. Journal. Project. Managers. 32, 116–124. doi:10.1016/j.ijproman.2013.01.007
VI. Iqbal, S., Choudhry, R.M., Holschemacher, K., Ali, A., Tamošaitienė, J., 2015. Risk management in construction projects. Technol. Econ. Dev. Econ. 21, 65– 78. doi:10.3846/20294913.2014.994582
VII. Kaplinski, O., 2013. Risk Management of Construction Works by Means of the Utility Theory: A Case Study. Procedia Engineering. 57, 533–539. doi:10.1016/j.proeng.2013.04.068
VIII. Muhammad Iqbal1*, Imtiaz Khan2 , Fawad Ahmad3 , Muhammad Zeeshan Ahad4 , Mehre Munir. : Factors Affecting the Performance of Construction Projects in, J. Mech. Cont.& Math. Sci., Vol.-14, No.-3, May-June (2019) pp 336-358
IX. Nieto-Morote, A., Ruz-Vila, F., 2011. A fuzzy approach to construction project risk assessment. International Journal of Project Management. 29, 220–231. doi:10.1016/j.ijproman.2010.02.002
X. Tang, W., Qiang, M., Duffield, C., Young, D., Lu, Y., 2007. Risk Management in the Chinese Construction Industry. Journal of Construction Engineering and Management. 133, 944–956. doi:10.1061/(ASCE)0733-9364(2007)133:12(944)

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GREEN BUILDING CONSTRUCTION IN INDIA AND BENEFITS OF SUSTAINABLE BUILDING MATERIALS

Authors:

D. P. Kothari, Anshumaan Pathak

DOI NO:

https://doi.org/10.26782/jmcms.2021.04.00001

Abstract:

The green building design aims to minimize the need for the non-renewable energy of these resources, optimize their sustainability and maximize their conservation, recycling and usage. The use of effective building materials and construction techniques is maximized. Architectural bioclimatic technology will also optimize on-site usage of sources and sinks. It requires only minimum electricity to fuel itself and efficient appliances to meet its lighting, air-conditioning and other needs. Green buildings architecture optimizes the use of renewable energies and efficient waste and water management methods to create practical and hygienic working conditions for indoor environments. Materials such as chemical, physical and mechanical material properties and an appropriate specification are the fundamental elements of construction design and responsible for the mechanical strength of the design. The construction of green buildings is also the first step in choosing and utilizing eco-friendly materials with or better characteristics than traditional building materials. Based on the practical, technical and financial requirements, construction materials are usually selected. But, given that sustainable development has been a core issue in recent decades, building industry that is directly or indirectly responsible for a substantial share of annual environmental destruction, by pursuing environmentally sound constructions and buildings should take responsibility for contributing to sustainable growth. The quickest way for manufacturers to start integrating environmental design practices into buildings would be the diligent procurement of eco-friendly sustainable construction materials, including options for new material uses, recycling and reusing, organic product creation and green resource use. This paper aims to show how green building materials will help reduce the impact on the atmosphere and create a cleaner building that can be healthy for the occupant or our environment. In the sustainable progress of a nation, the choice of building materials that have reduced environmental burdens is helpful.  

Keywords:

Green Building,Materials selection,Construction Industry,Rat Bond,Cavity Wall,Thermal insulation,Eco-friendly wall,Green Roof & Greenhouse,

Refference:

