The Effects of Local Variation in Thermal Conductivity on Heat Transfer of a Micropolar Fluid Flow Over a Porous Sheet
الموضوعات :
Reza Keimanesh
1
(Department of Mechanical Engineering,
K. N. Toosi University of Technology, Iran)
Cyrus Aghanajafi
2
(Department of Mechanical Engineering,
K. N. Toosi University of Technology, Iran)
الکلمات المفتاحية: Micropolar fluid, Thermal conductivity, magnetic field, Radiation,
ملخص المقالة :
This study is considering a micropolar fluid flow over a porous stretching sheet in the presence of thermal radiation and uniform magnetic field. The effects of local variation in thermal conductivity of micropolar fluid on heat transfer rate from the sheet are investigated; besides, the impacts of radiation, magnetic field and porous sheet on variations of thermal boundary layer thickness are considered. The results show that the increase of thermal conductivity thickens thermal boundary layer, so heat transfer rate decreases. In addition, intensification of magnetic field and the presence of radiation lower the absolute values of temperature gradient on the wall, and reduce the cooling rate of the sheet. On the contrary, the increase of suction and material parameter has positive influence on cooling rate of the sheet.
[1] Wang, C.Y., “Liquid film on an unsteady stretching Surface,” Quarterly of Applied Mathematics, Vol. 48, No. 4, 1990, pp. 601- 610.
[2] Mahapatra, T., Gupta, A.S., “Stagnation-point flow of a viscoelastic fluid towards a stretching surface,” International Journal of Non-linear Mechanics, Vol. 39, No. 5, 2004, pp. 811- 820.
[3] Miklavcic, M., Wang, C.Y., “Viscous flow due to a shrinking sheet,” Quarterly of Applied Mathematics, Vol. 64, No. 2, 2006, pp. 283- 290.
[4] Wang, C.Y., “Stagnation flow towards a shrinking sheet,” International Journal of Non-Linear Mechanics, Vol. 43, No. 5, 2008, pp. 377- 382.
[5] Fang, T., “Boundary layer flow over a shrinking sheet with power-law velocity,” International Journal of Heat and Mass transfer, Vol. 51, No. 25- 26, 2008, pp. 5838- 5843.
[6] Ishak, A., Lok, Y.Y., Pop, I., “Non-Newtonian power-law fluid flow past a shrinking sheet with suction,” Chemical Engineering Communications, Vol. 199, No. 1, 2012, pp. 142- 150.
[7] Bachok, N., Ishak, A., Pop, I., “Boundary layer stagnation-point flow and heat transfer over an exponentially stretching/shrinking sheet in a nanofluid,” International Journal of Heat and Mass transfer, Vol. 55, No. 25- 26, 2012, pp. 8122- 8128.
[8] Xu, H., Pop, I., You, X.C., “Flow and heat transfer in a nano-liquid film over an unsteady stretching surface,” International Journal of Heat and Mass Transfer, Vol. 60, 2013, pp. 646- 652.
[9] Eringen, A.C., “Simple microfluids,” International Journal of Engineering Science, Vol. 2, No. 2, 1964, pp. 205- 217.
[10] Sankara, K.K., Watson, L.T., “Micropolar flow past a stretching sheet,” Journal Mathematics and Physics (ZAMP), Vol. 36, No. 6, 1985, pp. 845- 853.
[11] Hassanien, I.A., Gorla, R.S.R., “Heat transfer to a micropolar fluid from a nonisothermal stretching sheet with suction and blowing,” Acta Mechanica, Vol. 84, No. 1, 1990, pp. 191- 199.
[12] Alomari, A.K., Noorani, M.S.M., Nazar, R., “Homotopy solution for flow of a micropolar fluid on a continuous moving surface,” International Journal for Numerical Methods in Fluids, Vol. 66, No. 5, 2011, pp. 608- 621.
[13] Yacob, N.A., Ishak, A., “Micropolar fluid flow over a shrinking sheet,” Meccanica, Vol. 47, No. 2, 2012, pp. 293- 299.
[14] Hassanien, I.A., Ibrahim, F.S., Gorla R.S.R., “Mixed convection boundary layer flow of a micropolar fluid on a horizontal plate,” Chemical Engineering Communications, Vol. 170, No. 1, 1998, pp. 117- 131.
