Effect of Eccentricity on Conjugate Natural Convection in Vertical Eccentric Annuli
Combined conduction-free convection heat transfer in
vertical eccentric annuli is numerically investigated using a finitedifference
technique. Numerical results, representing the heat transfer
parameters such as annulus walls temperature, heat flux, and heat
absorbed in the developing region of the annulus, are presented for a
Newtonian fluid of Prandtl number 0.7, fluid-annulus radius ratio 0.5,
solid-fluid thermal conductivity ratio 10, inner and outer wall
dimensionless thicknesses 0.1 and 0.2, respectively, and
dimensionless eccentricities 0.1, 0.3, 0.5, and 0.7. The annulus walls
are subjected to thermal boundary conditions, which are obtained by
heating one wall isothermally whereas keeping the other wall at inlet
fluid temperature. In the present paper, the annulus heights required
to achieve thermal full development for prescribed eccentricities are
obtained. Furthermore, the variation in the height of thermal full
development as function of the geometrical parameter, i.e.,
eccentricity is also investigated.
[1] E. E. Feldman, R. W. Hornbeck, and J. F. Osterle, "A numerical solution
of developing temperature for laminar developing flow in eccentric
annular ducts," Int. J. Heat Mass Transfer, vol. 25, no. 2, pp. 243-253,
1982.
[2] A. K. Mohanty and M. R. Dubey, "Buoyancy induced flow and heat
transfer through a vertical annulus," Int. J. Heat Mass Transfer, vol. 39,
no. 10, pp. 2087-2093, 1996.
[3] M. A. I. El-Shaarawi, H. I. Abualhamayel, and E. M. A. Mokheimer,
"Developing laminar forced convection in eccentric annuli," Heat and
Mass Transfer, vol. 33, pp. 353-362, 1998.
[4] M. A. I. El-Shaarawi and E. M. A. Mokheimer, "Developing free
convection in open-ended vertical eccentric annuli with isothermal
boundaries," Journal of Heat Transfer, vol. 121, pp. 63-72, 1999.
[5] E. M. A. Mokheimer and M. A. I. El-Shaarawi, "Developing mixed
convection in vertical eccentric annuli," Heat and Mass Transfer, vol.
41, pp. 176-187, 2004.
[6] E. M. A. Mokheimer and M. A. I. El-Shaarawi, "Maximum possible
induced flow rates in open-ended vertical eccentric annuli with uniform
heat flux," International journal for Numerical Methods in Heat & Fluid
Flow, vol. 15, no. 2, pp. 161-182, 2005.
[7] R. Hosseini, M. R. Heyrani-Nobari, and M. Hatam, "An experimental
study of heat transfer in an open-ended vertical eccentric annulus with
insulated and constant heat flux boundaries," Applied Thermal
Engineering, vol. 25, pp. 1247-1257, 2005.
[8] E. M. A. Mokheimer and S. Sami, "Conditions for pressure build-up due
to buoyancy effects on forced convection in vertical eccentric annuli
under thermal boundary condition of first kind," Heat and Mass
Transfer, vol. 43, no. 2 , pp. 175-189, 2006.
[9] E. Fattahi, M. Farhadi, and K. Sedighi, "Lattice Boltzmann simulation of
natural convection heat transfer in eccentric annulus," International
journal of thermal sciences, vol. 49, pp. 2353-2362, 2010.
[10] R. Hosseini, M. Alipour, and A. Gholaminejad, "Natural convection heat
transfer of concentric/eccentric annulus subjected to inner tube of
constant heat flux," in ASME/JSME 2011 8th Thermal Engineering Joint
Conference, 2011.
[11] F. M. Mahfouz, "Heat Convection within an eccentric annulus heated at
either constant wall temperature or constant heat flux," Journal of heat
transfer, vol. 134, no. 8, pp. 082502 (9 pages), 2012.
