Archive

Abstract:

Pulsatile flow of blood in an elastic circular tube with slip at the permeable walls is investigated in the present analysis solutions for axial and radial velocity has constructed. The volume tri crate of blood flow also measured in the axial direction. The expression for flow characteristic, velocity profile are obtained. Numerical results are shown in tabular form. The effect of slip velocity, size of the artery, viscosity on the flow are shown graphically and discussed briefly.

Keywords:

Refference:

I.Chandran K.B. Cardiovascular Biomechanics , New YorkUniversity ,1992

II.Kathleen Wilkie Human blood flow2003

III.An Introduction to Mathematical Physiology & Biology,Cambridge University Press,P.J. MAJUMDER1999

IV.Mathematical Biology J . D . Murray Springer 3rd. EditionP.1471532004

V.MHD Steady flow in a channel .With slip at the permeableBoundariesOld Makinde , E. OsalusiRom. Journ.Phys. Vol 51P319-328, Bucharest2006

AN APPROACH TO IMPROVE THE PERFORMANCE OF A POSITION CONTROL DC MOTOR BY USING DIGITAL CONTROL SYSTEM

Authors:

Md. Salauddin Khan, Masudul Islam, Md. Rasel Kabir, Lasker Ershad Ali

DOI NO:

https://doi.org/10.26782/jmcms.2016.07.00002

Abstract:

Bangladesh bureau of statistics (BBS) publish a statistical year book in every year where comprehensive and systematic summary of basic statistical information of Bangladesh covering wide range of fields. BBS also forecast different sectors such aseconomics, weather, agriculture etc in different time in this country. In this paper wemainly concern on the wheat, rice and maize foodgrain which plays a vital role ineconomic development of Bangladesh. The main purposes of this paper as to comparewhich techniques are better BBS’s or statistical techniques for forecasting. There aredifferent forecasting models are available in statistics among these we used Auto regressive (AR), Moving Average(MA), Autoregressive Moving Average (ARMA)and Auto regressive Integrated Moving Average (ARIMA) models. For this reason, weclarify the stationary and non-stationary series by graphical method. On the basis of that,the stationary model is being set up asthe forecasting purpose. After analyze, we compare the forecasting result of our selective foodgrain and find that forecasted valuesusing statistical techniques are nearest to the actual values compare to BBS’s project edvalues.

Keywords:

ARIMA,ARMA,Forecast,Foodgrain,

Refference:

I. Abdullah, L. (2012),ARIMA Model for Gold Bullion Coin Selling Prices Forecasting,International Journal of Advances in Applied Sciences. Vol. 1, No.4, pp. 153-158.

II. Anderson, T.W. (1984),An Introduction to Multivariate Statistical Analysis, 2nded.New York:John Wiley and Sons Inc.

III. Arumugan, P. and Anithakumari, V. (2013),Fuzzy Time Series Method for Forecasting TaiwanExport Data,International Journal of Engineering trendsand Technology. Vol.8,pp. 3342-3347.

IV. Box, G. E. P. and Jenkins, G. M. (1976),Time Series Analysis: Forecasting and Control,San Francisco: Holden-Day.

V. Brokwell, P.J. and Davis, R.A. (1997),Introduction to Time Series and Forecasting, Springer,New York.

VI.Clements, M. and Hendry, D. (1998),Forecasting Economic Time Series,United UniversityPress, Cambridge.

VII. Deepak, P., et al. (2015), A Comparison of forecasting methods: Fundamentals,Polling, Prediction Markets, and Experts,A Journal of Prediction Markets,Vol.23, No.2, pp.1-31.

VIII. Diebold, F. (2004),Elements of Forecasting, 3rded. Thomsos sourth-westrn,India.

IX. Ediger, S.A, (2006),ARIMAForecasting of Primary Energy Demand by Fuel inTurkey,Energypolicy, Vol. 35, pp.1-8.

X. Gouriroux, C. and Monfort, A. (1997),Time Series and Dynammic Models,Giampiero,M.Gallo Cambridge.

XI. Gujarati, D.N. (2004),Basic Econometrics, 4thed.,McGraw Hill, New York.

XII. Hannan, E.J. (1994),Multiple Time Series,New York: John Wiley & Sons Inc.

XIII. Kumar, et al. (2009),Surface flux modelingusing ARIMA technique in humansubtropicalmonsoon area,Journal of Atmospheric and Solar-TerrestrialPhysics. Vol. 71, pp. 1293-1298.

