Conjugate Effects of Heat and Mass Transfer on Natural Convection Flow along an Isothermal Sphere with Radiation Heat Loss

Affiliation(s)

Department of Natural Science, Stamford University, Stamford, Bangladesh.

Department of Engineering & Technology, Eastern University, Dhaka, Bangladesh.

Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka, Bangladesh.

Department of Natural Science, Stamford University, Stamford, Bangladesh.

Department of Engineering & Technology, Eastern University, Dhaka, Bangladesh.

Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka, Bangladesh.

ABSTRACT

Conjugate effects heat and mass transfer on* *free convection flow across an isothermal sphere immersed in a viscous incompressible fluid in the presence of species concentration with radiation heat loss has been investigated in this paper. The governing boundary layer equations are first transformed into a non-dimensional form and the resulting nonlinear systems of partial differential equations are then solved numerically using Finite—difference method with Keller-box Scheme. We have focused our attention on the evaluation velocity profiles, temperature profiles and species concentration profiles of the fluid as well as the local skin friction coefficient, local heat transfer rate and local species concentration transfer rate for a wide range of radiation parameter *Rd*, Schmidt number *Sc* and Prandlt number *Pr*.

Conjugate effects heat and mass transfer on

Cite this paper

S. Aktar, M. Ruma and M. Alim, "Conjugate Effects of Heat and Mass Transfer on Natural Convection Flow along an Isothermal Sphere with Radiation Heat Loss,"*Open Journal of Fluid Dynamics*, Vol. 3 No. 2, 2013, pp. 86-94. doi: 10.4236/ojfd.2013.32012.

S. Aktar, M. Ruma and M. Alim, "Conjugate Effects of Heat and Mass Transfer on Natural Convection Flow along an Isothermal Sphere with Radiation Heat Loss,"

References

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[2] L. E. Erickson, L. T. Fan and V. G. Fox, “Heat and Mass Transfer on a Moving Continuous Flat Plate with Suction or Injection,” Industrial and Engineering Chemistry Fundamentals, Vol. 5, No. 1, 1966, pp. 19-25. doi:10.1021/i160017a004

[3] R. S. R. Gorla, “Unsteady Mass Transfer in the Boundary Layer on a Continuous Moving Sheet Electrode,” Journal of the Electrochemical Society, Vol. 125, No. 6, 1978, pp. 865-869. doi:10.1149/1.2131569

[4] B. Gebhart and L. Pera, “The Nature of Vertical Natural Convection Flow Resulting from the Combined Buoyancy Effects of Thermal and Mass Diffusion,” International Journal of Heat and Mass Transfer, Vol. 14, No. 12, 1971, pp. 2025-2050. doi:10.1016/0017-9310(71)90026-3

[5] D. F. Fairbanks and C. R. Wick, “Diffusion and Chemical Reaction in an Isothermal Laminar Flow along a Soluble Flat Plate,” Industrial and Engineering Chemistry Research, Vol. 42, No. 3, 1950, pp. 471-475. doi:10.1021/ie50483a022

[6] M. A. Hossain and D. A. S. Rees, “Combined Heat and Mass Transfer in Natural Convection,” ASME Journal of Heat Transfer, Vol. 86, 1964, pp. 537-542. doi:10.1007/BF01179253

[7] S. P. Anjalidevi and R. Kandasamy, “Effects of Chemical Reaction, Heat and Mass Transfer Laminar Flow along a Semi Infinite Horizontal Plate,” Heat and Mass Transfer, Vol. 35, No. 6, 1999, pp. 465-467. doi:10.1007/s002310050349

[8] H. S. Takhar, A. J. Chamkha and G. Nath, “Flow and Mass Transfer on Stretching Sheet with Magnetic Field and Chemically Reactive Species,” International Journal of Engineering Science, Vol. 38, No. 12, 2000, pp. 1303-1314. doi:10.1016/S0020-7225(99)00079-8

[9] T. Chiang and J. Kaye, “On Laminar Free Convection from a Horizontal Cylinder,” Journal of Heat Transfer, Vol. 86, 1964, pp. 537-542. doi:10.1115/1.3688739

[10] E. M. Sparrow and L. Lee, “Analysis of Mixed Forced and Free Convection about a Horizontal Cylinder,” International Journal of Heat and Mass Transfer, Vol. 19, No. 2, 1977, pp. 229-232. doi:10.1016/0017-9310(76)90118-6

[11] J. H. Merkin, “Free Convection Boundary Layer on an Isothermal Horizontal Circular Cylinder,” Journal of Applied Mathematics and Physics (ZAMP), Vol. 29, No. 6, 1978, pp. 871-883.

