Effects of Chemical Reaction on the Unsteady Free Convection Flow past an Infinite Vertical Permeable Moving Plate with Variable Temperature

Affiliation(s)

Department of Mathematics, College of Science, Princess Norah Bint Abdulrahaman University, Riyadh, Saudi Arabia..

Department of Mathematics, College of Science, Princess Norah Bint Abdulrahaman University, Riyadh, Saudi Arabia..

ABSTRACT

Analytical solutions for the effect of chemical reaction on the unsteady free convection flow past an infinite vertical permeable moving plate with variable temperature has been studied. The plate is assumed to move with a constant velocity in the direction of fluid flow. The highly nonlinear coupled differential equations governing the boundary layer flow, heat and mass transfer are solved using two-term harmonic and non-harmonic functions. The parameters that arise in the perturbation analysis are Prandtl number (thermal diffusivity), Schmidt number (mass diffusivity), Grashof number (free convection), modified Grashof number, Chemical reaction parameter (rate constant), Skin friction coefficient and Sherwood number (wall mass transfer coefficient). The study has been compared with available exact solution in the literature and they are found to be in good agreement. It is observed that: The concentration increases during generative reaction and decreases in destructive reaction. The concentration increases with decreasing Schmidt number. The effect of increasing values of K leads to a fall in velocity profiles. The velocity decreases with increasing values of the Schmidt number. An increase in modified Grashof number leads to an increase in velocity profiles. The skin friction increases with decreasing Schmidt number. In generative reaction the skin friction decreases and in destructive reaction the skin friction increases.

Analytical solutions for the effect of chemical reaction on the unsteady free convection flow past an infinite vertical permeable moving plate with variable temperature has been studied. The plate is assumed to move with a constant velocity in the direction of fluid flow. The highly nonlinear coupled differential equations governing the boundary layer flow, heat and mass transfer are solved using two-term harmonic and non-harmonic functions. The parameters that arise in the perturbation analysis are Prandtl number (thermal diffusivity), Schmidt number (mass diffusivity), Grashof number (free convection), modified Grashof number, Chemical reaction parameter (rate constant), Skin friction coefficient and Sherwood number (wall mass transfer coefficient). The study has been compared with available exact solution in the literature and they are found to be in good agreement. It is observed that: The concentration increases during generative reaction and decreases in destructive reaction. The concentration increases with decreasing Schmidt number. The effect of increasing values of K leads to a fall in velocity profiles. The velocity decreases with increasing values of the Schmidt number. An increase in modified Grashof number leads to an increase in velocity profiles. The skin friction increases with decreasing Schmidt number. In generative reaction the skin friction decreases and in destructive reaction the skin friction increases.

Cite this paper

F. Mohammed Nasser El-Fayez, "Effects of Chemical Reaction on the Unsteady Free Convection Flow past an Infinite Vertical Permeable Moving Plate with Variable Temperature,"*Journal of Surface Engineered Materials and Advanced Technology*, Vol. 2 No. 2, 2012, pp. 100-109. doi: 10.4236/jsemat.2012.22016.

F. Mohammed Nasser El-Fayez, "Effects of Chemical Reaction on the Unsteady Free Convection Flow past an Infinite Vertical Permeable Moving Plate with Variable Temperature,"

References

[1] F. A. Bottemanne, “Theoretical Solution of Simultaneous Heat and Mass Transfer by Free Convection about a Vertical Flat Plate,” Applied Scientific Research, Vol. 25, No. 1, 1972, pp. 137-149. doi:10.1007/BF00382290

[2] T. S. Chen and C. F. Yuh, “Combined Heat and Mass Transfer in Natural Convection along a Vertical Cylinder,” International Journal of Heat and Mass Transfer, Vol. 23, No. 4, 1980, pp. 451-461. doi:10.1016/0017-9310(80)90094-0

[3] B. C. Sakiadis, “Boundary-Layer Behavior on Continuous Solid Surfaces: I. Boundary-Layer Equations for Two-Dimensional and Axi-symmetric Flow,” AIChE Journal, Vol. 7, No. 1, 1961, pp. 26-28. doi:10.1002/aic.690070108

[4] B. C. Sakiadis, “Boundary-Layer Behavior on Continuous Solid Surfaces: II. The Boundary Layer on a Continuous Flat Surface,” AIChE Journal, Vol. 7, No. 1, 1961, pp. 221-225. doi:10.1002/aic.690070211

[5] V. M. Soundalgekar, “Effects of Mass Transfer and Free-Convection Currents on the Flow past an Impulsively Started Vertical Plate,” Journal of Applied Mechanics, Vol. 46, No. 4, 1979, pp. 757-760. doi:10.1115/1.3424649

[6] V. M. Soundalgekar, N. S. Biraj-dar and V. K. Darwhekar, “Mass-Transfer Effects on the Flow past an Impulsively Started Infinite Vertical Plate with Variable Temperature or Constant Heat Flux,” Astrophysics and Space Science, Vol. 100, No. 1-2, 1984, pp. 159-164. doi:10.1007/BF00651593

[7] P. L. Chambre and J. D. Young, “On the Diffusion of a Chemically Reactive Species in a Laminar Boundary Layer Flow,” Physics of Fluids, Vol. 1, 1958, pp. 48-54. doi:10.1063/1.1724336

[8] K. V. Ramanamurthy and V. M. Govinda Rao, Proceedings of the first National Heat and Mass Transfer Conference, Chennai, 1971.