XIV. Lloret, et al. (2000),Time Series Modeling of Landings in NorthMediterranean Sea,ICESJournal of Marine Science: Journal du Conseil. Vol.57, pp. 171-184.

XV. Mitrea, C. A., Lee, C. K.M. and Wu,Z. (2009), A Comparison betweenNeural Networks and Traditional Forecasting Methods: A Case Study,International Journal of Engineering Business Management, Vol. 1, No. 2, pp.19-24.

XVI. Mucuk, M. and Uysal, D. (2009),Turkey’s Energy Demand,Current ResearchJournal of SocialSciences, Vol.1(3), pp. 123-128.

XVII. Pingfan, H. and Zhibo, T. (2014), A comparison study of the forec asingperformance of three international organizations,JEL codes: C30, C80.

XVIII. Prindyck,R.S. and Rubinfeld, D.L. (1981),Economic Models and EconomicForecasts,3rded.McGraw-Hill, Inc.

XIX. Slvanathan, E. A. (1991),A Note on the Accuracy of Business Economists GoldPrice Forecasts,Australian Journal of Management. Vol. 16, pp. 91-94

XX. Tseng, et al. (2001),Fuzzy ARIMA model for forecasting the foreign exchangemarket,FuzzySets and Systems. Vol. 118, pp. 1-11.

XXI. Wood, et al. (1996), Classifying Trend Movements in the MSCI U.S.A.Capitalmarket Index-A,Comparison of Regressions, ARIMA and Neural Network Method.Computers &Operation Research. Vol. 23, pp. 611-622.

MAGNETO-HYDRODYNAMIC FORCED CONVECTIVE BOUNDARY LAYER FLOW PAST A STRETCHING / SHRINKING SHEET

Authors:

Mohammad Wahiduzzaman, Runu Biswas, Md. Eaqub Ali

DOI NO:

https://doi.org/10.26782/jmcms.2016.07.00003

Abstract:

MHD boundary layer forced convection flow along a shrinking surface withvariable heat and mass flux in the presence of heat source is studied. The flow isproducedowing to linear shrinking of the sheet and is influenced by uniform transversemagnetic field. The boundary layer partial differential equations of momentum, heat andmass transfer equations are converted into nonlinear ordinary differential equations bysimilarity transformation. Numerical solution of the resulting boundary value problem isobtained using Nachtsheim-Swigert Shooting iteration scheme along with the sixth orderRunge-Kutta method. The effects of different parameter on velocity, temperature andconcentration are shown graphically. Skin friction coefficient, Nusselt number andSherwood number are also for different values of the parameter are also involved in thestudy.

Keywords:

Refference:

I.Chen, C.K. and Char, M.I (1988),“Heat transfer of a continuously stretchingsurface with suction and blowing”,Journal of Mathematical Analysis andApplications135[2], 568-580.

II.Ali, M.E. (1995), “Thermal boundary layer on a power-law stretched surfacewith suction or injection”,International Journal of Heat and Fluid Flow16[4], 280-290.

III.Elbashbeshy, “E.M.A. (1998).Heat transfer over a stretching surface withvariable surface heat flux”,Journal of Physics D: Applied Physics31 [16],1951-1954.

IV.Liao, S.J. (2005), “A new branch of solution of boundary layer flows over apermeable stretching plate”,International Journal of Heat and Mass Transfer48[12], 2529-2539.

V.Bhargava, R. Sharma, S. Takhar, H.S. and Bhargava, P (2007), “Numericalsolutions for Micropolar transport phenomena over nonlinear stretchingsheet”,Nonlinear Analysis: Modeling and Control12[1], 45-63.