[12] J. H. Merkin, “Mixed Convection from a Horizontal Circular Cylinder,” International Journal of Heat and Mass Transfer, Vol. 20, No. 1, 1977, pp. 73-77. doi:10.1016/0017-9310(77)90086-2

[13] D. B. Ingham, “Free-convection Boundary Layer on an Isothermal Horizontal Cylinder,” Zeitschrift für angewandte Mathematik und Physik ZAMP, Vol. 29, No. 6, 1978, pp. 871-883. doi:10.1007/BF01590813

[14] R. Nazar, N. Amin and I. Pop, “Free Convection Boundary Layer on an Isothermal Horizontal Circular Cylinder in a Micropolar Fluid,” Proceedings of the 12th International Heat Transfer Conference, Grenoble, 2002, pp. 525-530.

[15] M. J. Huang and C. K. Chen, “Laminar Free Convection from a Sphere with Blowing and Suction,” Journal of Heat Transfer, Vol. 109, No. 2, 1987, pp. 529-532. doi:10.1115/1.3248117

[16] T. Akther and M. A. Alim, “Effects of Pressure Work on Natural Convection Flow around a Sphere with Radiation Heat Loss,” Nonlinear Analysis: Modelling and Control, Vol. 15, No. 3, 2010, pp. 287-298.

[17] M. A. Alim, M. M. Rahman and S. Aktar, “Viscous Dissipation Effects on Natural Convection Flow along a Sphere with Radiation Heat Loss,” Proceedings of the 4th BSME-ASME International Conference on Thermal Engineering, 27-29 December 2008.

[18] Md. A. Hye, Md. M. Molla and M. A. H. Khan, “Conjugate Effects of Heat and Mass Transfer on Natural Convection Flow across an Isothermal Horizontal Circular Cylinder with Chemical Reaction,” Nonlinear Analysis: Modelling and Control, Vol. 12, 2007, pp. 191-201.

[19] H. B. Keller, “Numerical Methods in Boundary Layer Theory,” Annual Review of Fluid Mechanics, Vol. 10, No. 1, 2010, pp. 417-433. doi:10.1146/annurev.fl.10.010178.002221

[20] T. Cebeci and P. Bradshaw, “Physical and Computational Aspects of Convective Heat Transfer,” Springer, New York, 1984. doi:10.1007/978-3-662-02411-9

[21] R. Siegel and J. R. Howell, “Thermal Radiation Heat Transfer,” McGraw-Hill, New York,1972.

[1] R. M. Griffith, “Velocity Temperature and Concentration Distributions during Fiber Spinning,” Industrial and Engineering Chemistry Fundamentals, Vol. 3, No. 3, 1964, pp. 245-250. doi:10.1021/i160011a013

[2] L. E. Erickson, L. T. Fan and V. G. Fox, “Heat and Mass Transfer on a Moving Continuous Flat Plate with Suction or Injection,” Industrial and Engineering Chemistry Fundamentals, Vol. 5, No. 1, 1966, pp. 19-25. doi:10.1021/i160017a004

[3] R. S. R. Gorla, “Unsteady Mass Transfer in the Boundary Layer on a Continuous Moving Sheet Electrode,” Journal of the Electrochemical Society, Vol. 125, No. 6, 1978, pp. 865-869. doi:10.1149/1.2131569

[4] B. Gebhart and L. Pera, “The Nature of Vertical Natural Convection Flow Resulting from the Combined Buoyancy Effects of Thermal and Mass Diffusion,” International Journal of Heat and Mass Transfer, Vol. 14, No. 12, 1971, pp. 2025-2050. doi:10.1016/0017-9310(71)90026-3

[5] D. F. Fairbanks and C. R. Wick, “Diffusion and Chemical Reaction in an Isothermal Laminar Flow along a Soluble Flat Plate,” Industrial and Engineering Chemistry Research, Vol. 42, No. 3, 1950, pp. 471-475. doi:10.1021/ie50483a022