I. Adeed Khan, Muhammad Tehseen Khan, Muhammad Zeeshan Ahad, Mohammad Adil, Mazhar Ali Shah, Syed Khaliq Shah. : STRENGTH ASSESSMENT OF GREEN CONCRETE FOR STRUCTURAL USE. J. Mech. Cont.& Math. Sci., Vol.-15, No.-9, September (2020) pp 294-305. DOI : 10.26782/jmcms.2020.09.00024
II. Allen, Jennifer H., and Thomas Potiowsky. “Portland’s green building cluster: Economic trends and impacts.” Economic Development Quarterly 22, no. 4 (2008): 303-315.
III. Cooper, I. Which focus for building assessment methods: Environmental performance or sustainability? Build. Res. Inf. 1999, 27, 321-331.
IV. Edwards B, editor. Green buildings pay. 2nd ed. London; New York: Spon Press; 2003.
V. Fernandez, J.E. Material Architecture: Emergent Materials for Innovative Buildings and Ecological Construction Architectural Press: Amsterdam, The Netherlands and Boston, MA, USA, 2006.
VI. Hulme, J.; Radford, N. Sustainable Supply Chains That Support Local Economic Development; Prince’s Foundation for the Built Environment. 2010.
VII. Kats G. The cost and financial benefits of green buildings: a report to California’s sustainable building task force. Sacramento, CA: Sustainable Building Task Force; 2003.
VIII. Moeck M, Yoon JY. Green buildings and potential electric light energy savings. Journal of Architectural Engineering 2004; 10(4):143–59.
IX. Muse A, Plaut JM. An inside look at LEED: experienced practitioners reveal the inner workings of LEED. Journal of Green Building 2006; 1(1):3–8.
X. Pulselli RM, Simoncini E, and Pulselli FM, Bastianoni S., Energy analysis of building manufacturing, maintenance and use: building indices to evaluate housing sustainability. Energy and Buildings 2007; 39(5):620–8.
XI. Ries R, Bilec M, Gokhan NM, Needy KL. The economic benefits of green buildings: a comprehensive case study. The Engineering Economist 2 006; 51(3):259–95.
XII. Ries R, Bilec M, Gokhan NM, Needy KL. The economic benefits of green buildings: a comprehensive case study. The Engineering Economist 2006; 51(3):259–95.
XIII. Ross B, Lopez-Alcala M, Small III AA. Modeling the private financial returns from green building investments. Journal of Green Building 2006; 2(1):97–105.
XIV. Samiullah Qazi, Attaul Haq, Sajjad Wali Khan, Fasih Ahmad Khan, Rana Faisal Tufail. : EVALUATE THE INFLUENCE OF STEEL FIBERS ON THE STRENGTH OF CONCRETE USING PLASTIC WASTE AS FINE AGGREGATES. J. Mech. Cont.& Math. Sci., Vol.-15, No.-12, December (2020) pp 27-35. DOI : 10.26782/jmcms.2020.12.00003
XV. Seyfang, G. Community action for sustainable housing: Building a low carbon future. Energy Policy 2009a,doi:10.1016/j.enpol. 2009.10.027.
XVI. Thormark C. The effect of material choice on the total energy need and recycling potential of a building. Building and Environment 2006; 41(8):1019–26.
XVII. Wang W, Zmeureanua R, Rivard H. Applying multi-objective genetic algorithms in green building design optimization. Building and Environment 2005; 40(11):1512–25.
XVIII. Yu C. Environmentally sustainable acoustics in urban residential areas. Ph.D. dissertation. University of Sheffield, UK: School of Architecture; 2008.

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A PERFORMANCE EVALUATION OF TRAPEZOIDAL VARIANTS FOR NUMERICAL CUBATURE

Authors:

Kamran Malik, Muhammad Mujtaba Shaikh, Kashif Memon, Muhammad Saleem Chandio, Abdul Wasim Shaikh

DOI NO:

https://doi.org/10.26782/jmcms.2021.04.00002

Abstract:

In this work, double integration cubature schemes of Trapezoid type have been focused. Recently, some derivative-based Trapezoid-type schemes have been proposed in literature incorporating derivatives at means of the limits of integration. We carry out the exhaustive performance evaluation of the existing closed Newton-Cotes Trapezoidal (CNCT) double integral scheme with its derivative-based variants in recent literature. The derivative-free and derivative-based rules are discussed in basic forms with local error terms and composite forms with global error terms. The performance of the rules on some double integrals in the form of observed order of accuracy, computational costs and error drops demonstrates the encouraging performance of the derivative-based trapezoidal variants over the derivative-free scheme performing numerical experiments.

Keywords:

Cubature,Double integrals,Derivative-based schemes,Order of accuracy,computational cost,errors,Trapezoid,

Refference:

