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Natural convection flow from an isothermal horizontal circular cylinder in presence of heat generation. (English) Zbl 1213.76176

Summary: Natural convection laminar boundary layer flow from a horizontal circular cylinder with a uniform surface temperature at presence of heat generation has been investigated. The governing boundary layer equations are transformed into a non-dimensional form and the resulting nonlinear systems of partial differential equations are solved numerically applying two distinct methods namely (i) implicit finite difference method together with the Keller box scheme and (ii) series solution technique. The results of the surface shear stress in terms of the local skin friction and the surface rate of heat transfer in terms of the local Nusselt number for a selection of the heat generation parameter \(\gamma(= 0.0, 0.2, 0.5, 0.8, 1.0)\) are obtained and presented in both tabular and graphical formats. Without effect of the internal heat generation inside the fluid domain for which we take \(\gamma = 0.0\), the present numerical results show an excellent agreement with those of J.H. Merkin [Free convection boundary layer on an isothermal horizontal circular cylinders, in: ASME/AIChE, Heat Transfer Conference, St. Louis, MO, August 9-11, (1976)]. The effects of \(\gamma \) on the fluid velocity, temperature distribution, streamlines and isotherms are examined.

MSC:

76R10 Free convection
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[1] J.H. Merkin, Free convection boundary layer on an isothermal horizontal circular cylinders, in: ASME/AIChE, Heat Transfer Conference, St. Louis, MO, August 9-11, 1976.; J.H. Merkin, Free convection boundary layer on an isothermal horizontal circular cylinders, in: ASME/AIChE, Heat Transfer Conference, St. Louis, MO, August 9-11, 1976.
[2] Vajravelu, K.; Hadjinicolaou, A., Heat transfer in a viscous fluid over a stretching sheet with viscous dissipation and internal heat generation, International Communication Heat Mass Transfer, 20, 417-430 (1993)
[3] Chamkha, A. J.; Issa, Camille, Effects of heat generation/absorption and the thermophoresis on hydromagnetic flow with heat and mass transfer over a flat plate, International Journal of Numerical Methods for Heat & Fluid Flow, 10, 4, 432-448 (2000) · Zbl 0948.76636
[4] Mendez, F.; Trevino, C., The conjugate conduction-natural convection heat transfer along a thin vertical plate with non-uniform internal heat generation, International Journal of Heat Mass Transfer, 43, 2739-2748 (2000) · Zbl 0966.76087
[5] Molla, M. M.; Hossain, M. A.; Yao, L. S., Natural convection flow along a vertical wavy surface with heat generation/absorption, International Journal of Thermal Science, 43, 157-163 (2004)
[6] Sparrow, E. M.; Lee, L., Analysis of mixed convection about a circular cylinder, International Journal of Heat Mass Transfer, 19, 229-236 (1976)
[7] Merkin, J. H., Mixed convection a horizontal circular cylinder, International Journal of Heat Mass Transfer, 20, 73-77 (1977)
[8] Merkin, J. H., Free convection boundary layer on cylinders of elliptic cross-section, ASME Journal of Heat Transfer, 99, 453-457 (1977)
[9] Ingham, D. B., Free convection boundary layer on an isothermal horizontal cylinder, Zeitschrift Fur Angewandte Mathematik und Physik, 29, 871-883 (1978) · Zbl 0392.76081
[10] Hossain, M. A.; Alim, M. A., Natural convection-radiation interaction on boundary layer flow along a vertical thin cylinder, Heat and Mass Transfer, 32, 515-520 (1997)
[11] Hossain, M. A.; Kutubuddin, M.; Pop, I., Radiation-conduction interaction on mixed convection a horizontal circular cylinder, Heat and Mass Transfer, 35, 307-314 (1999)
[12] Molla, M. M.; Hossain, M. A.; Gorla, R. S.R., Natural convection flow from an isothermal horizontal circular cylinder with temperature dependent viscosity, Heat and Mass Transfer, 41, 594-598 (2005)
[13] I. Pop, R. Nazar, N. Amin, Free convection boundary layer on an isothermal horizontal circular cylinder in a micropolar fluid, Heat Transfer, in: Proceeding of the Twelfth International Conference, 2002.; I. Pop, R. Nazar, N. Amin, Free convection boundary layer on an isothermal horizontal circular cylinder in a micropolar fluid, Heat Transfer, in: Proceeding of the Twelfth International Conference, 2002. · Zbl 1106.76456
[14] Pop, I.; Nazar, R.; Amin, N., Free convection boundary layer on a horizontal circular cylinder wit constant heat flux in a micropolar fluid, International Journal Applied Mechanics & Engineering, 7, 2, 409-431 (2002) · Zbl 1106.76456
[15] Pop, I.; Grosan, T.; Amin, N.; Nazar, R., Free convection boundary layer on an isothermal sphere in a micropolar fluid, International Communication Heat Mass Transfer, 29, 3, 377-386 (2002)
[16] Chiang, T.; Ossin, A.; Tien, C. L., Laminar free convection from a sphere, ASME Journal of Heat Transfer, 86, 537-542 (1964)
[17] Huang, M. J.; Chen, C. K., Laminar free convection from a sphere with blowing and suction, ASME Journal of Heat Transfer, 109, 529-532 (1987)
[18] Chen, T. S.; Mocoglu, A., Analysis of mixed forced and free convection about a sphere, International Journal of Heat Mass Transfer, 20, 867-875 (1977) · Zbl 0379.76077
[19] Molla, M. M.; Hossain, M. A.; Gorla, R. S.R., Conjugate effect heat and mass transfer in natural convection flow from an isothermal sphere with chemical reaction, International Journal of Fluid Mechanics Research, 31, 4, 319-331 (2004)
[20] Cebeci, T.; Bradshaw, P., Physical and Computational Aspects of Convective Heat Transfer (1984), Springer: Springer New York · Zbl 0545.76090
[21] Keller, H. B., Numerical methods in boundary layer theory, Annual Review Fluid Mechanics, 10, 417-433 (1978)
[22] Butcher, J. C., Implicit Runge-Kutta process, Mathematics of Computation, 18, 50-55 (1974) · Zbl 0123.11701
[23] P.R. Nachtsheim, P. Swigert, Satisfaction of Asymptotic Boundary Conditions in Numerical Solutions Systems of Non-linear Equations of Boundary layer Type, NASA TN-D3004, 1965.; P.R. Nachtsheim, P. Swigert, Satisfaction of Asymptotic Boundary Conditions in Numerical Solutions Systems of Non-linear Equations of Boundary layer Type, NASA TN-D3004, 1965.
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