Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-25T05:55:41.278Z Has data issue: false hasContentIssue false
  • English
  • Français

Solar Radiation Assisted Mixed Convection Flow Along a Vertical Plate

Published online by Cambridge University Press:  05 June 2014

S. Siddiqa  and
M. A. Hossain
S. Siddiqa*
Affiliation:
Department of Mathematics, COMSATS Institute of Information Technology, Kamra Road, Attock, Pakistan
M. A. Hossain
Affiliation:
Fellow of Bangladesh Academy of Science, University of Dhaka, Dhaka, Bangladesh
*
[email protected]
Get access

Abstract

Solar radiation assisted mixed convection boundary layer flow of Newtonian fluid along a non- reflecting, non-absorbing and ideally transparent semi-infinite vertical plate is studied here. Beer's law is used to express the solar radiation term. It is convenient to transform the non-linear dimensionless parabolic partial differential equations into (i) primitive variable formulation (PVF) and (ii) stream function formulation (SFF) before applying the numerical schemes. Coupled equations thus obtained from PVF are integrated numerically through implicit finite difference method together with the Gaussian elimination technique whereas block tridiagonal Keller-box technique is adopted to simulate the system of equations obtained from SFF. Numerical results from these two methods are also compared graphically in order to test the validation of the two schemes. However, due to less computation time and accuracy numeric results of shear stress, local Nusselt number coefficient, velocity and temperature profiles are obtained via SFF. It is found that velocity as well as temperature of the non-absorbing fluid enhances owing to the increase in solar radiation parameter.