I. Babolian E., M. Masjed-Jamei and M. R. Eslahchi, On numerical improvement of Gauss-Legendre quadrature rules, Applied Mathematics and Computations, 160(2005) 779-789.
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III. Bhatti, A. A., M.S. Chandio, R.A. Memon and M. M. Shaikh, (2019), “A Modified Algorithm for Reduction of Error in Combined Numerical Integration”, Sindh University Research Journal-SURJ (Science Series) 51(4): 745-750.
IV. Burden R. L., J. D. Faires, Numerical Analysis, Brooks/Cole, Boston, Mass, USA, 9th edition, 2011.
V. Burg. C. O. E., Derivative-based closed Newton-cotes numerical quadrature, Applied Mathematics and Computations, 218 (2012), 7052-7065.
VI. Dehghan M., M. Masjed-Jamei and M. R. Eslahchi, The semi-open Newton- Cotes quadrature rule and its numerical improvement, Applied Mathematics and Computations, 171 (2005) 1129-1140.
VII. Dehghan M., M. Masjed-Jamei, and M. R. Eslahchi, “On numerical improvement of closed Newton-Cotes quadrature rules,” Applied Mathematics and Computation, vol. 165, no. 2,pp. 251–260, 2005.
VIII. Dehghan M., M. Masjed-Jamei, and M. R. Eslahchi, “On numerical improvement of open Newton-Cotes quadrature rules,” Applied Mathematics and Computation, vol. 175, no. 1, pp.618–627, 2006.
IX. Jain M. K., S. R. K. Iyengar and R. K. Jain, Numerical Methods for Scientific and Computation, New Age International (P) Limited, Fifth Edition, 2007.
X. Kamran Malik, Muhammad Mujtaba Shaikh, Muhammad Saleem Chandio, Abdul Wasim Shaikh. : ‘SOME NEW AND EFFICIENT DERIVATIVE-BASED SCHEMES FOR NUMERICAL CUBATURE’. J. Mech. Cont.& Math. Sci., Vol.-15, No.-10, October (2020) pp 67-78. DOI : 10.26782/jmcms.2020.10.00005
XI. Memon K., M. M. Shaikh, M. S. Chandio, A. W. Shaikh, “A Modified Derivative-Based Scheme for the Riemann-Stieltjes Integral”, 52(01) 37-40 (2020).
XII. Pal M., Numerical Analysis for Scientists and Engineers: theory and C programs, Alpha Science, Oxford, UK, 2007.
XIII. Petrovskaya N., E. Venturino, “Numerical integration of sparsely sampled data,” Simulation Modelling Practice and Theory,vol. 19, no. 9, pp. 1860–1872, 2011.
XIV. Ramachandran T. (2016), D. Udayakumar and R. Parimala, “Comparison of Arithmetic Mean, Geometric Mean and Harmonic Mean Derivative-Based Closed Newton Cotes Quadrature“, Nonlinear Dynamics and Chaos Vol. 4, No. 1, 2016, 35-43 ISSN: 2321 – 9238.
XV. Sastry S.S., Introductory methods of numerical analysis, Prentice-Hall of India, 1997.
XVI. Shaikh, M. M., (2019), “Analysis of Polynomial Collocation and Uniformly Spaced Quadrature Methods for Second Kind Linear Fredholm Integral Equations – A Comparison”. Turkish Journal of Analysis and NumberTheory,7(4)91-97. doi: 10.12691/tjant-7-4-1.
XVII. Shaikh, M. M., M. S. Chandio and A. S. Soomro, (2016), “A Modified Four-point Closed Mid-point Derivative Based Quadrature Rule for Numerical Integration”, Sindh University Research Journal-SURJ (Science Series) 48(2): 389-392.
XVIII. Zafar F., S. Saleem and C. O. E. Burg, New derivative based open Newton-Cotes quadrature rules, Abstract and Applied Analysis, Volume 2014, Article ID 109138, 16 pages, 2014.
XIX. Zhao, W., and H. Li, (2013) “Midpoint Derivative- Based Closed Newton-Cotes Quadrature”, Abstract And Applied Analysis, Article ID 492507.
XX. Zhao, W., Z. Zhang, and Z. Ye, (2014), “Midpoint Derivative-Based Trapezoid Rule for the Riemann- Stieltjes Integral”, Italian Journal of Pure and Applied Mathematics, 33: 369-376.

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A NEW HARMONIC MEAN DERIVATIVE-BASED SIMPSON’S 1/3-TYPE SCHEME FOR RIEMANN- STIELTJES INTEGRAL

Authors:

Kashif Memon, Muhammad Mujtaba Shaikh, Kamran Malik, Muhammad Saleem Chandio, Abdul Wasim Shaikh

DOI NO:

https://doi.org/10.26782/jmcms.2021.04.00003

Abstract:

In this research paper, a new harmonic mean derivative-based Simpson’s 1/3 scheme has been presented for the Riemann-Stieltjes integral (RS-integral). The basic and composite forms of the proposed scheme with local and global error terms have been derived for the RS-integral. The proposed scheme has been reduced using g(t) = t for Riemann integral. Experimental work has been discussed to verify the theoretical results of the new proposed scheme against existing schemes using MATLAB. The order of accuracy, computational cost and average CPU time (in seconds) of the new proposed scheme have been computed. Finally, it is observed from computational results that the proposed scheme is better than existing schemes.

Keywords:

Quadrature rule,Riemann-Stieltjes,Harmonic Mean,Simpson’s 1/3 rule,Local error,Global error,Cost-effectiveness,Time-efficiency,

Refference:

