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Technical Brief

An Analytical Solution for Boundary Layer Flows Over a Moving-Flat Porous Plate With Viscous Dissipation

[+] Author and Article Information
C. J. Toki

Department of Ecology and Environment,
Technological Educational
Institute of Ionian Islands,
Square of Kalvou, Zakynthos 29100,Greece
e-mail: Christina-toki@yahoo.com

1Corresponding author. Present address: Pediou Volis 32, Stavraki, 453 22, Ioannina, Greece.

Present address: Department of Mechanical Engineering, Curtin University, Sarawak Campus CDT 250, 98009 Miri, Sarawak, Malaysia

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received September 21, 2012; final manuscript received June 10, 2013; published online November 20, 2013. Assoc. Editor: Sharath S. Girimaji.

J. Fluids Eng 136(2), 024501 (Nov 20, 2013) (5 pages) Paper No: FE-12-1466; doi: 10.1115/1.4025142 History: Received September 21, 2012; Revised June 10, 2013

The problem of boundary layer flow of an incompressible fluid over a moving porous flat plate is investigated, by taking into account the heat due to viscous dissipation. The governing boundary layer equations of this flow field were solved analytically using the Laplace transform technique. These new exact analytical solutions for velocity and temperature were obtained with arbitrary Prandtl number and dissipation parameter (or Eckert number Ec). The corresponding solutions for nonporous plate are discussed. Applying numerical values into the analytical expressions of the temperature and heat transfer coefficient, we also discussed the effects of the dissipation parameter in the cases of water, gas, and ammonia flow. We can finally deduce that the fluid temperature of the present problem will increase in the case of viscous dissipation with positive Ec, but this temperature will decrease with negative Ec.