Keywords

Mixed convectionSolar radiationNon-absorbingNon-reflectingIdeally transparent
Type
Research Article
Information
Journal of Mechanics , Volume 31 , Issue 1 , February 2015 , pp. N1 - N8
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1.Sparrow, E. M., Eichorn, R. and Gregg, J. L., “Combined Forced and Free Convection in Boundary Layer Flow,” Physics of Fluids, 2, pp. 319–328 (1959).Google Scholar
2.Merkin, J. H., “The Effects of Buoyancy Forces on the Boundary Layer Flow over Semi-Infinite Vertical Flat Plate in a Uniform Free Stream,” Journal of Fluid Mechanics, 35, pp. 4398–4450 (1969).CrossRefGoogle Scholar
3.Lloyd, J. R. and Sparrow, E. M., “Combined Forced and Free Convection Flow on Vertical Surfaces,” International Journal of Heat and Mass Transfer, 13, pp. 434–438 (1970).CrossRefGoogle Scholar
4.Wilks, G., “Combined Forced and Free Convective Flow on Vertical Surfaces,” International Journal of Heat and Mass Transfer, 16, pp. 1958–1964 (1973).CrossRefGoogle Scholar
5.Tingwei, G., Bachrum, R. and Dagguent, M., “Influence De La Convective Natural Le Sur La Convection Force Andessus D'Une Surface Plane Vertical Voumise a Un Flux De Rayonnement,” International Journal of Heat and Mass Transfer, 25, pp. 1061–1065 (1982).Google Scholar
6.Raju, M. S., Liu, X. R. and Law, C. K., “A Formulation of Combined Forced and Free Convection Past Horizontal and Vertical Surfaces,” International Journal of Heat and Mass Transfer, 27, pp. 2215–2224 (1984).Google Scholar
7.Gebhart, B., Jaluria, Y., Mahajan, R. L. and Sammakia, B., Buoyancy-Induced Flows Transport, Hemisphere, New York (1988).Google Scholar
8.Hossain, M. A., Kutubuddin, M. and Pop, I., “Effect of Conduction-Radiation Interaction on the Mixed Convection Flow from a Horizaontal Cylinder,” Heat and Mass Transfer, 35, pp. 307–314 (1999).Google Scholar
9.Hossain, M. A., Anghel, M. and Pop, I., “Thermal Radiation Effects on Free Convection over a Rotating Axisymmetric Body with Application to a Rotating Hemisphere,” Archive of Mechanics, 54, pp. 55–74 (2002).Google Scholar
10.Hossain, M. A. and Munir, M. S., “Natural Convection Flow of a Viscous Fluid About a Truncated Cone with Temperature Dependent Viscosity and Thermal Conductivity,” International Journal of Numerical Methods Heat & Fluid Flow, 6, pp. 494–510 (2001).Google Scholar
11.Hossain, M. A. and Rees, D. A. S., “Radiation Conduction Interaction on Mixed Convection Flow Along a Slender Vertical Cylinder,” AIAA Journal of Thermophysics and Heat Transfer, 12, pp. 611–614, (1998).CrossRefGoogle Scholar
12.Molla, M. M. and Hossain, M. A., “Radiation Effect on Mixed Convection Laminar Flow Along a Vertical Wavy Surface,” International Journal of Thermal Sciences, 46, pp. 926–935 (2007).Google Scholar
13.Siddiqa, S., Asghar, S. and Hossain, M. A., “Radiation Effects on Natural Convection Flow over an Inclined Flat Plate with Temperature-Dependent Viscosity,” Proceedings of the Institute of Mechanical Engineers, Part C: J. Mechanical Engineering Science, 225, pp. 407–419 (2011).Google Scholar
14.Martynenko, O. G., Sokovishin, Yu. A. and Shapiro, M. V., “Free-Convection and Radiative Heat Transfer on a Vertical Plane Surface,” Inzhenerno-Fizicheskii Zhurnal, 32, pp. 1071–1079 (1977).Google Scholar
15.Salomatov, V. V. and Puzyrev, E. M., “Influence of Thermal Radiation on the Laminar Boundary Layer of a Nonabsorbing Fluid,” Inzhenerno-Fizicheskii Zhurnal, 20, pp. 1008–1014 (1971).Google Scholar
16.Sokovishin, Yu. A. and Shapiro, M. V., “Heat Transfer of a Vertical Cylinder by Free Convection and Radiation,” Inzhenerno-Fizicheskii Zhurnal, 33, pp. 694–699 (1977).Google Scholar
17.Siddiqa, S. and Hossain, M. A., “Mixed Convection Boundary Layer Flow over a Vertical Flat Plate with Radiative Heat Transfer,” Applied Mathematics, 3, pp. 705–716 (2012).Google Scholar
18.Fathalah, K. A. and Elsayed, M. M., “Natural Convection Due to Solar Radiation over a Non-Absorbing Plate with and Without Heat Losses,” International Journal of Heat & Fluid Flow, 2, pp. 41–45 (1980).Google Scholar
19.Chamkha, A. J., “Hydromagnetic Free Convection Flow over an Inclined Plate Caused by Solar Radiation,” Journal of Thermophysics and Heat Transfer, 11, pp. 312–314 (1997).Google Scholar
20.Chamkha, A. J., “Solar Radiation Assisted Natural Convection in Uniform Porous Medium Supported by a Vertical Flat Plate,” Journal of Heat Transfer, 119, pp. 89–96 (1997).CrossRefGoogle Scholar
21.Cooper, P. I., “Some Factors Affecting the Absorption of Solar Radiation in Solar Stills,” Solar Energy, 13, pp. 373–381 (1972).Google Scholar
22.Keller, H. B. and Cebeci, T., “Accurate Numerical Methods for Boundary Layer Flows of Two-Dimensional Flows,” Proceedings of the Second International Conference on Numerical Methods in Fluid Dynamics Lecture Notes in Physics, 8, pp. 92–100 (1971).CrossRefGoogle Scholar
23.Cebeci, T. and Bradshaw, P., Physical and Computational Aspects of Convective Heat Transfer, Springer, New York (1984).Google Scholar
24.Hossain, M. A., Kutubuddin, M. and Pop, I., “Effect of Conduction-Radiation Interaction on the Mixed Convection Flow from a Horizaontal Cylinder,” Heat and Mass Transfer, 35, pp. 307–314 (1999).Google Scholar
25.Hossain, M. A., Anghel, M. and Pop, I., “Thermal Radiation Effect on Free Convection over Axisym-metric Body with Application to a Rotating Hemisphere,” Archive of Mechanics, 54, pp. 55–74 (2002).Google Scholar