Analytical Investigation Of Heat Generating/Absorbing  Fluid On Mhd Fully Developed Steady Natural Convection Flow In A Vertical Micro-Channel With Symmetric And Asymmetric Heating

Authors

  • BABATUNDE AINA Department of Mathematics, Federal University Gashua, Yobe State-Nigeria Author
  • Enoch Suleiman Department of Mathematics, Federal University Gashua, Yobe State-Nigeria Author

DOI:

https://doi.org/10.60787/jnamp.v68no1.427

Keywords:

Natural Convection, Heat Generation/ Absorption, MHD, Micro-Channel, Symmetric and Asymmetric Heating

Abstract

This works investigates analytically the influence of heat generating and absorbing fluid behaviours on MHD steady natural convection flow in a vertical parallel plate micro-channel in presence of velocity slip and temperature jump conditions. Flow is assumed to be steady, laminar and fully developed. Exact solution of momentum and energy equations is derived separately for heat generating fluid and heat absorbing fluid. The effects of various flow parameters entering into the problem such as heat generating/absorbing parameter, Hartmann number, Knudsen number, and fluid - wall interaction parameter on the temperature, velocity, rate of heat transfer and skin frictions are provided and discussed with appropriate physical explanations. Results revealed that, increase in Hartmann number reduced the influence of the velocity, and skin friction. The role of heat generating/absorbing fluid parameter, Hartmann number, rarefaction parameter as well as fluid wall interaction parameter on temperature and velocity is significantly pronounced in the case of asymmetric heating. Furthermore, it is observed that that skin friction and rate of heat transfer at cooler wall increases with increase in heat generation parameter while the reverse trend in the case of heat absorption parameter.

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Author Biography

  • BABATUNDE AINA, Department of Mathematics, Federal University Gashua, Yobe State-Nigeria


    1 AND ENOCH SULEIMAN2
    Department of Mathematics, Federal University Gashua, Yobe State-Nigeria

    *Corresponding author: BABATUNDE AINA
    E-mail address: ainavicdydx@gmail.com 

References

Jianjun Ye, Jian Yang, Jinyang Zheng, Ping Xu, Chikong Lam, leong Wong and Yanbao Ma, Effeccts of wall temperature on the heat and mass transfer in microchannels using the DSMC method, Proceedings of the 2009 4th IEEE international conference on nanomicro engineered and molecular systems, 2009, pp.666-671

Chen C.K. and Weng H.C., Natural Convection in a Vertical Microchannel, J.Heat Transfer, 2005, 127, pp 1053-1056.

Basant K. Jha, Babatunde Aina and A. J. Ajiya, MHD Natural Convection Flow in a Vertical Parallel Plate Microchannel, Ain Shams Engineering Journal (Ain Shams University), 2015, 6, pp 289-295 (ELSEVIER)

Basant Kumar Jha, Babatunde Aina and S. B. Joseph, Natural Convection Flow in vertical Micro-channel with Suction/Injection, Journal of Process Mechanical Engineering, 2014, 228 (3), pp 171-180. (SAGE)

Basant K. Jha, Babatunde Aina and Zubairu Rilwanu, Steady Fully Developed Natural Convection flow in a Vertical Annular Microchannel having Temperature Dependent Viscosity: An Exact Solution, Alexandria Engineering Journal (Faculty of Engineering, Alexandria University), 2016 (55), 951-958 (ELSEVIER)

Basant K. Jha, Babatunde Aina and Sani Isa, MHD Natural Convection flow in a Vertical Micro-Concentric-Annuli in the Presence of Radial Magnetic Field: An Exact Solution, Ain Shams Engineering Journal (Ain Shams University), 2016, 7, pp 1061-1068 (ELSEVIER)

Basant K. Jha and Babatunde Aina, Mathematical Modeling and Exact Solution of Steady Fully Developed Mixed Convection Flow in a Vertical Micro-Porous-Annulus, Afrika Matematika (Journal of the African Mathematical Union), 2015, 26, pp 1199-1213 (SPRINGER)

Basant K. Jha, Babatunde Aina and A. J. Ajiya, Role of Suction/Injection on MHD Natural Convection flow in a Vertical Micro-channel, International Journal of Energy and Technology, 2015, 7 (2), pp 30-39.

Basant K. Jha, Babatunde Aina and S. A. Muhammad, Combined Effects of Suction/Injection and Wall Surface Curvature on Natural Convection Flow in a Vertical Annular Micro-channel, Journal of Thermophysics and Aeromechanics, 2015, 22 (2), pp 217-228 (SPRINGER)

Basant K. Jha, Babatunde Aina and Sani Isa, Fully Developed MHD Natural convection flow in a Vertical Annular Microchannel: AN EXACT SOLUTION, Journal of King Saud University (Science), 2015, 27, pp 253-259 (ELSEVIER)

Jha B. K., Transient Free Convective Flow in a Vertical Channel with Heat Sinks, Int. J. Appl. Mech. Eng, 2001, 6 (2), pp.279–28

McKenzie D.P., Roberts J.M. and Weiss N.O., Convection in the Earth's Mantle: Towards a Numerical Simulation, J. Fluid Mech, 1974, 62, pp.465–538.