[6] M. A. Hossain and D. A. S. Rees, “Combined Heat and Mass Transfer in Natural Convection,” ASME Journal of Heat Transfer, Vol. 86, 1964, pp. 537-542. doi:10.1007/BF01179253

[7] S. P. Anjalidevi and R. Kandasamy, “Effects of Chemical Reaction, Heat and Mass Transfer Laminar Flow along a Semi Infinite Horizontal Plate,” Heat and Mass Transfer, Vol. 35, No. 6, 1999, pp. 465-467. doi:10.1007/s002310050349

[8] H. S. Takhar, A. J. Chamkha and G. Nath, “Flow and Mass Transfer on Stretching Sheet with Magnetic Field and Chemically Reactive Species,” International Journal of Engineering Science, Vol. 38, No. 12, 2000, pp. 1303-1314. doi:10.1016/S0020-7225(99)00079-8

[9] T. Chiang and J. Kaye, “On Laminar Free Convection from a Horizontal Cylinder,” Journal of Heat Transfer, Vol. 86, 1964, pp. 537-542. doi:10.1115/1.3688739

[10] E. M. Sparrow and L. Lee, “Analysis of Mixed Forced and Free Convection about a Horizontal Cylinder,” International Journal of Heat and Mass Transfer, Vol. 19, No. 2, 1977, pp. 229-232. doi:10.1016/0017-9310(76)90118-6

[11] J. H. Merkin, “Free Convection Boundary Layer on an Isothermal Horizontal Circular Cylinder,” Journal of Applied Mathematics and Physics (ZAMP), Vol. 29, No. 6, 1978, pp. 871-883.

[12] J. H. Merkin, “Mixed Convection from a Horizontal Circular Cylinder,” International Journal of Heat and Mass Transfer, Vol. 20, No. 1, 1977, pp. 73-77. doi:10.1016/0017-9310(77)90086-2

[13] D. B. Ingham, “Free-convection Boundary Layer on an Isothermal Horizontal Cylinder,” Zeitschrift für angewandte Mathematik und Physik ZAMP, Vol. 29, No. 6, 1978, pp. 871-883. doi:10.1007/BF01590813

[14] R. Nazar, N. Amin and I. Pop, “Free Convection Boundary Layer on an Isothermal Horizontal Circular Cylinder in a Micropolar Fluid,” Proceedings of the 12th International Heat Transfer Conference, Grenoble, 2002, pp. 525-530.

[15] M. J. Huang and C. K. Chen, “Laminar Free Convection from a Sphere with Blowing and Suction,” Journal of Heat Transfer, Vol. 109, No. 2, 1987, pp. 529-532. doi:10.1115/1.3248117

[16] T. Akther and M. A. Alim, “Effects of Pressure Work on Natural Convection Flow around a Sphere with Radiation Heat Loss,” Nonlinear Analysis: Modelling and Control, Vol. 15, No. 3, 2010, pp. 287-298.

[17] M. A. Alim, M. M. Rahman and S. Aktar, “Viscous Dissipation Effects on Natural Convection Flow along a Sphere with Radiation Heat Loss,” Proceedings of the 4th BSME-ASME International Conference on Thermal Engineering, 27-29 December 2008.

[18] Md. A. Hye, Md. M. Molla and M. A. H. Khan, “Conjugate Effects of Heat and Mass Transfer on Natural Convection Flow across an Isothermal Horizontal Circular Cylinder with Chemical Reaction,” Nonlinear Analysis: Modelling and Control, Vol. 12, 2007, pp. 191-201.

[19] H. B. Keller, “Numerical Methods in Boundary Layer Theory,” Annual Review of Fluid Mechanics, Vol. 10, No. 1, 2010, pp. 417-433. doi:10.1146/annurev.fl.10.010178.002221

[20] T. Cebeci and P. Bradshaw, “Physical and Computational Aspects of Convective Heat Transfer,” Springer, New York, 1984. doi:10.1007/978-3-662-02411-9

[21] R. Siegel and J. R. Howell, “Thermal Radiation Heat Transfer,” McGraw-Hill, New York,1972.