I. Bartle, R.G. and Bartle, R.G., The elements of real analysis, (Vol. 2). John Wiley & Sons, 1964.
II. Burden, R.L., Faires, J.D., Numerical Analysis, Brooks/Cole, Boston, Mass, USA, 9th edition, 2011.
III. Dragomir, S.S., and Abelman S., Approximating the Riemann-Stieltjes integral of smooth integrands and of bounded variation integrators, Journal of Inequalities and Applications, 2013.1 (2013), 154.
IV. Malik K., Shaikh, M. M., Chandio, M. S. and Shaikh, A. W. : Some new and efficient derivative-based schemes for numerical cubature. J. Mech. Cont. & Math. Sci., Vol.-15, No.10 October (2020): pp 67-78. DOI : 10.26782/jmcms.2020.10.00005
V. Malik K., Shaikh, M. M., Chandio, M. S. and Shaikh, A. W. : Error analysis of closed Newton-Cotes cubature schemes for double integrals. J. Mech. Cont. & Math. Sci., Vol.-15, No.-11, November (2020) pp 95-107, 2020. DOI: 10.26782/jmcms.2020.11.00009
VI. Memon K, Shaikh MM, Chandio MS and Shaikh AW, A Modified Derivative-Based Scheme for the Riemann-Stieltjes Integral, Sindh University Research Journal-SURJ (Science Series) 52.1, (2020): 37-40.
VII. Memon K., Shaikh, M. M., Chandio, M. S. and Shaikh, A. W. : A new and efficient Simpson’s 1/3-type quadrature rule for Riemann-Stieltjes integral. J. Mech. Cont. & Math. Sci., Vol.-15, No.-11, November (2020) pp 132-148. DOI : 10.26782/jmcms.2020.11.00012
VIII. Memon K., Shaikh, M. M., Malik, K., M., Chandio, M. S. and Shaikh, A. W. : Heronian Mean Derivative-Based Simpson’s-type scheme for Riemann-Stieltjes integral, J. Mech. Cont. & Math. Sci., Vol.-16, No.-3, March (2021) pp 53-68. DOI : 10.26782/jmcms.2021.03.00005
IX. Memon K., Shaikh, M. M., Malik, K., M., Chandio, M. S. and Shaikh, A. W. : Efficient Derivative-Based Simpson’s 1/3-type scheme using Centroidal Mean for Riemann-Stieltjes integral, J. Mech. Cont. & Math. Sci., Vol.-16, No.-3, March (2021) pp 69-85. DOI : 10.26782/jmcms.2021.03.00006
X. Mercer, P.R., Hadamard’s inequality and Trapezoid rules for the Riemann-Stieltjes integral, Journal of Mathematica Analysis and Applications, 344 (2008), 921-926.
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XIII. Ramachandran Thiagarajan, Udayakumar.D, Parimala .R, Geometric mean derivative-based closed Newton-Cotes quadrature, International Journal of Pure & Engineering Mathematics, 4, 107-116, April 2016.
XIV. Ramachandran Thiagarajan, Udayakumar.D, Parimala .R, Harmonic mean derivative-based closed Newton-Cotes quadrature, IOSR-Journal of Mathematics, 12, 36-41, May-June 2016.
XV. Ramachandran Thiagarajan, Udayakumar.D, Parimala .R, Heronian mean derivative- based closed Newton cotes quadrature, International Journal of Mathematical Archive, 7, 53-58, July 2016.
XVI. Ramachandran Thiagarajan, Parimala .R, Centroidal mean derivative–based
closed Newton cotes quadrature, International Journal of Science and Research, 5, 338-343, August 2016.
XVII. Zhao, W., and H. Li, Midpoint Derivative-Based Closed Newton-Cotes
Quadrature, Abstract And Applied Analysis, Article ID 492507, (2013).
XVIII. Zhao, W., Z. Zhang, and Z. Ye, Midpoint Derivative-Based Trapezoid Rule
for the Riemann-Stieltjes Integral, Italian Journal of Pure and Applied
Mathematics, 33, (2014), 369-376.
XIX. Zhao, W., Z. Zhang, and Z. Ye, Composite Trapezoid rule for the Riemann
-Stieltjes Integral and its Richardson Extrapolation Formula, Italian Journal of
Pure and Applied Mathematics, 35 (2015), 311-318.

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SIMILARITY SOLUTION OF HEAT AND MASS TRANSFER FOR LIQUID EVAPORATION ALONG A VERTICAL PLATE COVERED WITH A THIN POROUS LAYER

Authors:

Md. Hasanuzzaman, Md. Mosharrof Hossain, M.M. Ayub Hossain

DOI NO:

https://doi.org/10.26782/jmcms.2021.04.00004

Abstract:

In this paper, heat and mass transfer for liquid evaporation along a vertical plate covered with a thin porous layer has been investigated. The continuity, momentum, energy and mass balance equations, which are coupled nonlinear partial differential equations are reduced to a set of two nonlinear ordinary differential equations and solved analytically and numerically by using the shooting technique in MATLAB. The effect of various parameters like the Froude number, the porosity, the Darcy number, the Prandtl number, the Lewis number and the driving parameters on the temperature and concentration profiles are presented and discussed. It is viewed that the heat transfer performance is enhanced by the presence of a porous layer. The local Nusselt number and the local Sherwood numbers are computed and analyzed both numerically and graphically.

