Natural Convection Flow of Heat Generating/Absorbing Fluid near a Vertical Plate with Ramped Temperature
ABSTRACT
This study considers a theoretical analysis of natural convection flow of heat generating/absorbing fluid near an infinite vertical plate with ramped temperature. It is assumed that the bounding plate has a ramped temperature profile. Exact solutions of energy and momentum equations are obtained using the Laplacetransform techniques. Solutions are obtained for different values of the Prandtl number (Pr) and the heat sink parameter (S). Results of the ramped and isothermal temperature and velocity as well as Nusselt number and skin friction have been compared and presented with the help of graphs.
This study considers a theoretical analysis of natural convection flow of heat generating/absorbing fluid near an infinite vertical plate with ramped temperature. It is assumed that the bounding plate has a ramped temperature profile. Exact solutions of energy and momentum equations are obtained using the Laplacetransform techniques. Solutions are obtained for different values of the Prandtl number (Pr) and the heat sink parameter (S). Results of the ramped and isothermal temperature and velocity as well as Nusselt number and skin friction have been compared and presented with the help of graphs.
Cite this paper
B. Jha, A. Samaila and A. Ajibade, "Natural Convection Flow of Heat Generating/Absorbing Fluid near a Vertical Plate with Ramped Temperature," Journal of Encapsulation and Adsorption Sciences, Vol. 2 No. 4, 2012, pp. 61-68. doi: 10.4236/jeas.2012.24009.
B. Jha, A. Samaila and A. Ajibade, "Natural Convection Flow of Heat Generating/Absorbing Fluid near a Vertical Plate with Ramped Temperature," Journal of Encapsulation and Adsorption Sciences, Vol. 2 No. 4, 2012, pp. 61-68. doi: 10.4236/jeas.2012.24009.
References
[1] [1] M. A. Al-Nimr, “Analytical Solution for Transient Laminar Fully Developed Free-Convection in Vertical Concentric Annuli,” Heat Mass Transfer, Vol. 36, No. 9, 1993, pp. 2385-2395. doi:10.1016/S0017-9310(05)80122-X [2] D. P. McKenzie, J. M. Roberts and N. O. Weiss, “Convection in the Earth’s Mantle: Towards a Numerical Simulation,” Journal of Fluid Mechanics, Vol. 62, No. 3, 1974, pp. 465-538 doi:10.1017/S0022112074000784 [3] F. P. Foraboschi and I. D. Federico, “Heat Transfer in Laminar Flow of Non-Newtonian Heat Generating Fluids,” International Journal of Heat and Mass Transfer, Vol. 7, No. 3, 1964, pp. 315-318. doi:10.1016/0017-9310(64)90107-3 [4] J. C. Crepeau and R. Clerksean, “Similarity Solutions of Natural Convection with Internal Heat Generation,” Journal of Heat Transfer, 1997, pp. 119-183. [5] J. A. Chamkha, “Hydromagnetic Three Dimensional Free Convection on a Vertical Stretching Surface with Heat Generation or Absorption,” International Journal of Heat and Fluid Flow, Vol. 20, No. 1, 1999, pp. 84-92 doi:10.1016/S0142-727X(98)10032-2 [6] A. K. Singh, “Stokes Problem for a Porous Vertical Plate with Heat Sinks by Finite Difference Method,” Astrphysics and Space Science, Vol. 103, No. 2, 1984, pp. 241248. [7] K. Vajravelu and K. S. Sastri, “Laminar Free Convection Heat Transfer of a Viscous Incompressible Heat Generating Fluid Flow Past a Vertical Porous Plate in the Presence of Free-Stream Oscillations. II,” Acta Mechanica, Vol. 31, No. 1-2, 1978, pp. 80-100. [8] K. Vajravelu, “Natural Convection at a Heated Semi-Infinite Vertical Plate with Temperature Dependent Heat Sources or Sinks,” Indian Academic Science, Vol. 88A, No. 4, 1979, pp. 369-376. doi:10.1007/BF02842483 [9] B. K. Jha, “Transient Free Convective Flow in a Vertical Channel with Heat Sinks,” International Journal