VI.Khedr, M.E., Chamka, A.J. and Bayomi, M. (2009), “MHD flow of amicropolar fluid past a stretched permeable surface with heat generation orabsorption”,Nonlinear Analysis: Modeling and Control14[1], 27-40.

VII.S. P. Anjali Devi and J. W. S. Raj (2014), “Numerical Simulation of Magneto-hydrodynamic Forced Convective Boundary Layer Flow past aStretching/Shrinking Sheet Prescribed with Variable Heat Flux in thePresence of Heat Source and Constant Suction ”,Journal of Applied FluidMechanics,7[3], 415-423, 2014.

DEFORMATION OF AN INFINITE DIELECTRIC MEDIUM WITH A HOLE IN THE SHAPE OF PASCAL LIMACON

Authors:

D.C. Sanyal

DOI NO:

https://doi.org/10.26782/jmcms.2016.07.00004

Abstract:

A two dimensional problem of electrostriction with a hole in the of Pascal's limacon is solvcd by complwx variable method. The distributions of stresses in an infinite dielection plate when the hole is filled up by air is subjected to an electric filed unifrom at infinity as well as it is acted on by appiled two dimensional tractions at infinity. The hoop stress is calculated on the boundary of the hole.

Keywords:

Refference:

I. Stratton, J.D.: Electromagnetic Theory, Mc Graw- Hill, new York (1941).

II. Landau, L.D. Electrodynamics of continuous Media Addision Wesley (1960).

III. Knops, R.J. Quart Jour. Math. Vol.16(1963) p.377.

IV. Maikap G.H. and Sengupta, P.R. Acta Cien. Ind. Vol.17(1991) p.498.

ON THE EXACT SOLVABILITY OF SOME POTENTIALS

Authors:

Soumya Das, Kusumika Kundu, P. S. Majumdar

DOI NO:

https://doi.org/10.26782/jmcms.2017.01.00001

Abstract:

In the present paper it is shown that shape invariance is not a necessary condition for exact solvability of a potential in Quantum mechanics .Our contention is established by considering Eckart and Morse II potentials.

Keywords:

Exact solvability,Shape independence,Eckart Potential,Morse II Potential,

Refference:

1) Cooper F., Ginocchio J N and Khare A 1987, Phys .Rev .D 36, 2458
2) Genedenshtein, L. 1983, JETP Lett 38, 356 .
3) Ginocchio, J. N. 1985 Ann.Phys 159, 467.
4) Ter Haar, D. 1960 Problems in quantum mechanics (Infosearch, London, 1960).
5) Eckart, C. 1930 , Phys Rev 35, 1303 .
6) Morse, P. M. 1929 Phys Rev 34, 57.
7) Dutt, R. Khare, A. Sukhatme 1986 Phys let B 181, 295 .
8) Cooper, F. and Freedman, B. 1983 Ann.Phys 146, 262.
9) Feynmam, R. P. 1939 Phys Rev 56, 340.

SIMILARITY SOLUTION OF NATURAL CONVECTIVE BOUNDARY LAYER FLOW AROUND A VERTICAL SLENDER BODY WITH SUCTION AND BLOWING

Authors:

Md. Hasanuzzaman, Akio Miyara

DOI NO:

https://doi.org/10.26782/jmcms.2017.01.00002

Abstract:

In this paper, the similarity solution of natural convective laminar boundary layer flow around a vertical slender body with suction and blowing has been investigated. Firstly, the governing boundary layer partial differential equations have been made dimensionless and then simplified by using Boussinesq approximation. Secondly, similarity transformations are introduced on the basis of detailed analysis in order to transform the simplified coupled partial differential equations into a set a ordinary differential equations. The transformed complete similarity equations are solved numerically by using Fourth order Runge-Kutta method as well as MATLAB. Finally, the flow phenomenon has been characterized with the help of obtained flow controlling parameters such as suction parameter, buoyancy parameter, Prandtl number, body-radius parameter and other driving parameters. The effects of dimensionless parameters on the velocity and temperature distributions are presented graphically. It is found that a small suction or blowing can play a significant role on the patterns of flow and temperature fields.