Keywords:

Similarity solution,evaporation,vertical plate,liquid film,porous layer,

Refference:

I.A. Ali Hayat, Mohammed R. Salman, : HOMOTOPY PERTURBATION METHOD FOR PERISTALTIC TRANSPORT OF MHD NEWTONIAN FLUID IN AN INCLINED TAPERED ASYMMETRIC CHANNEL WITH THE IMPACT OF POROUS MEDIUM AND CONVECTIVE THERMAL AND CONCENTRATION. J. Mech. Cont.& Math. Sci., Vol.-15, No.-9, September (2020) pp 125-141. DOI : 10.26782/jmcms.2020.09.00010
II.A.T. Wassel, A.F. Mills, Design methodology for a counter-current falling film evaporative condenser, ASME J. Heat Transfer 109 (1987) 784–787.
III. B. Gebhart, L. Pera, The nature of vertical natural convection flows resulting from the combined buoyancy effects of thermal and mass diffusion, Int. J. Heat Mass Transfer 14 (1971) 2028–2050.
IV. B. Alazmi, K. Vafai, Analysis of fluid and heat transfer interfacial conditions between a porous medium and a fluid layer, Int. J. Heat Mass Transfer 44 (2001) 1735–1749.
V. D.A.S. Rees, K. Vafai, Darcy–Brinkman free convection from a heated horizontal Surface, Numer. Heat Transfer, Pt A 35 (1999) 191–204.
VI E. Mezaache, M. Daguenet, Effects of inlet conditions on film evaporation along an inclined plate, Solar Energy 78 (2005) 535–542.
VII. H. Peres-Blanco, W.A. Bird, Study of heat and mass transfer in a vertical-tube evaporative cooler, ASME J. Heat Transfer 106 (1984) 210–215.
VIII. I.L. Maclaine-Cross, P.J. Banks, Coupled heat and mass transfer in regenerators-prediction using an analogy with heat transfer, J. Heat Mass Transfer 15 (1972) 1225–1242.
IX. I.L. Maclaine-Cross, P.J. Banks, A general theory of wet surface heat exchangers and its application to regenerative evaporative cooling, ASME J. Heat Transfer 103 (1981) 579–585.
X. J.C. Han, L.R. Glicksman, W.M. Rohsenow, An investigation of heat transfer and friction for rib-roughened surfaces, Int. J. Heat Mass Transfer 21 (1978) 1143–1156.
XI. Jin-Sheng Leu, Jiin-Yuh Jang and Yin Chou, Heat and mass transfer for liquid film evaporation along a vertical plate covered with a thin porous layer, Int. J. Heat and Mass Transfer 49 (2006) 1937–1945.

XII. Khader M. M., Megahed Ahmed M., Numerical simulation using the finite difference method for the flow and heat transfer in a thin liquid film over an unsteady stretching sheet in a saturated porous medium in the presence of thermal radiation, Journal of King Saud University – Engineering Sciences 25(2013), 29 – 34.
XIII. Rafiuddin, Noushima Humera. G., : NUMERICAL SOLUTION OF UNSTEADY TWO – DIMENSIONAL HYDROMAGNETICS FLOW WITH HEAT AND MASS TRANSFER OF CASSON FLUID. J. Mech. Cont.& Math. Sci., Vol.-15, No.-9, September (2020) pp 17-30. DOI : 10.26782/jmcms.2020.09.00002
XIV. S. Ergyn, Fluid flow through packed columns, Chem. Eng. Progr. 48 (1952) 89–94.
XV. T.S. Chen, C.F. Yuh, Combined heat and mass transfer in natural convection on inclined surfaces, Numer. Heat Transfer 2 (1979) 233– 250.
XVI. T.R. Shembharkar, B.R. Pai, Prediction of film cooling with a liquid coolant, Int. J. Heat Mass Transfer 29 (1986) 899–908.
XVII. T.S. Zhao, Coupled heat and mass transfer of a stagnation point flow in a heated porous bed with liquid film evaporation, Int. J. Heat Mass Transfer 42 (1999) 861–872.
XVIII. W.W. Baumann, F. Thiele, Heat and mass transfer in evaporating two-component liquid film flow, Int. J. Heat Mass Transfer 33 (1990) 267–273.
IX. W.M. Yan, T.F. Lin, Evaporative cooling of liquid film through interfacial heat and mass transfer in a vertical channel—II. Numerical study, Int. J. Heat Mass Transfer 34 (1991) 1113–1124.
XX. W.M. Yan, C.Y. Soong, Convection heat and mass transfer along an inclined heated plate with film evaporation, Int. J. Heat Mass Transfer 38 (1995) 1261–1269.
XXI. Y.L. Tsay, Heat transfer enhancement through liquid film evaporation into countercurrent moist air flow in a vertical plate channel, Heat Mass Transfer 30 (1995) 473–480.