[12] M. A. I. El-Shaarawi and S. A. Haider, "Critical conductivity ratio for
conjugate heat transfer in eccentric annuli," International Journal of
Numerical Methods for Heat & Fluid Flow, vol. 11, no. 3, pp. 255-277,
2001.
[13] M. A. I. El-Shaarawi, E. M. A. Mokheimer, and A. Jamal, "Conjugate
effects on steady laminar natural convection heat transfer in vertical
eccentric annuli," International Journal for Computational Methods in
Engineering Science and Mechanics, vol. 6, no. 4, pp. 235-250, 2005.
[14] M. A. I. El-Shaarawi, E. M. A. Mokheimer, and A. Jamal, "Geometry
effects on conjugate natural convection heat transfer in vertical eccentric
annuli," International Journal of Numerical Methods for Heat & Fluid
Flow, vol. 17, no. 5, pp. 461-493, 2007.
[15] A. Jamal, M. A. I. El-Shaarawi, and E. M. A. Mokheimer, "Critical
conductivity ratio and wall thickness for conjugate natural convection
heat transfer in vertical eccentric annuli," Numerical heat Transfer, Part
A: Applications, vol. 59, pp. 719-737, 2011.
[16] W. C. Reynolds, R. E. Lundberg, and P. A. McCuen, "Heat transfer in
annular passages. General formulation of the problem for arbitrary
prescribed wall temperatures or heat fluxes," Int. J. Heat Mass Transfer,
vol. 6, pp. 483-493, 1963.
[17] W. F. Hughes and E.W. Gaylord, Basic Equations of Engineering
Science. Schaum Outline Series, 1964, pp. 150-151.
[18] A. Jamal, Conjugate free convection heat transfer in vertical eccentric
annuli, MS Thesis, Mechanical Engineering Department, King Fahd
University of Petroleum and Minerals (KFUPM), Dhahran, Saudi
Arabia, 2002, pp. 52-57.
[1] E. E. Feldman, R. W. Hornbeck, and J. F. Osterle, "A numerical solution
of developing temperature for laminar developing flow in eccentric
annular ducts," Int. J. Heat Mass Transfer, vol. 25, no. 2, pp. 243-253,
1982.
[2] A. K. Mohanty and M. R. Dubey, "Buoyancy induced flow and heat
transfer through a vertical annulus," Int. J. Heat Mass Transfer, vol. 39,
no. 10, pp. 2087-2093, 1996.
[3] M. A. I. El-Shaarawi, H. I. Abualhamayel, and E. M. A. Mokheimer,
"Developing laminar forced convection in eccentric annuli," Heat and
Mass Transfer, vol. 33, pp. 353-362, 1998.
[4] M. A. I. El-Shaarawi and E. M. A. Mokheimer, "Developing free
convection in open-ended vertical eccentric annuli with isothermal
boundaries," Journal of Heat Transfer, vol. 121, pp. 63-72, 1999.
[5] E. M. A. Mokheimer and M. A. I. El-Shaarawi, "Developing mixed
convection in vertical eccentric annuli," Heat and Mass Transfer, vol.
41, pp. 176-187, 2004.
[6] E. M. A. Mokheimer and M. A. I. El-Shaarawi, "Maximum possible
induced flow rates in open-ended vertical eccentric annuli with uniform
heat flux," International journal for Numerical Methods in Heat & Fluid
Flow, vol. 15, no. 2, pp. 161-182, 2005.
[7] R. Hosseini, M. R. Heyrani-Nobari, and M. Hatam, "An experimental
study of heat transfer in an open-ended vertical eccentric annulus with
insulated and constant heat flux boundaries," Applied Thermal
Engineering, vol. 25, pp. 1247-1257, 2005.
[8] E. M. A. Mokheimer and S. Sami, "Conditions for pressure build-up due
to buoyancy effects on forced convection in vertical eccentric annuli
under thermal boundary condition of first kind," Heat and Mass
Transfer, vol. 43, no. 2 , pp. 175-189, 2006.
