ISSN (Print): 2333-8490

ISSN (Online): 2333-8431

Website: http://www.sciepub.com/journal/ajma

Editor-in-chief: Grigori Rozenblum

You are here

Currrent Issue: Volume 5, Number 1, 2017

Article

Matehmatical Study of Thermosolutal Convection in Heterogeneous Vscoelastic Fluid in the Presence of Porous Medium

1Department Applied Sciences (Mathematics), Chandigarh Engineering College Landarn, Mohali, Punjab, India


American Journal of Mathematical Analysis. 2017, 5(1), 12-16
doi: 10.12691/ajma-5-1-3
Copyright © 2017 Science and Education Publishing

Cite this paper:
Anil Kumar. Matehmatical Study of Thermosolutal Convection in Heterogeneous Vscoelastic Fluid in the Presence of Porous Medium. American Journal of Mathematical Analysis. 2017; 5(1):12-16. doi: 10.12691/ajma-5-1-3.

Correspondence to: Anil  Kumar, Department Applied Sciences (Mathematics), Chandigarh Engineering College Landarn, Mohali, Punjab, India. Email: dranilkumar73@rediffmail.com

Abstract

The present paper a thermo-solutal convection in Walters B' heterogeneous visco-elastic fluid through Brinkman permeable effect is investigated. The investigation of thermosolutal convection is proposed by its complexities of double diffusive dissemination and importance of geophysics and nuclear physics. The results are investigation of the oscillatory modes exists under different conditions and non-oscillatory modes are unstable.

Keywords

References

[1]  Chandrasekhar, S.. Hydrodynamic and Hydromagnetic Stability. Clarendon Press, Oxford, UK, 1961.
 
[2]  Veronis, G.. On Finite Amplitude Instability in Thermohaline Convection. J. Marine Res. 23. pp. 1-17. 1965.
 
[3]  Tabor, H. and Matz, R.. Solar Pond Project, Solar Energy. 9. pp. 177-182. 1965.
 
[4]  Shirtcliffe, T.G.L.. Thermosolutal Convection: Observation of an Overstable Mode. Nature (London). 213. pp. 489-490. 1967.
 
[5]  Lister, P.E.. On the Thermal Balance of a Mid-Ocean Ridge. Geophys. J. Roy. Astr. Soc. 26. pp. 515-535. 1972.
 
Show More References
[6]  [McDonnel, J.A.M.. Cosmic Dust. John Wiley and Sons, Toronto. p. 330. 1978.
 
[7]  Vest, C.M. and Arpaci, V.S.: Overstability of a Viscoelastic Fluid Layer Heated From Below. J. Fluid Mech. 36. pp. 613-619. 1969.
 
[8]  Bhatia, P.K. and Steiner, J.M.: 1972. Convective Instability in a Rotating Viscoelastic Fluid Layer. Zeitschrift fur Angewandte Mathematik und Mechanik. 52. pp. 321-327. 1972.
 
[9]  Sharma, R.C. and Sharma, K.C.. Thermal Instability of a Rotating Maxwell Fluid Through Porous Medium. Metu J. Pure Appl. Sci. 10. pp. 223-229. 1977.
 
[10]  Sharma, R.C.: Thermal Instability in a Viscoelastic Fluid in Hydromagnetics. Acta Physica Hungarica. 38. pp. 293-298. 1975.
 
[11]  Oldroyd, J.G.: Non-Newtonian Effects in Steady Motion of Some Idealized Elastico-Viscous liquids. Proc. Royal Society London. A245. pp. 278-297. 1958.
 
[12]  Walters, K.. The Motion of Elastico-Viscous Liquid Contained Between Coaxial Cylinders. J. Mech. Appl. Math. 13. pp. 444-453. 1960.
 
[13]  Walters, K.: The Solution of Flow Problems in Case of Materials With Memory. J. Mecanique. 1. pp. 469-479. 1962.
 
[14]  Chakraborty, G. and Sengupta, P.R.. MHD Flow of Unsteady Viscoelastic (Walters Liquid B’) Conducting Fluid Between Two Porous Concentric Circular Cylinders. Proc. Nat. Acad. Sciences India. 64. pp. 75-80.1994.
 