Crepeau J.C. and Clarksean R., Similarity Solutions of Natural Convection with Internal Heat Generation, ASME J. Heat Transfer 119 (1997) 183–185.

Baker I., Faw R.E. and Kulacki F.A., Post-Accident Heat Removal Part I: Heat Transfer within an Internally Heated non Boiling Liquid Layer, Nucl. Sci. Eng, 1976, 61, pp.222–230

Delichatsios M.A. Air Entrainment into Buoyant Jet Flames and Pool Fires, In: P.J. DiNenno, et al., (Eds.), The SFPA Handbook of Fire Protection Engineering, NFPA Publications, Quincy, MA, 1988, pp.306–314.

Westphal B.R., Keiser D.D., Rigg R.H., and Laug D.V., Production of Metal Waste Forms from Spent Nuclear Fuel Treatment, DOE Spent Nuclear Fuel Conference, Salt Lake City, UT, 1994, pp. 288–294

Chamkha A. J., Non-Darcy fully developed mixed convection in a porous medium channel with heat generation/absorption and hydromagnetic effects, Numerical Heat Transfer, Part A, 1997, 32, 653-675

R.M. Inman, Experimental study of temperature distribution in laminar tube flow of a fluid with internal heat generation, Int. J. Heat Mass Transfer, 1962, 5, 1053

Ostrach S., Laminar Natural Convection Flow and Heat Transfer of Fluids with and without Heat Sources in Channels with Constant wall Temperatures, NACA TN, 1952, pp 2863

Low G. M., Stability of Compressible Laminar Boundary Layer with Internal Heat Sources or Sinks, J. Aero. Sci., 1955, 22, 329

Chambre P. L., Laminar Boundary Layer with Distributed Heat sources or Sinks, Appl. Sci. Res. Sec. A., 1957, 6, 393

Toor H. L., Heat Transfer in Forced Convection with Internal Heat Generation, J. Am. Inst. Chem. Eng. 1958, 4, 319

Gee R. E. and Lyon J. B., Non Isothermal Flow of Viscous Non-Newtonian Fluids, Ind. Eng. Chem., 1957, 49, 956.

Modejski J., Temperature Distribution in Channel Flow with Friction, Int. J. Heat Mass Transfer, Vol. 6, 919630, pp 49.

Toor H. L., The energy equation for viscousflow, Ind. Eng. Chem. 48 (1956) 922

Moalem D., Steady state heat transfer with porous medium with temperature dependent heat generation, Int. J. Heat Mass Transfer, 1976, 19, 529.

Foraboschi F. P. and Federico I. D., Heat Transfer in Laminar Flow of Non-Newtonian Heat Generating Fluids, Int. J. Heat Mass Transfer, 1964, 7, 315

Jha BK, Oni MO and Aina B. Steady fully developed mixed convection flow in a vertical micro-concentric-annulus with heat generating/absorbing fluid: an exact solution. Ain Shams Eng J2016. https://doi.org/10.1016/j.asej.2016.08.005

Basant K. Jha and Babatunde Aina, Impact of Heat Generation/Absorption on MHD Mixed Convection flow in a Vertical Tube having Time Periodic Boundary Condition: Steady Periodic Regime, Heat Pipe Science and Technology, An International Journal, 2016, 7(1−2),

pp 123−147

Basant Kumar Jha and Babatunde Aina, "Investigation of heat generation/absorption on natural convection flow in a vertical annular micro-channel: An exact solution", Multidiscipline Modeling in Materials and Structures, 2018, Vol. 14 Issue: 1, pp.143-167

Eckert, E .R. G., and Drake, R. M., Jr. Analysis of Heat and Mass Transfer, Mcgraw-Hill, New York, 1972: Chap. 11.

Goniak R., and Duffa G. “Corrective Term in Wall Slip Equations for Knudsen Layer” J. Thermophys. Heat Transfer, 1995; 9: 383-384.

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Published

2024-10-23

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How to Cite

Analytical Investigation Of Heat Generating/Absorbing  Fluid On Mhd Fully Developed Steady Natural Convection Flow In A Vertical Micro-Channel With Symmetric And Asymmetric Heating. (2024). The Journals of the Nigerian Association of Mathematical Physics, 68, 163-178. https://doi.org/10.60787/jnamp.v68no1.427

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