Keywords:

Similarity solution,natural convective,vertical slender body,suction or blowing,

Refference:

1) Clarke, J. F. Riley, N. : Natural convection induced in a gas by the presence of a hot porous horizontal surface, Q. J. Mech. Appl. Math., 28, 373–396, 1975.

2) Schneider, W. : A similarity solution for combined forced and free convection flow over a horizontal plate, Int. J. Heat Mass Transfer, 22, 1401–1406, 1979.

3) Merkin, J. H. Ingham, D. B.: Mixed convection similarity solutions on a horizontal surface, ZAMP, 38, 102–116, 1987.

4) Ramanaiah, G. Malarvizhi, G. and Merkin, J. H.: A unified treatment of mixed convection on a permeable horizontal plate, Wäfirme-und Stoffübertragung, 26, 187–192, 1991.

5) Deswita, L. Nazar, R. Ahmad R. Ishak, A and Pop, I.: Similarity Solutions of Free Convection Boundary Layer Flow on a Horizontal Plate with Variable Wall Temperature, European Journal of Scientific Research, 27(2), 188–198, 2009.

6) Hossain, M. M. T. and Mojumder, R. : Similarity solution for the steady natural convection boundary layer flow and heat transfer above a heated horizontal surface with transpiration, Int. J. Appl. Math. Mech., 6(4), 1–16, 2010.

7) Hossain, M. M. T. Mojumder, R. and Hossain, M. A. : Solution of natural convection boundary layer flow above a semi-infinite porous horizontal plate under similarity transformations with suction and blowing, Daffodil International University Journal of Science and Technology, 6(1), 43–51, 2011.

8) Hossain, M. M. T. Mandal, B. and Hoossain, M. A. : Similarity Solution of Unsteady Combined Free and Force Convective Laminar Boundary Layer Flow about a Vertical Porous Surface with Suction and Blowing, Procedia Engineering, 56,134–140, 2013.

9) Van Dyke, M. : Free convection from a vertical needle, Problems of Hydrodynamics and Continuum Mechanics (SIAM Publication, Philadelphia, Penn.), 1969.

10) Kuiken, H. K. : The thick free-convective boundary layer along a semi-infinite isothermal vertical cylinder, ZAMP, 25, 497, 1974.

HIGH DOF INTERPRETED EMG DATA BASED PROSTHETIC ARM

Authors:

Biswarup Neogi, Sudipta Ghosh, Debasish Kundu, Bipasha Chakrabarti, Swati Barui

DOI NO:

https://doi.org/10.26782/jmcms.2017.01.00003

Abstract:

EMG is the detection of the electrical activity associated with muscle contraction. It is obtained by measurement of the electrical activity of a muscle during contraction. EMG signals are directly linked to the desire of movement of the person. Robot arms are versatile tools found in a wide range of applications. While the user moves his arm, (EMG) activity is recorded from selected muscles, using surface EMG electrodes. By a decoding procedure the muscular activity is transformed to kinematic variables that are used to control the robot arm. This patent is the innovative design of a new low-cost series elastic robotic arm. The arm is unique in that it achieves reasonable performance for the envisioned tasks with high DOF. There are numerous dimensions over which robotic arms can be evaluated, such as backlash, payload, speed, bandwidth, repeatability, compliance, human safety, and cost, to name a few. In robotics research, some of these dimensions are more important than others: for grasping and object manipulation, high repeatability and low backlash are important. To develop the articulated innovative arm design of the robot with high DOF equations were developed for both forward and inverse kinematics. Forward kinematics gives the location of the end effector in the “universe” frame. The inverse kinematics gives the joint angles needed in order for the to the robot arm reach the goal frame. This high DOF based prosthetic arm operates according to EMG database. The EMG signal is obtained for different users for different arm movements using signal acquisition system. The EMG signals are used as input to the Microcontroller and converted to digital ones in the comparator. According to these signals the program built in the microcontroller make decisions to control the motors to drive the prosthesis arm.

Keywords:

EMG signals,Robot arm,high DOF,Microcontroller comparator,Prosthetic arm,

Refference:

1) Eason, G., Noble B. and Sneddon, I. N. “On certain integrals of Lipschitz-Hankel type involving products of Bessel functions,” Phil. Trans. Roy. Soc. London, vol. A247, pp. 529–551, April 1955.