[9] U. N. Das, R. Deka and V. M. Soundalgekar, “Effects of Mass Transfer on Flow past an Impulsively Started Infinite Vertical Plate with Constant Heat Flux and Chemical Reaction,” Forschung im Ingenieurwesen, Vol. 60, No. 10, 1994, pp. 284-287. doi:10.1007/BF02601318

[10] P. Ganesan and H. P. Rani, “Transient Natural Convection along Vertical Cylinder with Heat and Mass Transfer,” Heat and Mass Transfer, Vol. 33, No. 5-6, 1998, pp. 449-455. doi:10.1007/s002310050214

[11] P. Ganesan and H. P. Rani, “On Diffusion of Chemically Reactive Species in Convective Flow along a Vertical Cylinder,” Chemical Engineering and Processing, Vol. 39, No. 2, 2000, pp. 93-105. doi:10.1016/S0255-2701(99)00018-5

[12] M. M. Abdelkhalek, “The Skin Friction in the MHD Mixed Convection Stagnation Point with Mass Transfer,” International Communications in Heat and Mass Transfer, Vol. 33, No. 2, 2006, pp. 248-257. doi:10.1016/j.icheatmasstransfer.2005.09.008

[13] M. M. Ab-delkhalek, “Mixed Convection in a Square Cavity by a Perturbation Technique,” Computational Materials Science, Vol. 42, No. 2, 2008, pp. 212-219. doi:10.1016/j.commatsci.2007.07.004

[14] M. M. Abdelkhalek, “Hydromagnetic Stagnation Point Flow by a Perturbation Technique,” Computational Materials Science, Vol. 42, No. 3, 2008, pp. 497-503. doi:10.1016/j.commatsci.2007.08.013

[15] M. M. Abdelkhalek, “Heat and Mass Transfer in MHD Flow by Perturbation Technique,” Computational Materials Science, Vol. 43, No. 2, 2008, pp. 384-391. doi:10.1016/j.commatsci.2007.12.003

[16] M. M. Abdelkhalek, “Unsteady MHD Convection and Mass Transfer Flow of Micropolar Fluids past a Vertical Permeable Moving Plate with heat Absorption,” Indian Journal of Physics, Vol. 80, No. 6, 2006, pp. 625-635.

[17] M. M. Abdelkhalek, “Thermal Radiation Effects on Hydromagnetic Flow,” Computer Assisted Mechanics and Engineering Sciences, Vol. 14, No. 3, 2007, pp. 471-484.

[18] M. M. Abdelkhalek, “Radiation and Dissipation Effect on Unsteady MHD Micropolar Flow past an Infinite Vertical Plate in a Porous Medium with Time Dependent Suction,” Indian Journal of Physics, Vol. 82, No. 4, 2008, pp. 415-434.

[19] M. M. Abdelkhalek, “Heat and Mass Transfer in MHD Free Convection from a Moving Permeable Vertical Surface by a Perturbation Technique,” Communications in Nonli-near Science and Numerical Simulation, Vol. 14, No. 5, 2009, pp. 2091-2102. doi:10.1016/j.cnsns.2008.06.001

[20] S. A. Zarea, F. M. El-Fayez and M. M. A. khalek, “Perturbation Technique Algo-rithm for Mixed Convection Flow in a Confined Saturated Porous Medium with Temperature,” Arab Journal of Nuclear Sciences and Applications, Accepted, 2010.

[21] B. Gebhart, Y. Jaluria, R. L. Mahajan and B. Sammakia, “Buoyancy-Induced Flows and Transport,” Hemisphere Publishing Corporation, New York, 1988.

[22] R. Muthucumaraswany and P. Ganesan, “Diffusion and First-Order Chemical Reaction on Impulsively Started infinite Vertical Plate with Variable Temperature,” International Journal of Thermal Science, Vol. 41, No. 5, 2002, pp. 475-479.

[1] F. A. Bottemanne, “Theoretical Solution of Simultaneous Heat and Mass Transfer by Free Convection about a Vertical Flat Plate,” Applied Scientific Research, Vol. 25, No. 1, 1972, pp. 137-149. doi:10.1007/BF00382290

[2] T. S. Chen and C. F. Yuh, “Combined Heat and Mass Transfer in Natural Convection along a Vertical Cylinder,” International Journal of Heat and Mass Transfer, Vol. 23, No. 4, 1980, pp. 451-461. doi:10.1016/0017-9310(80)90094-0

[3] B. C. Sakiadis, “Boundary-Layer Behavior on Continuous Solid Surfaces: I. Boundary-Layer Equations for Two-Dimensional and Axi-symmetric Flow,” AIChE Journal, Vol. 7, No. 1, 1961, pp. 26-28. doi:10.1002/aic.690070108