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CONSTITUTIVE MATERIAL MODEL FOR BLOCK MASONRY AND ITS MECHANICAL PROPERTIES

Authors:

Muhammad Junaid Iqbal, Akhtar Gul, Yasir Irfan Badrashi, Syed Azmat Ali Shah, Eid Badshah, Zohaib Hassan, Wisal Ahmed

DOI NO:

https://doi.org/10.26782/jmcms.2021.04.00005

Abstract:

This research work aims at the development of a material model for concrete block masonry used in the load-bearing wall as well as masonry infill. To accomplish this, various tests were performed on concrete block (solid) units and concrete block masonry assemblage. A concrete block having a size of 12 x 8 x 6 inches, were fabricated in a mortar ratio of 1:4, 1:2:2, 1:8 and 1:4:4. The compressive strength of concrete block prisms having size 24.36 x 8.04 x 18.72 inches, was also determined by conducting the compressive strength test. The shear strength of square prisms, having size 26.76 x 8.04 x 25.20 inches, was found by applying diagonal loading. To investigate the bond shear strength of concrete block masonry, triplet tests were carried out on block masonry prisms. Before conduct, a test on block assemblage specimens, the constituent materials of block assemblage i.e. block and mortar were also tested for different properties. The average compressive strength of concrete block (12”x8”x6”) was 302.25 psi and the average unit weight was 119.83 lb/ft3. The compressive strength of mortars of 1:4, 1:2:2, 1:8 and 1:4:4 was 2367, 1752,815 and 1332 psi respectively.

Keywords:

Concrete Solid Blocks,Cement,sand and khaka mortar,Compressive Strength,Shear Strength,bond Shear strength,

Refference:

I. Ali, Q. et al., 2012. Experimental Investigation on the Characterization of Solid Clay Brick Masonry for Lateral Shear Strength Evaluation. International Journal of Earth Sciences and Engineering, 05(4), pp. 782-791
II. Ahmad A, Hamid, B.E Abboud, and H.G Harris. To evaluate the use of concrete blocks in modeling of concrete block masonry under axial compression.
III. Ahmad Jan Durrani, Amr Salah Elnashai, Youssef M.A. Hashash, Sung Jig Kim and Arif Masud., : ‘The Kashmir earthquake of October 8, 2005 a quick look.’
IV. Ali, et al. 2012.development of shear strength constitutive material model for brick masonry. Department of Civil Engineering, University of Engineering and Technology, Peshawar. Shahzada Khan (2011), “Seismic Risk Assessment of Buildings in Pakistan (Case Study Abbottabad City), PhD thesis, Department of Civil Engineering, University of Engineering and Technology, Peshawar.
V. ASTM-C-109, Specifications and Standards of Compressive Strength of Cement Sand Mortar.
VI. ASTM-E-519, Specifications and Standards of Principle Tensile Strength of Masonry Assemblage.
VII. ASTM-C-1314-03b, Specification and testing procedure about the compressive strength of the masonry assemblage.
VIII. ASTM C-140-03, Specification and testing procedure about the compressive strength of the concrete masonry units.
IX. EN-1052-3, European Standard for Bond Shear Strength of Masonry Assemblage.
X. Blocks and Bricks Review by Andrew Brown, Distinction between light weight aggregate block and dense grade aggregate block.
XI. Rafiq Adil, Muhammad Fahad, Mohammad Adil, : ‘Macro-Scale Numerical Modeling of Unreinforced Brick Masonry Squat Pier Under In-Plane Shear’. J. Mech. Cont.& Math. Sci., Vol.-15, No.-11, November (2020) pp 72-84. DOI : 10.26782/jmcms.2020.11.00007
XII. Muhammad Rizwan, Hanif Ullah, Ezaz Ali Khan, Nayab Khan, Talha Rasheed. : ‘EXPERIMENTAL INVESTIGATION OF MECHANICAL PROPERTIES OF SOLID CONCRETE BLOCK MASONRY EMPLOYING DIFFERENT MORTAR RATIOS’, J. Mech. Cont.& Math. Sci., Vol.-16, No.-1, January (2021) pp 107-120. DOI : 10.26782/jmcms.2021.01.00009

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A NEW SECOND ORDER DERIVATIVE FREE METHOD FOR NUMERICAL SOLUTION OF NON-LINEAR ALGEBRAIC AND TRANSCENDENTAL EQUATIONS USING INTERPOLATION TECHNIQUE

Authors:

Sanaullah Jamali, Zubair Ahmed Kalhoro, Abdul Wasim Shaikh, Muhammad Saleem Chandio

DOI NO:

https://doi.org/10.26782/jmcms.2021.04.00006

Abstract:

Its most important task in numerical analysis to find roots of nonlinear equations, several methods already exist in literature to find roots but in this paper, we introduce a unique idea by using the interpolation technique. The proposed method derived from the newton backward interpolation technique and the convergence of the proposed method is quadratic, all types of problems (taken from literature) have been solved by this method and compared their results with another existing method (bisection method (BM), regula falsi method (RFM), secant method (SM) and newton raphson method (NRM)) it's observed that the proposed method have fast convergence. MATLAB/C++ software is used to solve problems by different methods. 

