IJPAM: Volume 108, No. 2 (2016)

NSM SOLUTION ON TRANSIENT NATURAL CONVECTIVE
VISCOUS FLUID FLOW PAST A VERTICAL CONE

Y. Immanuel$^1$, Bapuji Pullepu$^2$, M. Selva Rani$^2$
$^1$Department of Mathematics
Sathyabama University
Chennai, INDIA
$^2$Department of Mathematics
SRM University
Kattankulathur, INDIA

Abstract. The unsteady free convective flow of the non-isothermal vertical cone with wall surface temperature varying as power function of distance from the apex $(x = 0)$ with the effects of viscous dissipation is considered here. The dimensionless parabolic integro-partial differential equations that are non-linear, unsteady and coupled are solved using a new method NSM technique. The velocity, temperature profiles and the local as well as average skin-friction and Nusselt number have been studied and analyzed graphically for the effect of viscous dissipation for various parameters of angle $\phi$, Prandtl number $Pr$ and $n$ (exponent in power law variation in surface temperature). The present results are compared with available results in literature and are found to be in good agreement.

Received: February 13, 2016

Revised: February 13, 2016

Published: October 1, 2016

AMS Subject Classification: 80M20, 76D10, 76M20, 74S30

Key Words and Phrases: natural convection, network simulation method, non-uniform surface temperature, PSPICE, vertical cone, viscous dissipation
Download paper from here.

Bibliography

1
H.J. Merk and J.A. Prins, Thermal convection in laminar boundary layers I, Appl. Sci. Res., 4 (1953), 11-24.

2
H.J. Merk and J.A. Prins, Thermal convection in laminar boundary layers II, Appl. Sci. Res., 4 (1954), 195-206.

3
R.G. Hering and R.J. Grosh, Laminar free convection from a non-isothermal cone, Int. J. Heat Mass Transfer, 5 (1962), 1059-1068.

4
R.G. Hering, Laminar free convection from a non-isothermal cone at low Prandtl number, Int. J. Heat Mass Transfer, 8 (1965), 1333-1337.

5
K.T. Yang, J.L. Novotny and Y.S. Cheng, Laminar free convection from a non-isothermal plate immersed in a temperature stratified medium, Int. J. Heat Mass Transfer, 15 (1972), 1097-1109.

6
H.S. Takhar and V.M. Soundalgekar, Combined convection past a vertical semi infinite plate with viscous dissipation, Mech. Res. Commun., 14(5/6) (1987), 307-315.

7
I. Pop and H.S. Takhar, Compressibility effects in laminar free convection from a vertical cone, Appl. Sci. Res., 48 (1991), 71-82.

8
M.A. Hossain and S.C. Paul, Free convection from a vertical permeable circular cone with non-uniform surface temperature, Acta Mech., 151 (2001), 103-114.

9
I. Pop, T. Grosan and M. Kumari, Mixed convection along a vertical cone for fluids of any Prandtl number: case of constant wall temperature, Int. J. of Numerical Methods for Heat and Fluid Flow., 13(7) (2003), 815-829.

10
Bapuji Pullepu, K. Ekambavanan and A.J. Chamkha, Unsteady laminar natural convection flow past an isothermal vertical cone, Int. J. Heat and Technology, 25(2) (2007), 17-27.

11
Bapuji Pullepu, K. Ekambavanan and I. Pop, Finite difference analysis of aminar free convection flow past a non isothermal vertical cone, Heat Mass Transfer., 44(5) (2008), 517-526.

12
Bapuji Pullepu, K. Ekambavanan and A.J. Chamkha, Laminar natural convection from a non-isothermal vertical cone, Nonlinear Anal. Model. Control., 13(1) (2007), 47-60.

13
S.G. Mohiddin, S. Vijayakumar Verma and N.Ch.S.N. Iyengar, Radiation and mass transfer effects on MHD free convective flow past a vertical cone with variable surface conditions in the presence of viscous dissipation, Int. Electr. Eng. Math. Soc., 8 (2010), 22-37.

14
P.M. Kishore, V. Rajesh, and S. Vijayakumar Verma, Viscoelastic buoyancy-driven MHDfree convective heat and mass transfer past avertical cone with thermal radiation and viscous dissipation effects, Int. J. Math. Mech., 6(15) (2010), 67-87.