[15]  Sharma, R.C. and Kumar, P.. On the Stability of Two Superposed Walters Elastico-Viscous Liquid B’. Czech. J. Phys. 47. pp. 197-204. 199 1997.
 
[16]  Sharma, R.C. and Kumar, P.. Rayleigh- Taylor Instability of Two Superposed Walters B’ Elastico-Viscous Fluids in Hydromagnetics. Proc. Nat. Acad. Sci. India. 68. pp.151-161. 1998.
 
[17]  Kumar, P.. Effect of Rotation on Thermal Instability in Walters B’ Elastico-Viscous Fluid. Proc. Nat. Acad. Sci. India. 71, pp. 33-41. 2001.
 
[18]  Kumar, P., Mohan, H. and Singh, G.J.. Stability of Two Superposed Viscoelastic Fluid-Particle Mixtures. Z. Angew. Math. Mech. 86. pp. 72-77. 2006.
 
[19]  Pawan Preet Kaur, SP Agrawal and Anil Kumar (2014). Analysis of heat transfer in hydrodynamic rotating flow of viscous fluid through a non homogenious porous medium with constant heat source / sink, International J. of Engg. Research & Indu. Appls., Vol.7, No. I, pp 9-24.
 
[20]  Pawan Preet Kaur, SP Agrawal and Anil Kumar (2013). Finite Difference Technique for Unsteady MHD Periodic Flow of Viscous Fluid through a Planer Channel, American Journal of Modeling and Optimization, USA, Vol. 1, No. 3, 47-55.
 
[21]  Anil Kumar, CL Varshney and Sajjan Lal (2013). Perturbation technique of MHD free convective flow through infinite vertical porous plate with constant heat flux, International Journal of Mathematical Modeling and Physical Sciences, India Vol. 01, (02) pp 1-5, 2013.
 
[22]  Anil Kumar and S P Agrawal (2013). Mathematical and Simulation of lid driven cavity flow at different aspect ratios using single relaxation time lattice Boltzmann technique, American Journal of theoretical and Applied Statistics, USA vol 2 (3), pp 87-93.
 
[23]  Anil Kumar, R. K. Saket, C L Varshney and Sajjan Lal. Finite difference technique for reliable MHD steady flow through channels permeable boundaries, International Journal of Biomedical Engineering and Technology (IJBET) UK, Vol. 4(2) pp 101-110, 2010.
 
Show Less References

Article

On Weak Solutions of Systems of Strongly Nonlinear Parabolic Variational Inequalities

1Mathematics Department, Helwan University, Faculty of Science, Cairo, Egypt


American Journal of Mathematical Analysis. 2017, 5(1), 7-11
doi: 10.12691/ajma-5-1-2
Copyright © 2017 Science and Education Publishing

Cite this paper:
A.T. El-Dessouky. On Weak Solutions of Systems of Strongly Nonlinear Parabolic Variational Inequalities. American Journal of Mathematical Analysis. 2017; 5(1):7-11. doi: 10.12691/ajma-5-1-2.

Correspondence to: A.T.  El-Dessouky, Mathematics Department, Helwan University, Faculty of Science, Cairo, Egypt. Email: adeltohamy60@gmail.com

Abstract

In this paper we prove the existence of weak solutions for systems of variational inequalities of strongly nonlinear parabolic operators: where

Keywords

References

[1]  Br𝐞́zis, H. and Browder, F.E., Strongly nonlinear parabolic initial boundary value problems.Proc.Nat.Acad.Sci.U.S.A.76, 1979, 38-40.
 
[2]  Browder, F.E., and Br𝐞́zis, H., Strongly nonlinear parabolic variational inequalities. Proc. Nat. Acad. Sci. U.S.A .77, 2, 1980, 713-715.
 
[3]  El-Dessouky, A.T., Strongly nonlinear parabolic variational inequalities. J. of Mathematical Analysis and Applications, 181, 1994, 498-504.
 
[4]  Landes, R., and Mustonen, V., A strongly nonlinear parabolic initial boundary value problem. Arkiv for Matematik, 25, 1987, 29-40.
 
[5]  Landes, R., A note on strongly nonlinear parabolic equations of Higher order. Diff. and Integral equations,Vol.3, No.5, 1990, 851-862.
 