2) Maxwell, J. Clerk A Treatise on Electricity and Magnetism, 3rd ed., vol. 2. Oxford: Clarendon, 1892, pp.68–73.

3) Jacobs, I. S. and Bean, C. P. “Fine particles, thin films and exchange anisotropy,” in Magnetism, vol. III, G. T. Rado and H. Suhl, Eds. New York: Academic, 1963, pp. 271–350.

4) Elissa, K. “Title of paper if known,” unpublished.

5) Nicole, R. “Title of paper with only first word capitalized,” J. Name Stand. Abbrev., in press.

6) Yorozu, Y., Hirano, M., Oka, K. and Tagawa, Y. “Electron spectroscopy studies on magneto-optical media and plastic substrate interface,” IEEE Transl. J. Magn. Japan, vol. 2, pp. 740–741, August 1987 [Digests 9th Annual Conf. Magnetics Japan, p. 301, 1982].

7) Young, M. The Technical Writer’s Handbook. Mill Valley, CA: University Science, 1989.

8) Grepl R. Modelování mechatronických systémů v Matlab/SimMechanics. 1. vyd. Praha: BEN – technická literatura, 2007. 152 pp. ISBN 978-80-7300-226-8.

9) Mostýn V., Skařupa J. Teorie průmyslových robotů. 1. vyd. Košice: Edícia vedeckej a odbornej literatúry – Strojnícka fakulta TU v Košiciach, VIENALA Košice, 2000. 150 pp. ISBN 80-88922-35-6.

10) Carrozza M. C., Massa B., Dario P., Zecca M., Micera S., Pastacaldi P. A two dof finger for a biomechatronic artificial hand. Technol. Health Care, vol. 10, no. 2, 2002, pp. 77–89.

NUMEROUS EXACT SOLUTIONS OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS BY TAN–COT METHOD

Authors:

Md. Alamin Khan, Abu Hashan Md. Mashud, M. A. Halim

DOI NO:

https://doi.org/10.26782/jmcms.2017.01.00004

Abstract:

This theoretical investigation is made in order to get the new exact solitary wave solutions of nonlinear partial differential equations (PDEs). The well-known Tan-Cot Function method is employed to obtain the exact solutions of Joseph–Egri equation (TRLW), Sharma–Tasso–Olver equation (STO), mKdV (modified Korteweg-de Vries) equation with additional first order dispersion term, and KdV (Korteweg-de Vries) equation with additional fifth order dispersion term,. The results which have been found in this theoretical work could be applicable to understand the characteristics and elastic behavior of nonlinear structures including solitons as well as play an important role in wide range of physical applications

Keywords:

Nonlinear PDEs,Exact solutions,Tan-Cot function method,Joseph–Egri equation,Sharma–Tasso–Olver equation,mKdV equation with additional first order dispersion term,KdV equation with additional fifth order dispersion term, soliton solutions,

Refference:

1) Wazwaz, A.M. “Solitons and periodic solutions for the fifth-order KdV
equation,” App. Math. Lett., vol. 19, pp. 1162-1167, November 2006.
2) Malfliet, W. “Solitary wave solutions of nonlinear wave equations,” Am. J.
Phys., vol. 60, pp. 650-654, February1992.
3) Russel, J.S. Report on Waves, Fourteenth Meeting of the British Association
for the Advancement of Science, New York, 1844, pp. 311-390.
4) Zabusky N.J. and Kruskal, M.D. ‘‘Interaction of solitons in a collision less
plasma and the recurrence of initial states,” Phys. Rev. Lett., vol. 15, pp. 240
243, August 1965.
5) Khater, A.H. Malfliet, W. Callebaut, D.K. and Kamel, E.S. “The tanh method, a
simple transformation and exact analytical solutions for nonlinear reaction
diffusion equations,” Chaos Solitons Fractals, vol. 14, pp. 513-522, August 2002.
6) Wazwaz, A.M. “Two reliable methods for solving variants of the KdV equation
with compact and noncompact structures,” Chaos Solitons Fractals, vol. 28, pp.
454-462, April 2006.
7) El-Wakil S.A. and Abdou, M.A. “New exact travelling wave solutions using
modified extended tanh-function method.” Chaos Solitons Fractals, vol. 31, pp.
840-852, February 2007.
8) Fan, E. ‘‘Extended tanh-function method and its applications to nonlinear
equations,” Phys. Lett. A, vol. 277, pp. 212-218, December 2000.