of Applied Mechanics and Engineering, Vol. 6, No. 2, 2001, pp. 279-286 [10] B. K. Jha, A. K. Singh and H. S. Takhar, “Transient Free Convective Flow in a Vertical Channel Due to Asymmetric Heating,” International Journal Applied Mechanical Engineering, Vol. 8, No. 3, 2003, pp. 497-502. [11] A. K. Singh, H. R. Gholami and V. M. Soundalgeker, “Transient free convective flow between two vertical parallel plates,” Heat Mass Transfer, Vol. 31, No. 5, 1996, pp. 329-331. doi:10.1007/BF02184046 [12] T. Paul, B. K. Jha and A. K. Singh, “Transient Free Convective Flow in a Vertical Channel with Constant Temperature and Constant Heat Flux,” Heat Mass Transfer, Vol. 32, No. 1-2, 1996, pp. 61-63. doi:10.1007/s002310050092 [13] P. Chandran, N. C. Sacheti and K. A. Singh, “Natural Convection near a Vertical Plate with Ramped Wall Temperature,” Heat Mass Transfer, Vol. 41, No. 5, 2005, pp. 459-464. doi:10.1007/s00231-004-0568-7
[1] [1] M. A. Al-Nimr, “Analytical Solution for Transient Laminar Fully Developed Free-Convection in Vertical Concentric Annuli,” Heat Mass Transfer, Vol. 36, No. 9, 1993, pp. 2385-2395. doi:10.1016/S0017-9310(05)80122-X [2] D. P. McKenzie, J. M. Roberts and N. O. Weiss, “Convection in the Earth’s Mantle: Towards a Numerical Simulation,” Journal of Fluid Mechanics, Vol. 62, No. 3, 1974, pp. 465-538 doi:10.1017/S0022112074000784 [3] F. P. Foraboschi and I. D. Federico, “Heat Transfer in Laminar Flow of Non-Newtonian Heat Generating Fluids,” International Journal of Heat and Mass Transfer, Vol. 7, No. 3, 1964, pp. 315-318. doi:10.1016/0017-9310(64)90107-3 [4] J. C. Crepeau and R. Clerksean, “Similarity Solutions of Natural Convection with Internal Heat Generation,” Journal of Heat Transfer, 1997, pp. 119-183. [5] J. A. Chamkha, “Hydromagnetic Three Dimensional Free Convection on a Vertical Stretching Surface with Heat Generation or Absorption,” International Journal of Heat and Fluid Flow, Vol. 20, No. 1, 1999, pp. 84-92 doi:10.1016/S0142-727X(98)10032-2 [6] A. K. Singh, “Stokes Problem for a Porous Vertical Plate with Heat Sinks by Finite Difference Method,” Astrphysics and Space Science, Vol. 103, No. 2, 1984, pp. 241248. [7] K. Vajravelu and K. S. Sastri, “Laminar Free Convection Heat Transfer of a Viscous Incompressible Heat Generating Fluid Flow Past a Vertical Porous Plate in the Presence of Free-Stream Oscillations. II,” Acta Mechanica, Vol. 31, No. 1-2, 1978, pp. 80-100. [8] K. Vajravelu, “Natural Convection at a Heated Semi-Infinite Vertical Plate with Temperature Dependent Heat Sources or Sinks,” Indian Academic Science, Vol. 88A, No. 4, 1979, pp. 369-376. doi:10.1007/BF02842483 [9] B. K. Jha, “Transient Free Convective Flow in a Vertical Channel with Heat Sinks,” International Journal of Applied Mechanics and Engineering, Vol. 6, No. 2, 2001, pp. 279-286 [10] B. K. Jha, A. K. Singh and H. S. Takhar, “Transient Free Convective Flow in a Vertical Channel Due to Asymmetric Heating,” International Journal Applied Mechanical Engineering, Vol. 8, No. 3, 2003, pp. 497-502. [11] A. K. Singh, H. R. Gholami and V. M. Soundalgeker, “Transient free convective flow between two vertical parallel plates,” Heat Mass Transfer, Vol. 31, No. 5, 1996, pp. 329-331. doi:10.1007/BF02184046 [12] T. Paul, B. K. Jha and A. K. Singh, “Transient Free Convective Flow in a Vertical Channel with Constant Temperature and Constant Heat Flux,” Heat Mass Transfer, Vol. 32, No. 1-2, 1996, pp. 61-63. doi:10.1007/s002310050092 [13] P. Chandran, N. C. Sacheti and K. A. Singh, “Natural Convection near a Vertical Plate with Ramped Wall Temperature,” Heat Mass Transfer, Vol. 41, No. 5, 2005, pp. 459-464. doi:10.1007/s00231-004-0568-7