Article

Analysis of Ground Water Quality by Fuzzy Comprehensive Evaluation in Cauvery Delta Region, Tamil Nadu, India

1Associate professor of Mathematics, A.D.M College for women (Autonomous), Nagapattinam, India

2Research scholar, Department of Mathematics, A.D.M College for women (Autonomous), Nagapattinam, India


American Journal of Mathematical Analysis. 2017, 5(1), 1-6
doi: 10.12691/ajma-5-1-1
Copyright © 2017 Science and Education Publishing

Cite this paper:
R. Sophia Porchelvi, P. Selvavathi. Analysis of Ground Water Quality by Fuzzy Comprehensive Evaluation in Cauvery Delta Region, Tamil Nadu, India. American Journal of Mathematical Analysis. 2017; 5(1):1-6. doi: 10.12691/ajma-5-1-1.

Correspondence to: R.  Sophia Porchelvi, Associate professor of Mathematics, A.D.M College for women (Autonomous), Nagapattinam, India. Email: sophiaporchelvi@gmail.com

Abstract

The present study consisted of the estimation of some physicochemical parameters and quality of ground water from Cauvery delta region, Tamil Nadu (India).The water sample were collected from various parts of Cauvery delta region. Ten parameters (via TDS, turbidity, pH, Chloride, Calcium, Phosphate, Zinc, Copper, Iron and lead) were selected to assess the ground water quality degree by using fuzzy comprehensive evaluation method. The water samples were grouped into five categories according to Surface Water Quality Standards (as per IS: 2296). Some of the concentrations of PH, turbidity, phosphate were between the class A and class C with the exemption of the parameters (TDS, chloride, calcium, zinc, copper, iron, lead) which exceeds class C. From the analysis, these exceeding parameters were found to be the main pollutant in the sampling areas and hence the study further revealed that the water is not safe for drinking but suitable for aquatic life and also for irrigation purpose in some extend.

Keywords

References

[1]  Bhatt, K.B., & Saklani, S. (1996), “Hydrogeochemistry of the Upper Ganges River”, India. Journal of the Geological Society of India, 48, 171-182.
 
[2]  Karanth, K. R. (1987), “Groundwater assessment, development and management”, New Delhi: Tata-McGraw Hill.
 
[3]  Nisi, B., Buccianti, A., Vaselli, O., Perini, G., Tassi, F., Minissale, A., et. (2008), “Hydrogeochemistry and strontium isotopes in the ArnoRiver Basin (Tuscany,Italy): Constraints on natural controls by statistical modeling”, Journal of Hydrology, 360, 166-183.
 
[4]  Schot, P. P., & Van der Wal, J. (1992), “Human impact on regional groundwater composition through intervention in natural flow patterns and changes in land use”, Journal of Hydrology, 134, 297-313.
 
[5]  Fetters, C. W. (1990), “Applied hydrology”, New Delhi: CBS.
 
Show More References
[6]  Freeze, R. A., & Cherry, J.A. (1979), “Groundwater. Englewood Cliffs: Prentice Hall”, pp.604.
 
[7]  Qian Zhang, Shengli Wang, Muhammad Yousaf, Shuixian Wang, Zhongren Nan, Jianmin Ma, Depeng Wang, Fei Zang, “Hydrochemical characteristics and water quality assessment of surface water at Xiahe county in Tibetan Plateau pastoral of China”, August 2016.
 
[8]  Chidya R C G, Sajidu S M I, Mwatseteza J Fetc. Evaluation and assessment of water quality in Likangala River and its catchment area. Physics and Chemistry of the Earth, Parts A/B/C. 2011, 36(14-15): 865-871.
 
[9]  Yang W D Q L Q. A Research on the Motivation Forces of the Natural Pasture and Sustainable Development in Xiahe County. 2007.
 
[10]  Sun W, Xia C, Xu Metc. Application of modified water quality indices as indicators to assess the spatial and temporal trends of water quality in the Dongjiang River. Ecological Indicators. 2016, 66:306-312.
 