[9] E. Fattahi, M. Farhadi, and K. Sedighi, "Lattice Boltzmann simulation of
natural convection heat transfer in eccentric annulus," International
journal of thermal sciences, vol. 49, pp. 2353-2362, 2010.
[10] R. Hosseini, M. Alipour, and A. Gholaminejad, "Natural convection heat
transfer of concentric/eccentric annulus subjected to inner tube of
constant heat flux," in ASME/JSME 2011 8th Thermal Engineering Joint
Conference, 2011.
[11] F. M. Mahfouz, "Heat Convection within an eccentric annulus heated at
either constant wall temperature or constant heat flux," Journal of heat
transfer, vol. 134, no. 8, pp. 082502 (9 pages), 2012.
[12] M. A. I. El-Shaarawi and S. A. Haider, "Critical conductivity ratio for
conjugate heat transfer in eccentric annuli," International Journal of
Numerical Methods for Heat & Fluid Flow, vol. 11, no. 3, pp. 255-277,
2001.
[13] M. A. I. El-Shaarawi, E. M. A. Mokheimer, and A. Jamal, "Conjugate
effects on steady laminar natural convection heat transfer in vertical
eccentric annuli," International Journal for Computational Methods in
Engineering Science and Mechanics, vol. 6, no. 4, pp. 235-250, 2005.
[14] M. A. I. El-Shaarawi, E. M. A. Mokheimer, and A. Jamal, "Geometry
effects on conjugate natural convection heat transfer in vertical eccentric
annuli," International Journal of Numerical Methods for Heat & Fluid
Flow, vol. 17, no. 5, pp. 461-493, 2007.
[15] A. Jamal, M. A. I. El-Shaarawi, and E. M. A. Mokheimer, "Critical
conductivity ratio and wall thickness for conjugate natural convection
heat transfer in vertical eccentric annuli," Numerical heat Transfer, Part
A: Applications, vol. 59, pp. 719-737, 2011.
[16] W. C. Reynolds, R. E. Lundberg, and P. A. McCuen, "Heat transfer in
annular passages. General formulation of the problem for arbitrary
prescribed wall temperatures or heat fluxes," Int. J. Heat Mass Transfer,
vol. 6, pp. 483-493, 1963.
[17] W. F. Hughes and E.W. Gaylord, Basic Equations of Engineering
Science. Schaum Outline Series, 1964, pp. 150-151.
[18] A. Jamal, Conjugate free convection heat transfer in vertical eccentric
annuli, MS Thesis, Mechanical Engineering Department, King Fahd
University of Petroleum and Minerals (KFUPM), Dhahran, Saudi
Arabia, 2002, pp. 52-57.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:63775", author = "A. Jamal and M. A. I. El-Shaarawi and E. M. A. Mokheimer", title = "Effect of Eccentricity on Conjugate Natural Convection in Vertical Eccentric Annuli", abstract = "Combined conduction-free convection heat transfer in
vertical eccentric annuli is numerically investigated using a finitedifference
technique. Numerical results, representing the heat transfer
parameters such as annulus walls temperature, heat flux, and heat
absorbed in the developing region of the annulus, are presented for a
Newtonian fluid of Prandtl number 0.7, fluid-annulus radius ratio 0.5,
solid-fluid thermal conductivity ratio 10, inner and outer wall
dimensionless thicknesses 0.1 and 0.2, respectively, and
dimensionless eccentricities 0.1, 0.3, 0.5, and 0.7. The annulus walls
are subjected to thermal boundary conditions, which are obtained by
heating one wall isothermally whereas keeping the other wall at inlet
fluid temperature. In the present paper, the annulus heights required
to achieve thermal full development for prescribed eccentricities are
obtained. Furthermore, the variation in the height of thermal full
development as function of the geometrical parameter, i.e.,
eccentricity is also investigated.", keywords = "Conjugate natural convection, eccentricity, heat transfer, vertical eccentric annuli.", volume = "7", number = "6", pages = "1309-6", }