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References

Venkataraman, V., and Kannan, K., 2004, “Numerical Solution of Stokes Problem for Free Convection Effects in Dissipative Dusty Medium,” Int. J. Mech. Math. Sci., 72, pp. 3975–3988. [CrossRef]
Mahmound, M. A. A., and Megahed, A. M., 2009, “Effects of Viscous Dissipation and Head Generation (Absorption) in a Thermal Boundary Layer of a Non-Newtonian Fluid Over a Continuously Moving Permeable Flat Plate,” J. Appl. Mech Tech. Phys., 50(5), pp. 819–825. [CrossRef]
Sakiadis, B. C., 1961, “Boundary-Layer Behavior on Continuous Solid Surfaces: I. Boundary Layer Equations for Two-Dimensional and Axisymmetric Flow,” AIChE J., 7, pp. 26–28. [CrossRef]
Sakiadis, B. C., 1961, “Boundary-Layer Behavior on Continuous Solid Surfaces: II. Boundary Layer on Continuous Flat Surface,” AIChE J., 7, pp. 221–225. [CrossRef]
White, FrankM., 1974, Viscous Fluid Flow, McGraw-Hill, New York, p. 254.
Murty, T. V. R., and Soundalgekar, V. M., 1995, “Viscous Dissipation Effects on Heat Transfer in Flow Past a Continuously Moving Porous Plate,” Proc. Math. Soc. Banaras Hindu University, 11, pp. 53–58. Retrieved January 23, 2012, http://drs.nio.org/drs/handle/2264/2403.
Kishore, P. M., Rajesh, V., and Verma, S. V., 2010, “Effects of Heat Transfer and Viscous Dissipation on MND Free Convection Flow Past an Exponentially Accelerated Vertical Plate With Variable Temperature,” J. Naval Arch. Marine Eng., 7, pp. 101–110. [CrossRef]
Drymonitou, M. A., Geroyannis,V. S., and Goudas, C. L., 1980, “Numerical Treatment of the Unsteady Hydromagnetic Thermal Boundary Layer Problem,” Astrophys. Space Sci., 71, pp. 87–100. [CrossRef]
Gschwendtner, M. A., 2004, “The Eckert Number Phenomenon: Experimental Investigations on the Heat Transfer From a Moving Wall in the Case of a Rotating Cylinder,” Heat Mass Trans., 40, pp. 551–559. [CrossRef]
Koo, J., and Kleinstreuer, C., 2004, “Viscous Dissipation Effects in Microtubes and Microchannels,” Int. J. Heat Mass Trans., 47, pp. 3159–3169. [CrossRef]
Chien, C.-H., 2006, “Effect of Viscous Dissipation on Heat Transfer in a Non-Newtonian Liquid Film Over an Unsteady Stretching Sheet,” J. Non-Newtonian Fluid Mech.,135 (2–3), pp. 128–135. [CrossRef]
Raptis, A., and Perdikis, C., 2006, “Viscous Flow Over a Non-Linearly Stretching Sheet in the Presence of a Chemical Reaction and Magnetic Field,” Int. J. Non-Linear Mech., 41(4), pp. 527–529. [CrossRef]
Suneetha, S., Bhaskar Reddy, N., and Ramachandra Prasad, V., 2008, “Thermal Radiation Effects on MHD Free Convection Flow Past an Impulsively Started Vertical Plate With Variable Surface Temperature and Concentration,” J. Naval Arch. Marine Eng., 5(2), pp. 57–70. [CrossRef]
Anjali Devi, S. P., and Ganga, B., 2010, “Dissipation Effects on MHD Nonlinear Flow and Heat Transfer Past a Porous Surface With Prescribed Heat Flux,” J. Appl. Fluid Mech., 3(1), pp. 1–6. Available at: http://www.sid.ir/en/VEWSSID/J_pdf/1125201001.pdf
Poonia, H., and Chaudhary, R. C., 2010, “MHD Free Convection and Mass Transfer Flow Over an Infinite Vertical Porous Plate With Viscous Dissipation,” Theor. Appl. Mech., 37(4), pp. 263–287. [CrossRef]
Abdul Hamid, R., Arifin, N. M., Nazar, R., and Ali, F. M., 2011, “Effects of Joule Heating and Viscous Dissipation on MHD Marangoni Convection Boundary Layer Flow,” J. Sci. Technol., 3(1), pp. 67–77. Available at: http://penerbit.uthm.edu.my/ojs/index.php/JST/article/viewFile/211/95
Mustafa, M., Hayat, T., Pop, I., and Aziz, A., 2011, “Unsteady Boundary Layer Flow of a Casson Fluid Due to an Impulsively Started Moving Flat Plat,” Heat Transfer Asian Res., 40(6), pp. 563–576. [CrossRef]
Subhas Abel, M., Kulkarni AnantKumar, and Ravikumara, R., 2011, “MHD Flow, and Heat Transfer With Effects of Buoyancy, Viscous and Joules Dissipation Over a Nonlinear Vertical Stretching Porous Sheet With Partial Slip,” Engineering, 3, pp. 285–291. [CrossRef]
Sudheer Babu, M., Satya Narayana, P. V., Sankar Reddy, T., and Umamaheswara Reddy, D., 2011, “Radiation and Chemical Reaction Effects on an Unsteady MHD Convection Flow Past a Vertical Moving Porous Plate Embedded in a Porous Medium With Viscous Dissipation,” Adv. Appl. Sci. Res., 2(5), pp. 226–239. Available at: http://www.pelagiaresearchlibrary.com/advances-in-applied-science/vol2-iss5/AASR-2011-2-5-226-239.pdf
Mustafa, N., Asghar, S., and Hayat, T., 2012, “Analytical and Numerical Solution for Viscous Dissipation Effect on the Heat Transfer in a Deformable Channel,” Int. J. Numer. Methods Fluids, 68(5), pp. 537–545. [CrossRef]
Toki, C. J., 2009, “Free Convection Gas Flow Near a Vertical Porous Plate With Heat Sources/Sinks,” Z. Angew. Math. Mech.89(11), pp. 881–888. [CrossRef]
Toki, C. J., and Tokis, J. N., 2007, “Exact Solutions for the Unsteady Free Convection Flows on a Porous Plate With Time-Dependent Heating,” Z. Angew. Math. Mech., 87(1), pp. 4–13. [CrossRef]
Toki, C. J., 2008, “Free Convection and Mass Transfer Flow Near a Moving Vertical Porous Plate: An Analytical Solution,” ASME J. Appl. Mech., 75(1), p. 011014. [CrossRef]
Spiegel, M. R., 1965, Laplace Transforms, McGraw-Hill, New York, Chap. 2, p. 72.

Figures

Grahic Jump Location
Fig. 1

Effects of the Eckert number on the temperature profiles of water flows near porous and nonporous flat plate, which is moved with uniform velocity

Grahic Jump Location
Fig. 2

Effects of the Eckert number on the temperature profiles of air flows near porous and nonporous flat plate, which is moved with uniform velocity

Grahic Jump Location
Fig. 3

Effects of the Eckert number on the temperature profiles of ammonia flows near porous flat plate, which is moved with uniform velocity

Grahic Jump Location
Fig. 4

Variation of the heat transfer coefficient as function of the Eckert number in the case of the water flows and air flows near porous and nonporous flat plates, which are moved with uniform velocity

Grahic Jump Location
Fig. 5

Variation of the heat transfer coefficient as function of the Eckert number in the case of ammonia near porous and nonporous flat plates, which are moved with uniform velocity

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