[11]  S. Suratman* M I M S, Y.Y. Hee, E.A. Bedurus & M.T. Latif. “A Preliminary Study of Water Quality Index in Terengganu River Basin, Malaysia. 2015.
 
[12]  Cheng H, Ouyang W, Hao Fetc., “The non-point source pollution in livestock-breeding areas of the Heihe River basin in Yellow River”. Stochastic Environmental Research and Risk Assessment. 2006, 21(3): 213-221.
 
[13]  Gyawali S, Techato K, Yuangyai Cetc., “Assessment of Relationship between Land uses of Riparian Zone and Water Quality of River for Sustainable Development of River Basin, A Case Study of U-Tapao River Basin”, Thailand Procedia Environmental Sciences. 2013, 17:291-297.
 
[14]  Zampella R A, Procopio N A, Lathrop R Getc. “Relationship of Land-Use/Land-Cover Patterns and Surface-Water Quality in The Mullica River Basin”. Journal of the American Water Resources Association. 2007, 43(3):594-604.
 
[15]  Giri S, Qiu Z. “Understanding the relationship of land uses and water quality in Twenty First Century: A review”. J Environ Manage. 2016, 173:41-48.
 
[16]  Yu D, Shi P, Liu Yetc. “Detecting land use-water quality relationships from the viewpoint of ecological restoration in an urban area”. Ecological Engineering. 2013, 53:205-216.
 
[17]  Zhang B, Song X, Zhang Yetc. “Hydrochemical characteristics and water quality assessment of surface water and groundwater in Songnen plain, Northeast China”. Water Res. 2012, 46(8): 2737-2748.
 
[18]  Effendi H. “River Water Quality Preliminary Rapid Assessment Using Pollution Index”. Procedia Environmental Sciences. 2016, 33:562-567.
 
[19]  Shrestha S, Kazama F. “Assessment of surface water quality using multivariate statistical techniques: A case study of the Fuji river basin, Japan”. Environmental Modelling & Software. 2007, 22(4): 464-475.
 
[20]  Singh E J, Gupta A, Singh N R. “Groundwater quality in Imphal West district, Manipur, India, with multivariate statistical analysis of data”. Environ Sci Pollut Res Int. 2013, 20(4):2421-2434.
 
[21]  Belkhiri, L., Boudoukha, A., Mouni, L., (2010), A multivariate Statistical Analysis of Groundwater Chemistry Data, International Journal of Environmental Research, 5(2), 537-544.
 
[22]  BIS (1991), Specifications for Drinking Water, IS:10500:1991, Bureau of Indian Standard New Delhi, India.
 
[23]  Ghasemi, J., Saaidpour, S., (2007), Quantitative structure-property relationship study of n-octanol-water partition coefficients of some diverse drugs using multiple linear regression, Analitica Chimica Acta, 604 (2), 99-106.
 
[24]  Iyer, Padmanabha C.S., Sindhu, M., Kulkarni, S., Tambe, S., Kulkarni, D., (2003), Journal of Environmental Monitoring, 5, pp 324-327.
 
[25]  Jain, C. K., Sharma, M. K., (1997), “Relationship among water quality parameters of groundwater of Jammu District”, Pollution research, 16(4), pp 241-246.
 
[26]  Jain, C. K., Sharma, M. K., (2000), “Regression analysis of groundwater quality data of Sagar District Madhya Pradesh”, Indian Journal of Environmental Health, 42(4), 159-168.
 
[27]  Joarder, M. A., Raihan, F., Alam, J. B., Hasanuzzaman, S., (2008), “Regression analysis of Groundwater quality data of Sunamjang District,Bangladesh”, International Journal of Environmental Research, 2(3), pp 291-296.
 
[28]  Jothivenkatachalam, K., Nithya, A., Chandra Mohan, S., 2010. “Correlation analysis of drinking water quality in and around Perur block of Coimbatore District, Tamil Nadu, India”, Rasayan Journal Chemistry, 3(4), 649-654.
 
[29]  Kumar, A., Garg, S. N., Gopal, K., (1994), “Relationship between electrical conductivity and Cationic and anionic contents in groundwater”, Indian Journal of Environmental Protection, 14(7), 595-603.
 
[30]  Kumar A., (2004), “Water Pollution”. Nisha Enterprises, New Delhi, 1.
 