9) Wazwaz, A. M. “The tanh-function method: Solitons and periodic solutions for
the Dodd-Bullough-Mikhailov and the Tzitzeica-Dodd-Bullough equations.”
Chaos Solitons and Fractals, vol. 25, pp. 55-63, July 2005.
10) Xia, T.C. Li, B. and Zhang, H.Q. ‘‘New explicit and exact solutions for the
Nizhnik Novikov-Vesselov equation,” Appl. Math. E-Notes, vol. 1, pp. 139
142, 2001.
11) Parkes, E.J. and Duffy, B.R.‘‘An automated tanh-function method for finding
solitary wave solutions to nonlinear evolution equations,” Comput. Phys.
Commun., vol. 98, pp. 288-300, November 1996.
12) Jawad, Anwar J. M. ‘‘New exact solutions of nonlinear partial differential
equations using tan-cot function method,” Studies in Mathematical Sciences,
vol. 5, pp. 13-25, November 2002.
13) Jawad, Anwar J. M. ‘‘New exact solutions of nonlinear partial differential
equations using tan-cot function method,” Studies in Mathematical Sciences,
vol. 5, pp. 13-25, November 2002.
14) Feng, Z.S. ‘‘The first integer method to study the Burgers-Korteweg-de Vries
equation.” J. Phys. A. Math. Gen., vol. 35, pp. 343-349, September 2002.
15) Ding T.R. and Li., C.Z. Ordinary differential equations. Peking: Peking
University Press, 1996.
16) Mitchell A.R. and Griffiths, D.F. The finite difference method in partial
differential equations. John Wiley & Sons, 1980.
17) Yusufoglu E. and Bekir, A. Solitons and periodic solutions of coupled
nonlinear evolution equations by using Sine-Cosine method, Inter. J. Comput.
Math., vol. 83, pp. 915-924, May 2006.
18) Shaikh,A.A.,Mashud, A.H.M., Uddin, M.S. and Khan, M.A-A. (2017) ‘Non-
instantaneous deterioration inventory model with price and stock dependent
demand for fully backlogged shortages under inflation’, Int. J. Business
Forecasting and Marketing Intelligence, Vol. 3, No. 2, pp.152–164.
19) Shaikh,A.A., Mashud, A.H.M., Uddin, M.S. and Khan, M.A-A. (2018) ‘A non-instantaneous inventory model having different deterioration rates with stock and price dependent demand under partially backlogged shortages’, Uncertain Supply Chain Management,Vol. 6.
20) Shaikh,A.A.,Mashud, A.H.M., Uddin, M.S. and Khan, M.A-A. (2017) ‘Non-
instantaneous deterioration inventory model with price and stock dependent
demand for fully backlogged shortages under inflation’, Int. J. Business
Forecasting and Marketing Intelligence, Vol. 3, No. 2, pp.152–164.

DEFORMATION OF AN AELOTROPIC SEMI-INFINITE ELASTIC PLATE WITH SEMI-CUBICAL PARABOLIC BOUNDARY

Authors:

D.C. Sanyal

DOI NO:

https://doi.org/10.26782/jmcms.2017.07.00001

admin August 26, 2017

Abstract:

The paper is dealt with the problem of deformation of an aelotropic semi-infinite elastic plate with semi-cubical boundary. A part of the boundary near the vertex is under the action of normal pressure and the rest is free. The problem is solved by using complex variable technique and reducing the problem to that of solving Hilbert equation in a closed form.