[4] B. C. Sakiadis, “Boundary-Layer Behavior on Continuous Solid Surfaces: II. The Boundary Layer on a Continuous Flat Surface,” AIChE Journal, Vol. 7, No. 1, 1961, pp. 221-225. doi:10.1002/aic.690070211

[5] V. M. Soundalgekar, “Effects of Mass Transfer and Free-Convection Currents on the Flow past an Impulsively Started Vertical Plate,” Journal of Applied Mechanics, Vol. 46, No. 4, 1979, pp. 757-760. doi:10.1115/1.3424649

[6] V. M. Soundalgekar, N. S. Biraj-dar and V. K. Darwhekar, “Mass-Transfer Effects on the Flow past an Impulsively Started Infinite Vertical Plate with Variable Temperature or Constant Heat Flux,” Astrophysics and Space Science, Vol. 100, No. 1-2, 1984, pp. 159-164. doi:10.1007/BF00651593

[7] P. L. Chambre and J. D. Young, “On the Diffusion of a Chemically Reactive Species in a Laminar Boundary Layer Flow,” Physics of Fluids, Vol. 1, 1958, pp. 48-54. doi:10.1063/1.1724336

[8] K. V. Ramanamurthy and V. M. Govinda Rao, Proceedings of the first National Heat and Mass Transfer Conference, Chennai, 1971.

[9] U. N. Das, R. Deka and V. M. Soundalgekar, “Effects of Mass Transfer on Flow past an Impulsively Started Infinite Vertical Plate with Constant Heat Flux and Chemical Reaction,” Forschung im Ingenieurwesen, Vol. 60, No. 10, 1994, pp. 284-287. doi:10.1007/BF02601318

[10] P. Ganesan and H. P. Rani, “Transient Natural Convection along Vertical Cylinder with Heat and Mass Transfer,” Heat and Mass Transfer, Vol. 33, No. 5-6, 1998, pp. 449-455. doi:10.1007/s002310050214

[11] P. Ganesan and H. P. Rani, “On Diffusion of Chemically Reactive Species in Convective Flow along a Vertical Cylinder,” Chemical Engineering and Processing, Vol. 39, No. 2, 2000, pp. 93-105. doi:10.1016/S0255-2701(99)00018-5

[12] M. M. Abdelkhalek, “The Skin Friction in the MHD Mixed Convection Stagnation Point with Mass Transfer,” International Communications in Heat and Mass Transfer, Vol. 33, No. 2, 2006, pp. 248-257. doi:10.1016/j.icheatmasstransfer.2005.09.008

[13] M. M. Ab-delkhalek, “Mixed Convection in a Square Cavity by a Perturbation Technique,” Computational Materials Science, Vol. 42, No. 2, 2008, pp. 212-219. doi:10.1016/j.commatsci.2007.07.004

[14] M. M. Abdelkhalek, “Hydromagnetic Stagnation Point Flow by a Perturbation Technique,” Computational Materials Science, Vol. 42, No. 3, 2008, pp. 497-503. doi:10.1016/j.commatsci.2007.08.013

[15] M. M. Abdelkhalek, “Heat and Mass Transfer in MHD Flow by Perturbation Technique,” Computational Materials Science, Vol. 43, No. 2, 2008, pp. 384-391. doi:10.1016/j.commatsci.2007.12.003

[16] M. M. Abdelkhalek, “Unsteady MHD Convection and Mass Transfer Flow of Micropolar Fluids past a Vertical Permeable Moving Plate with heat Absorption,” Indian Journal of Physics, Vol. 80, No. 6, 2006, pp. 625-635.

[17] M. M. Abdelkhalek, “Thermal Radiation Effects on Hydromagnetic Flow,” Computer Assisted Mechanics and Engineering Sciences, Vol. 14, No. 3, 2007, pp. 471-484.

[18] M. M. Abdelkhalek, “Radiation and Dissipation Effect on Unsteady MHD Micropolar Flow past an Infinite Vertical Plate in a Porous Medium with Time Dependent Suction,” Indian Journal of Physics, Vol. 82, No. 4, 2008, pp. 415-434.

[19] M. M. Abdelkhalek, “Heat and Mass Transfer in MHD Free Convection from a Moving Permeable Vertical Surface by a Perturbation Technique,” Communications in Nonli-near Science and Numerical Simulation, Vol. 14, No. 5, 2009, pp. 2091-2102. doi:10.1016/j.cnsns.2008.06.001

[20] S. A. Zarea, F. M. El-Fayez and M. M. A. khalek, “Perturbation Technique Algo-rithm for Mixed Convection Flow in a Confined Saturated Porous Medium with Temperature,” Arab Journal of Nuclear Sciences and Applications, Accepted, 2010.

[21] B. Gebhart, Y. Jaluria, R. L. Mahajan and B. Sammakia, “Buoyancy-Induced Flows and Transport,” Hemisphere Publishing Corporation, New York, 1988.

[22] R. Muthucumaraswany and P. Ganesan, “Diffusion and First-Order Chemical Reaction on Impulsively Started infinite Vertical Plate with Variable Temperature,” International Journal of Thermal Science, Vol. 41, No. 5, 2002, pp. 475-479.