15
P.M. Kishore, V. Rajesh and S. Vijayakumar Verma, The effects of thermal radiation and viscous dissipation on MHD heat and mass diffussion flow past a surface embedded in a porous medium, Int. J. of Appl. Math and Mech., 6(11) (2010), 79-97.

16
Bapuji pullepu, A.J. Chamkha and I. Pop, Unsteady laminar free convection flow past a non-isothermalvertical cone in the presence of a magnetic field, Chem. Eng. Commun., 199(3) (2012), 354-367.

17
S.M.M. EL-Kabeir and E.A. EL-Sayed, Effects of thermal radiation and viscous dissipation on MHD viscoelastic free convection past a vertical isothermal cone surface with chemical reaction, Int. J. Energy. Tech., 4(10) (2012), 1-7.

18
L.W. Nagel, PSPICE, A Computer Program to Simulate Semiconductor Circuits, Chapters 4, 5, 6, Memo UCB/ERL M520, PhD Thesis, University of California.

19
K. Rektorys, The method of discretization in time for PDE, D. Reidel Publishers, Dordrechet, The Netherlands, 1982.

20
F. Alhama and C.F. Gonzalez-Fernandez, Heat Transfer and the Network simulation method, NSM, Research signpost, Trivandrum (2002), 35-58.

21
J. Zueco, F. Alhama and C.F. Gonzalez-Fernandez, Analysis of laminar forced convection with network simulation in thermal entrance region of ducts, Int. J. Thermal Science, 43(5) (2004), 443-451.

22
F. Alhama, A. Campo and J Zueco, Numerical solution of the heat conduction equation with the electro-thermal analogy and the code PSPICE, Appl. Math. Compu., 162 (2005), 103-113.

23
J. Z. Jordan, Numerical study of an unsteady free convective MHD flow of a dissipative fluid along a vertical plate subject to a constant heat flux, Int. J. Engg. Sci., 44 (2006), 1380-1393.

24
O. A. Beg, J. Zueco, S.K. Ghosh and HeidariAlireza, Unsteady MHD heat transfer in a semi-infinite porous medium with thermal radiation flux : Analytical Numerical Study, Adv. Numer. Anal. 2011(2011), 1-17.

25
J. Zueco, O.A. Beg, H.S. Takhar and G. Nath, Network simulation of laminar convective heat and mass transfer over a vertical slender cylinder with uniform surface heat and mass flux, JAFM, 4(2)1 (2011), 13-23.

26
J. Z. Jordan, Network method to study the transient heat transfer problem in a vertical channel with viscous dissipation, Int. commun. Heat Mass Transfer., 33 (2006), 1079-1087.

27
J. Zueco, O.A. Beg, H.S. Takhar and V.R. Prasad, Thermophoretic Hydromagnetic Dissipative Heat and Mass Transfer with Lateral Mass Flux, Heat Source, Ohmic Heating and Thermal Conductivity Effects Network Simulation Numerical Study, Appl. Therm. Eng., 29 (2009), 2808-2815.

28
J. Z. Jordan, Network simulation method applied to radiation and viscous dissipation effects on MHD unsteady free convection over vertical porous plate, Appl. Math. Modelling., 31 (2007), 2019-2033.

29
J. Zueco and O.A. Beg, Network simulation solutions for laminar radiating dissipative magneto-gas dynamic heat transfer over a wedge in non-Darcian porous regime, Math. Comput. Model., 50 (2009), 439-452.

30
P. Eguia, J. Zueco, E. Granada and D. Patino, NSM solution for unsteady MHD Couette flow of a dusty conducting fluid with variable viscosity and electric conductivity, Appl. Math. Modelling., 35 (2011), 303-316.

31
O.A. Beg, J. Zueco and H.S. Takhar, Unsteady magnetohydrodynamic Hartmann-Couette flow and heat transfer in a Darcian channel with Hall current, ionslip, viscous and Joule heating effects: Network numerical solutions, Commun. Nonlinear. Sci. Numer. Simulat., 14 (2009), 1082-1097.

32
B. Gebhart, Effects of viscous dissipation in natural convection, J. Fluid Mech., 14 (1962), 225-232.

.




DOI: 10.12732/ijpam.v108i2.12 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 108
Issue: 2
Pages: 363 - 385


Google Scholar; DOI (International DOI Foundation); WorldCAT.

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).