Keywords:

Nonlinear equation,Interpolation,convergence,number of iteration,Accuracy ,

Refference:

I. Ababneh, O. Y. (2016). New Fourth Order Iterative Methods Second Derivative Free. Journal of Applied Mathematics and Physics, 04(03), 519–523. https://doi.org/10.4236/jamp.2016.43058
II. Ali, A., Saeed Ahmed, Muhmmmad Tanveer, M., Mehmood, Q., & Wazeer, W. (2015). MODIFIED TWO-STEP FIXED POINT ITERATIVE METHOD FOR SOLVING NONLINEAR FUNCTIONAL EQUATIONS. Sci.Int.(Lahore), 27(3), 1737–1739.
III. Allame, M., & Azad, N. (2012). On Modified Newton Method for Solving a Nonlinear Algebraic Equations by Mid-Point. World Applied Sciences Journal, 17(12), 1546–1548.

IV. Hafiz, M. A., & Bahgat, M. S. M. (2013). Solving Nonlinear Equations Using Two-Step Optimal Methods. In Annual Review of Chaos Theory, Bifurcations and Dynamical Systems (Vol. 3). www.arctbds.com.
V. Homeier, H. H. H. (2005). On Newton-type methods with cubic convergence. Journal of Computational and Applied Mathematics, 176(2), 425–432. https://doi.org/10.1016/j.cam.2004.07.027
VI. Intep, S. (2018). A review of bracketing methods for finding zeros of nonlinear functions. Applied Mathematical Sciences, 12(3), 137–146. https://doi.org/10.12988/ams.2018.811
VII. Li, Y.-T., & Jiao, A.-Q. (2009). Some Variants of Newton’s Method with Fifth-Order and Fourth-Order Convergence for Solving Nonlinear Equations. In Darbose International Journal of Applied Mathematics and Computation (Vol. 1, Issue 1). http//:ijamc.darbose.com
VIII. Liu, X., & Wang, X. (2013). A Family of Methods for Solving Nonlinear Equations with Twelfth-Order Convergence. Applied Mathematics, 04(02), 326–329. https://doi.org/10.4236/am.2013.42049
IX. Mehtre, V. V. (2019). Root Finding Methods: Newton Raphson Method. International Journal for Research in Applied Science and Engineering Technology, 7(11), 411–414. https://doi.org/10.22214/ijraset.2019.11065
X. Ozbzn, A. Y (2004). Some New Variants of Newton’s Method. Applied Mathematics Letters, 17, 677–682. https://doi.org/10.1016/j
XI. Omran, H. H. (2013). Modified Third Order Iterative Method for Solving Nonlinear Equations. In Journal of Al-Nahrain University (Vol. 16, Issue 3).
XII. Qureshi ++, U. K., Shaikh, A. A., & Solangi, M. A. (2017). Modified Free Derivative Open Method for Solving Non-Linear Equations. SINDH UNIVERSITY RESEARCH JOURNAL (SCIENCESERIES), 49(004), 821–824. https://doi.org/10.26692/sujo/2017.12.0065
XIII. Qureshi, U. K, Ansari, ++ M Y, & Syed, M. R. (2018). Super Linear Iterated Method for Solving Non-Linear Equations. SINDH UNIVERSITY RESEARCH JOURNAL (SCIENCESERIES) Super, 50(1), 137–140. https://doi.org/10.26692/sujo/2018.1.0024
XIV. Qureshi, U. K, Bhatti, A. A., Kalhoro, Z. A., & Ali, Z. (2019). On the Development of Numerical Iterated Method of Newton Raphson method for Estimating Nonlinear Equations. University of Sindh Journal of Information and Communication Technology (USJICT), 3(2). http://sujo2.usindh.edu.pk/index.php/USJICT/
XV. Qureshi, U. K, Jamali, S., & Kalhoro, Z. A. (2021). MODIFIED QUADRATURE ITERATED METHODS OF BOOLE RULE AND WEDDLE RULE FOR SOLVING NON-LINEAR EQUATIONS. J. Mech. Cont. & Math. Sci., Vol.-16, No.-2, February (2021) pp 87-101. DOI : 10.26782/jmcms.2021.02.00008
XVI. Qureshi, U. K, Kalhoro, Z. A., Shaikh, A. A., & Jamali, S. (2020). Sixth Order Numerical Iterated Method of Open Methods for Solving Nonlinear Applications Problems. Proceedings of the Pakistan Academy of Sciences: A. Physical and Computational Sciences, 57(November), 35–40.
XVII. Qureshi, U. K., Solanki, N., & Ansari, M. Y. (2019). Algorithm of Difference Operator for Computing a Single Root of Nonlinear Equations. In Punjab University Journal of Mathematics (Vol. 51, Issue 4).
XVIII. Sangah, A. A., Shaikh, A. A., & Shah, S. F. (2016). Comparative Study of Existing Bracketing Methods with Modified Bracketing Algorithm for Solving Nonlinear Equations in Single Variable. SINDH UNIVERSITY RESEARCH JOURNAL (SCIENCE SERIES), 48(1), 171–174.
XIX. Shah, F. A., Noor, M. A., & Batool, M. (2014). Derivative-free iterative methods for solving nonlinear equations. Applied Mathematics and Information Sciences, 8(5), 2189–2193. https://doi.org/10.12785/amis/080512
XX. Subash, R., & Sathya, S. (2011). NUMERICAL SOLUTION OF FUZZY MODIFIED NEWTON-RAPHSON METHOD FOR SOLVING NON-LINEAR EQUATIONS. International Journal of Current Research, 3(11), 390–392. http://www.journalcra.com
XXI. Suhadolnik, A. (2013). Superlinear bracketing method for solving nonlinear equations. Applied Mathematics and Computation, 219(14), 7369–7376. https://doi.org/10.1016/j.amc.2012.12.064
XXII. Umar Sehrish, Muhammad Mujtaba Shaikh, Abdul Wasim Shaikh. : A NEW QUADRATURE-BASED ITERATIVE METHOD FOR SCALAR NONLINEAR EQUATIONS. J. Mech. Cont.& Math. Sci., Vol.-15, No.-10, October (2020) pp 79-93. DOI : 10.26782/jmcms.2020.10.00006
XXIII. Yasmin, N., & Junjua, M. (2012). SOME DERIVATIVE FREE ITERATIVE METHODS FOR SOLVING NONLINEAR EQUATIONS. Academic Research International, 2 (1), 75–82. www.savap.org.pkwww.journals.savap.org.pk