[15] Mehraban Rad, P., Aghanajafi, C., “The Effect of Thermal Radiation on Nanofluid Cooled Microchannels,” Journal of fusion energy, Vol. 28, No. 1, 2009, pp. 91- 100.
[16] Ali, F.M., Nazar, R., Arifin, N.M., Pop, I., “Unsteady flow and heat transfer past an axisymmetric permeable shrinking sheet with radiation effect,” International Journal for Numerical Methods in Fluids, Vol. 67, No. 10, 2011, pp. 1310- 1320.
[17] Hussain, M., Ashraf, M., Nadeem, S., Khan, M., “Radiation effects on the thermal boundary layer flow of a micropolar fluid towards a permeable stretching sheet,” Journal of the Franklin Institute, Vol. 350, No. 1, 2013, pp. 194- 210.
[18] Ouaf, M.E.M., “Exact solution of thermal radiation on MHD flow over a stretching porous sheet,” Applied Mathematics and Computation, Vol. 170, No. 2, 2005, pp. 1117- 1125.
[19] Fang, T., Zhang, J., “Closed-form exact solution of MHD viscous flow over a shrinking sheet,” Communications in Nonlinear Science and Numerical Simulation, Vol. 14, No. 7, 2009, pp. 2853- 2857.
[20] Taklifi, A., Aghanajafi, C., Akrami, H., “The effect of MHD on a porous fin attached to a vertical isothermal surface,” Transport in porous media, Vol. 85, No. 1, 2010, pp. 215- 231.
[21] Noor, N.F.M., Abbasbandy, S., Hashim, I., “Heat and mass transfer of thermophoretic MHD flow over an inclined radiate isothermal permeable surface in the presence of heat source/sink,” International Journal of Heat and Mass Transfer, Vol. 55, No. 7- 8, 2012, pp. 2122- 2128.
[22] Taklifi, A., Aghanajafi, C., “MHD non-Darcian flow through a non-isothermal vertical surface embedded in a porous medium with radiation,” Meccanica, Vol. 47, No. 4, 2012, pp. 929- 937.
[23] Mukhopadhyay, S., “MHD boundary layer flow and heat transfer over an exponentially stretching sheet embedded in a thermally stratified medium,” Alexandria Engineering Journal, Vol. 52, No. 3, 2013, pp. 259- 265.
[24] Jena, S.K., Mathur, M.N., “Similarity solutions for laminar free convection flow of a thermomicropolar fluid past a non-isothermal vertical flat plate,” International Journal of Engineering Science, Vol. 19, No. 11, 1981, pp. 1431- 1439.
[25] Guram, G.S., Smith, A.C., “Stagnation flow of micropolar fluids with strong and weak interactions,” Computers & Mathematics with Applications, Vol. 6, No. 2, 1980, pp. 213- 233.
[26] Ahmadi, G., “Self-similar solution of imcompressible micropolar boundary layer flow over a semi-infinite plate,” International Journal of Engineering Science, Vol. 14, No. 7, 1976, pp. 639- 646.
[27] Peddieson, J., “An application of the micropolar fluid model to the calculation of turbulent shear flow,” International Journal of Engineering Science, Vol. 10, No. 1, 1972, pp. 23- 32.
[28] Grubka, L.J., Bobba, K.M., “Heat transfer characteristics of a continuous, stretching surface with variable temperature,” ASME Journal of Heat Transfer, Vol. 107, No. 1, 1985, pp. 248- 250.
[29] Ali, M.E., “Heat transfer characteristics of a continuous stretching surface,” Heat and Mass Transfer, Vol. 29, No. 4, 1994, pp. 227- 234.
[30] Chen, C.H., “Laminar mixed convection adjacent to vertical, continuously stretching sheets,” Heat and Mass Transfer, Vol. 33, No. 5, 1998, pp. 471- 476.
[31] Ishak, I., “Thermal boundary layer flow over a stretching sheet in a micropolar fluid with radiation effect,” Meccanica, Vol. 45, No. 3, 2010, pp. 367- 373.
[32] Mahmoud, M. A. A., “Thermal radiation effects on MHD flow of a micropolar fluid over a stretching surface with variable thermal conductivity,” Physica A, Vol. 375, No. 2, 2007, pp. 401- 410.