Keywords:

Aelotropic medium,semi-cubical boundary,Hilbert equation,

Refference:

1) Kolossoff, G. V.: On One Application of the Theory of Functions of a
complex variable to a Plane Problem in the Mathematical Theory of
Elasticity, a dissertation at Dorpat (Yurieff) University (1909).
2) Muskhelishville, N. I.: Fundamental Problems of the Mathematical Theory of Elasticity ,Mir Publishers Moscow (1949).
3) Muskhelishville, N. I.: Singular Integral Equations Mir Publishers, Moscow
(1946).
4) Muskhelishville, N. I.: Some Basic Problems of the Mathematical Theory
of Elasticity, Moscow (1949). 5) Lechnitzky, S. G.: Theory of Elasticity of Anisotropic Bodies, Mir
Publishers, Moscow (1981). 6) Maikap, G. H. and Sengupta, P. R.: Proc. Math. Soc. B.H.U, Vol. 5 (1989),
p-87.
7) Paria, G.: Bull. Cal. Math. Soc., Vol. 44 (1952), p-180.
8) Paria, G.: J. Appl. Mech. AMSE., Vol. 24 (1957), p-122.
9) Ahmed, A.: Bull. Cal. Math. Soc., Vol. 62 (1970), p-123.
10) Milne-Thomson, L.M.: Plane Elastic Systems, Springer (1961)

Journal Vol – 12 No -1, July 2017

LAMINAR CONVECTION OVER A VERTICAL PLATE WITH CONVECTIVE BOUNDARY CONDITION

Authors:

Asish Mitra

DOI NO:

https://doi.org/10.26782/jmcms.2017.07.00002

admin August 26, 2017

Abstract:

In the present numerical study, laminar convection over a vertical plate with convective boundary condition is presented. It is found that the similarity solution is possible if the convective heat transfer associated with the hot fluid on the left side of the plate is proportional to x^1/2, and the thermal expansion coefficient β is proportional to x^-1. The numerical solutions thus obtained are analyzed for a range of values of the embedded parameters and for representative Prandtl numbers of 0.72, 1, 3 and 7.1. The results of the present simulation are then compared with the reports published in literature and find a good agreement.

Keywords:

Convective Boundary Condition,Laminar Convection,Matlab,Numerical Simulation,Vertical Plate,

Refference:

1) Blasius, H., “Grenzschichten in Flussigkeiten mit kleiner reibung,” Z. Math Phys.,
vol. 56, pp. 1–37, 1908.
2) Weyl, H., “On the Differential Equations of the Simplest Boundary Layer Problem,” Ann. Math., vol. 43, pp. 381–407, 1942.

3) Magyari, E., “The Moving Plate Thermometer,” Int. J. Therm. Sci., 47, pp. 14361441, 2008.

4) Cortell, R., “Numerical Solutions of the Classical Blasius Flat-Plate Problem,” Appl. Math. Comput., vol. 170, pp. 706–710, 2005.

5) He, J. H., “A Simple Perturbation Approach to Blasius Equation,” Appl. Math. Comput., vol. 140, pp. 217–222, 2003.

6) Bataller, R. C., “Radiation Effects for the Blasius and Sakiadis Flows With a Convective Surface Boundary Condition,” Appl. Math. Comput., vol. 206, pp. 832–840, 2008.

7) Aziz, A., “A Similarity Solution for Laminar Thermal Boundary Layer Over a Flat Plate With a Convective Surface Boundary Condition,” Commun. Nonlinear Sci. Numer. Simul., vol. 14, pp. 1064–1068, 2009.

8) Makinde, O. D., and Sibanda, P., “Magnetohydrodynamic Mixed Convective Flow and Heat and Mass Transfer Past a Vertical Plate in a Porous Medium With Constant Wall Suction,” ASME J. Heat Transfer, vol. 130, pp. 112602, 2008.

9) Makinde, O. D., “Analysis of Non-Newtonian Reactive Flow in a Cylindrical Pipe,” ASME J. Appl. Mech., vol. 76, pp. 034502, 2009.

10) Cortell, R., “Similarity Solutions for Flow and Heat Transfer of a Quiescent Fluid Over a Nonlinearly Stretching Surface,” J. Mater. Process. Technol., pp. 176–183, 2008.