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DESIGN OF FULLY AUTOMATIC HYBRID SOLAR BASED WATER IRRIGATION, CROPS PROTECTION, AND WATER HARVESTING SYSTEM

Authors:

Anwar Parviz, Muhammad Noman

DOI NO:

https://doi.org/10.26782/jmcms.2021.04.00007

Abstract:

Since water scarcity is an emerging problem in Pakistan; Water Resources Preservation is a matter of substantial importance. When excess water is used for agricultural purposes, it may damage the crops. Manual control and management of water for agricultural purposes take a lot of effort and time. This research work is an effort to propose and implement a fully automated solar irrigation system that may solve the problem of excessive usage of water for agricultural purposes. This proposed system, after sensing various indicators such as wind, temperature, soil, and rain, turns the water motor on and off accordingly and thus ensures calculated and wise usage of water. Moreover, our proposed system has a covering mechanism that covers the model during the rain and when needed.

Keywords:

Crops,solar irrigation system,water scarcity,motor,

Refference:

I. Adnan, Shahzada, and Azmat Hayat Khan. “Effective rainfall for irrigated agriculture plains of Pakistan.” Pakistan Journal of Meteorology 6.11 (2009): 61-72.
II. Government of Bangladesh (GOB); United Nations Development Program (UNDP). “The Probable Impacts of Climate Change on Poverty and Economic Growth and Options of Coping with Adverse Effects of Climate Change in Bangladesh”, Policy Study: Dhaka, Bangladesh, 2009
III. Gunturi, Venkata Naga Rohit. “Microcontroller based automatic plant irrigation system.”International Journal of Advancements in Research & Technology 2.4 (2013): 194-198
IV. Kirby, J.M.; Mainuddin, M.; Mpelasoka, F.; Ahmad, M.D.; Palash, W.; Quadir, M.E.; Shah-Newaz, S.M.; Hossain, M.M. “The impact of climate change on regional water balances in Bangladesh”, Clim. Chang. 2016, 135, 481–491
V. Mirza, M.M.Q. “Modeling the Effects of Climate Change on Flooding in Bangladesh”, Ph.D. Thesis, International Global Change Institute (IGCI), University of Waikato, Hamilton, New Zealand, 1997.
VI. Spash, C.L. “Climate change: Need for new economic thought”, Econ. Political Wkly. 2007, 42, 483–490.
VII. Spash, C.L. “The economics of climate change impacts à la Stern”, Novel and nuanced or rhetorically restricted? Ecol. Econ. 2007, 63, 706–713.
VIII. Worthington, E. Barton, ed. “Arid land irrigation in developing countries”, Environmental problems and effects. Elsevier, 2013.

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