[31]  Cheng J, Tao J-p. “Fuzzy Comprehensive Evaluation of Drought Vulnerability Based on the Analytic Hierarchy Process”. Agriculture and Agricultural Science Procedia. 2010, 1:126-135.
 
[32]  Ren J C D S L W H. “A Model Of Multi-Objective Comprehensive Evaluation For Power Plant Projects”. 2002.
 
[33]  Liu Y, Fang P, Bian Detc. “Fuzzy comprehensive evaluation for the motion performance of autonomous underwater vehicles”, Ocean Engineering. 2014, 88:568-577.
 
[34]  Dahiya S, Singh B, Gaur Setc. “Analysis of groundwater quality using fuzzy synthetic evaluation”. J Hazard Mater. 2007, 147(3): 938-946.
 
[35]  Liu L, Zhou J, An Xetc. “Using fuzzy theory and information entropy for water quality assessment in Three Gorges region, China”, Expert Systems with Applications. 2010, 37(3):2517- 2521.
 
[36]  WANG Jian-Hua L X-G, Jiang Ming,LI Xiao-Yan and TIAN Jing-Han, “Fuzzy Synthetic Evaluation of Wetland Soil Quality Degradation: A Case Study on the Sanjiang Plain”, Northeast China1. 2009.
 
[37]  Piplani R, Wetjens D. “Evaluation of entropy-based dispatching in flexible manufacturing systems”. European Journal of Operational Research. 2007, 176(1):317-331.
 
[38]  E. Ertugrul Karsak* E T. “Fuzzy multi-criteria decision-making procedure for evaluating advanced manufacturing system investments”.
 
[39]  Shan Feng a L D X b. “Decision support for fuzzy comprehensive evaluation of urban development”. 1999.
 
[40]  Guo L, Gao J, Yang Jetc. “Criticality evaluation of petrochemical equipment based on fuzzy comprehensive evaluation and a BP neural network”. Journal of Loss Prevention in the Process Industries. 2009, 22(4):469-476.
 
[41]  G.Annadurai S R B, V.R.Srinivasamoorthy. “Mathematical modeling of phenol degradation system using fuzzy comprehensive evaluation”. 2000.
 
[42]  Pan Jun Meng Li Z Z. “The Method of Quadratic Combination Weighting Fuzzy Comprehensive Evaluation applied in Water Quality Assessment”. 2014.
 
[43]  Bi X, Isaili R A M, Zheng Q. “Evaluation of Wastewater Treatment Quality in the West Bank- Palestine Based on Fuzzy Comprehensive Evaluation Method”. 2015:219-221
 
[44]  Zhou Z, Zhang X, Dong W. “Fuzzy Comprehensive Evaluation for Safety Guarantee System of Reclaimed Water Quality”. Procedia Environmental Sciences. 2013, 18:227-235.
 
[45]  Gharibi H, Mahvi A H, Nabizadeh Retc. “A novel approach in water quality assessment based on fuzzy logic”. J Environ Manage. 2012, 112:87-95.
 
[46]  Environment M o t. Surface Water Quality Trends In Ontario 1964-1979.
 
[47]  Simões F d S, Moreira A B, Bisinoti M Cetc. “Water quality index as a simple indicator of aquaculture effects on aquatic bodies”. Ecological Indicators. 2008, 8(5):476-484.
 
[48]  Akkoyunlu A, Akiner M E. “Pollution evaluation in streams using water quality indices: A case study from Turkey's Sapanca Lake Basin”. Ecological Indicators. 2012, 18:501-511.
 
[49]  Hoseinzadeh E, Khorsandi H, Wei Cetc. “Evaluation of Aydughmush River water quality using the National Sanitation Foundation Water Quality Index (NSFWQI), River Pollution Index (RPI), and Forestry Water Quality Index (FWQI)”. Desalination and Water Treatment. 2014, 54(11):2994-3002.
 
[50]  Gautam S K, Maharana C, Sharma Detc. “Evaluation of groundwater quality in the Chotanagpur plateau region of the Subarnarekha river basin, Jharkhand State, India”. Sustainability of Water Quality and Ecology. 2015, 6:57-74.
 
Show Less References