Effect of Thermal Radiation on Heat Transfer Overan Unsteady Stretching Surface in A Micropolar Fluid with Variable Heat Flux

Effect of Thermal Radiation on Heat Transfer Overan Unsteady Stretching Surface in A Micropolar Fluid with Variable Heat Flux

N.T.Eldabe E.M.A. Elbashbeshy T.G. Emam E.M. Elsaid 

Department of Mathematics, Faculty of Education, Ain Shams University, Heliopolis, Cairo, Egypt

Mathematics Department, Faculty of Science, Ain Shams University, Abbassia, Cairo, Egypt

Mathematics Department, The German University in Cairo-GUC, New Cairo City, Cairo, Egypt

Department of Communications, Faculty of Engineering, Akhbar El Yom Academy, 6 October, Egypt.

Corresponding Author Email: 
essamscience80@yahoo.com
Page: 
93-98
|
DOI: 
https://doi.org/10.18280/ijht.300114
Received: 
N/A
| |
Accepted: 
N/A
| | Citation

OPEN ACCESS

Abstract: 

Effect of thermal radiation on flow and heat transfer over an unsteady stretching surface in a micropolar fluid with variable heat flux is studied. The governing partial differential boundary layer equations are transformed into a system of ordinary differential equations containing the material parameter K, radiation parameter R, unsteadiness parameter A and Prandtl number Pr. These equations are solved numerically by mathematica program. Comparison of the numerical results is made with previously published results under the special cases, the results are found to be in good agreement. The effects of the unsteadiness parameter A, material parameter K, radiation parameter R and Prandtl number Pr on the flow and heat transfer are studied.

1. Introduction
2. Formulation of The Problem
3. Numerical Solutions
4. Skin Friction Coefficient, Couple Stress and Nusselt Number
5. Results and Discussion
6. Conclusion
  References

[1] B. C. Sakiadis, Boundary Layer Behavior on Continuous Solid Surfaces: I. Boundary Layer Equations for Two Dimensional and Axisymmetric

Flow, AIChE J, vol. 7, pp. 26-28, 1961.

[2] B. C. Sakiadis, Boundary Layer Behavior On Continuous Solid Surfaces: II. Boundary Layer Equations on a Continuous Flat Surface, AIChE. J,

vol.7, pp. 221-225, 1961.

[3] L. J. Crane, Flow Bast a Stretching Plane, Z. Amgew Math. Phys, vol. 21, pp. 645-647, 1970.

[4] M. E. Ali, Heat Transfer Characteristics of Continuous Stretching Surface, Warme-Und Stoffuber tragung, vol. 29, pp.227-234, 1994.

[5] M. E. Ali, On Thermal Bboundary Layer on a Power Law Stretched Surface with Suction or Injection, Int. J. Heat Mass Flow, vol.16, pp. 280-290, 1995.

[6] E. M. A Elbashbeshy, Heat Transfer over a Stretching Surface with Variable Heat Flux, J. Phys.D:Appl.Phys, vol. 31, pp. 1951-1955, 1998.

[7] A. Ishak, R. Nazar and I. Pop, Unsteady Mixed Convection Boundary Layer Flow Due to a Stretching Vertical Surface, Arabian J.Sce. Engng , vol. 31, pp. 65-182, 2006.

[8] E. M. A. Elbashbeshy and M. A. A. Bazid, Heat Transfer over a Continuously Moving Plate Embedded in Non-Darcian Porous Medium, Int. J.

Heat and Mass Transfer, vol. 43, pp. 3087-3092, 2000.

[9] H. T. Andersson, J. B. Arseth and B. S. Dandapat, Heat Transfer in a Liquid Film on an Unsteady Stretching Surface, Int .J .Heat Transfer, vol. 43, pp. 69-74, 2000.

[10] E. M. A . Elbashbeshy and M. A. A. Bazid, Heat Transfer over an Unsteady Stretching Surface, Heat Mass Transfer, vol.41, pp.1-4, 2004.

[11] A. Ishak, R. Nazar and I .Pop, Heat Transfer over an Unsteady Stretching Surface with Prescribed Heat Flux, Can. J. of Phys, vol.86, pp. 853-855, 2008.

[12] E. M. A.Elbashbeshy and D. A. Aldawody, Effects of Thermal Radiation and Magnetic Field on Unsteady Mixed Convection Flow and Heat Transfer over a Porous Stretching Surface, Int. J. of Nonlinear Science, vol. 9, pp. 448-454, 2010.

[13] E. M. A. Elbashbeshy and D. A. Aldawody, Effects of Thermal Radiation and Magnetic Field on Unsteady Mixed Convection Flow and Heat Transfer over a Porous Stretching Surface in the Presence of Internal Heat Generation/Absorption, Int.J.of Energy and Technology, vol.2, pp. 1-8, 2010.

[14] E. M. A. Elbashbeshy and D. A. Aldawody, Heat Transfer over an Unsteady Stretching Surface with Variable Heat Flux in the Presence of Heat Source or Sink, Computer and Mathematics with Applications, vol. 60, pp. 2806-2811, 2010.

[15] P. Chandran, N. C. Sacheti and A. K. Singh, Hydromagnetic Flow and Heat Transfer Past a Continuously Moving Porous Boundary, Int. J. Commun .Heat Mass Transfer , vol.23, pp.889-898, 1996.

[16] I. Pop et al, A Note on MHD Flow over a Stretching Permeable Surface, Mech. Res.Commun, vol. 25, pp. 263-269, 1998.

[17] S. Mukhopadhyay, G. C. Layek and S. A. Samad, Study of MHD Boundary Layer Flow over a Heated Stretching Sheet with Variable Viscosity, Int. J. Hat Mass Transfer, vol. 48, pp. 4460-4466, 2005.

[18] H. I. Anderson, K. H. Bech and B. S. Dandapat, MHD Flow of a Power Law Fluid over a Stretching Sheet , Int. J. Non-linear Mech, vol.27, pp. 929-936, 1992.

[19] A. C. Ering, Theory of Micropolar Fluids, J. Math. Mech, vol. 16, pp. 1-18, 1966.

[20] A. C. Ering, Theory of Micropolar Fluids, J. Math. Mech. Appl, vol.38, pp. 480-496, 1972.

[21] H. A. M. Elarabawy, Effect of Suction/Injection on the Flow of a Micropolar Fluid Past a Continuously Moving Plate in the Presence of Radiation, Int. J. of heat and mass transfer, vol. 46, pp. 1471-1477 , 2003.

[22] E. M. A. Elbashbeshy and D. A. Aldawody, Heat Transfer over an Unsteady Stretching Surface in a Micropolar Fluid in the Presence of Magnetic Field and Thermal Radiation, Can. J. Phys, vol.89, pp. 295-298, 2011.

[23] M. A. Rahman, M. A. Samad. and M. S. Alam, Heat transfer in a Micropolar Fluid along a Non Linear Stretching Sheet with a Temperature Dependent Viscosity and Variable Surface Temperature, Int. J. Thermophys, vol. 30, pp. 1649-1670, 2009.

[24] A. Ishak, R. Nazar and I .Pop, Unsteady Boundary Flow over a Stretching Sheet in a Micropolar Fluid, Int. J. of Mathematical. Physical, and Engineering. Science, vol.2, pp. 161-165, 2008.

[25] N . Bachok , A .Ishak. and R . Nazar, Flow and Heat Transfer over an Unsteady Stretching Sheet in a Micropolar Fluid with Prescribed Surface Heat Flux, Int. J. of Mathematical Models and Methods in Applied Sciences, vol.4, pp.167-176, 2010