## Main Article Content

## Abstract

In this paper we investigate convective heat transfer characteristics of steady hydromagnetic slip flow over a porous rotating disk taken into account the temperature dependent density, viscosity and thermal conductivity in the presence of Hall current, viscous dissipation and Joule heating. Using von-Karman similarity transformations we reduce the governing equations for flow and heat transfer into a system of ordinary differential equations which are highly nonlinear and coupled. The resulting nondimensional equations are solved numerically by applying Nachtsheim-Swigert iteration technique. The results show that when modeling a thermal boundary layer, with temperature dependent fluid properties, consideration of Prandtl number as constant within the boundary layer, produces unrealistic results. therefore Therefore it must be treated as variable throughout the boundary layer. Results also show that the slip factor significantly controls the flow and heat transfer characteristics.

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## Article Details

* * References

- ABOUL-HASSAN, A.L. and ATTIA, H.A. 1997. Flow due to a rotating disk with Hall effect. Phys. Lett. A., 228: 286-290.
- ANDERSSON, H.I. and de KORTE, E. (2002). MHD flow of a power law fluid over a rotating disk. European J. Mech. B./Fluids, 21: 317-324.
- ARIKOGLU, A. and OZKOL, I. 2006. On the MHD and slip flow over a rotating disk with heat transfer. Int. J. Numer Methods Heat Fluid Flow, 28: 172-184.
- ATTIA, H.A. 1998. Unsteady MHD flow near a rotating porous disk with uniform suction or injection. Fluid Dyn. Res., 23: 283-290.
- ATTIA, H.A. 2006. Unsteady flow and heat transfer of viscous incompressible fluid with temperature-dependent
- viscosity due to a rotating disc in a porous medium. J. Phys. A, Math. Gen., 39: 979-991.
- BENTON, E.R. 1965. On the flow due to a rotating disc. J. Fluid Mech., 24: 781-800.
- COCHRAN, W.G. 1934. The flow due to a rotating disc. Proc. Cambridge Phil. Soc. 30: 365-375.
- EL-MISTIKAWY, T.M.A., ATTIA, H.A. and MEGAHED, A.A. 1991. The rotating disk flow in the presence of weak magnetic field. Proc. Fourth Conf. Theoret. Appl. Mech., Cairo, Egypt, 5–7 November 1991, pp. 69-82.
- EL-MISTIKAWY, T.M.A. and ATTIA, H.A. 1990. The rotating disk flow in the presence of strong magnetic field. Proc. Third int. Cong. Fluid Mech., Cairo, Egypt, 2-4 January 1990, 3: 1211-1222.
- GAD-EL-HAK, M. 1999. The fluid mechanics of micro devices-the free scholar lecture. J. Fluid Eng-T. Asme., 121: 5-33.
- HERRERO, J., HUMPHREY, J.A.C. and GIRALT, F. 1994. Comparative analysis of coupled flow and heat transfer between co-rotating discs in rotating and fixed cylindrical enclosures, Am. Soc. Mech. Eng., Heat Transfer Div. 300: 111-121.
- HERWIG, H. and KLEMP, K. 1988. Variable property effects of fully developed laminar flow in concentric annuli. ASME J. Heat Trans., 110: 314-320.
- JAYARAJ, S. 1995. Thermophoresis in laminar flow over cold inclined plates with variable properties. Heat Mass Trans., 40: 167-174.
- KELSON, N. and DESSEAUX, A. 2000. Note on porous rotating disk flow. ANZIAM J. 42(E): C837-C855.
- KUIKEN, H.K. 1971. The effect of normal blowing on the flow near a rotating disk of infinite extent. J. Fluid Mech., 47: 789-798.
- MALEQUE, A.K. and SATTAR, A.M. 2005a. Steady laminar convective flow with variable properties due to a porous rotating disk. J. Heat Trans., 127: 1406-1409.
- MALEQUE, A.K. and SATTAR, A.M. 2005b. The effects of variable properties and Hall current on steady MHD laminar convective fluid flow due to a porous rotating disk. Int. J. Heat Mass Trans., 48: 4963-4972.
- MIKLAVCIC, M. and WANG, C.Y. 2004. The flow due to a rough rotating disk. Z. Angew. Math. Phys., 55: 235-246.
- NACHTSHEIM, P.R. and SWIGERT, P. 1965. Satisfaction of asymptotic boundary conditions in numerical solution of system of nonlinear of boundary layer type. NASA TN-D3004.
- OSALUSI, E., SIDE, J. and HARRIS, R. 2008. Thermal-diffusion and diffusion-thermo effects on combined heat and mass transfer of a steady MHD convective and slip flow due to a rotating disk with viscous dissipation and Ohmic heating. Int. Commu. Heat Mass Trans., 35: 908-915.
- OSALUSI, E. and SIBANDA, P. 2006. On v ariable laminar convective flow properties due to a porous rotating disk in a magnetic field. Rom. J. Phys., 51: 933-944.
- OWEN, J.M. and ROGERS, R.H. 1989. Flow and heat transfer in rotating disc system, Rotor–Stator Systems, vol. 1, Research Studies Press, Taunton, UK and John Wiley, NY.
- ROGER, M.G. and LANCE, G.N. 1960. The rotationally symmetric flow of a viscous fluid in presence of infinite rotating disc. J. Fluid Mech., 7: 617-631.
- SPARROW, E.M., BEAVERS, G.S. and HUNG, L.Y. 1971. Flow about a porous-surface rotating disk. Int. J. Heat Mas Tranfer., 14: 993-996.
- TAKHAR, H.S., SINGH, A.K. and NATH, G. (2002). Unsteady MHD flow and heat transfer on a rotating disk in an ambient fluid. Int. J. Therm. Sci., 41: 147-155.
- VON KARMAN, T. 1921. Uber laminare und turbulente reibung. ZAMM, 1: 233-255.
- ZAKERULLAH, M. and ACKROYD, J.A.D. 1979. Laminar natural convection boundary layers on horizontal circular discs. J. Appl. Math. Phys., 30: 427- 435.

#### References

ABOUL-HASSAN, A.L. and ATTIA, H.A. 1997. Flow due to a rotating disk with Hall effect. Phys. Lett. A., 228: 286-290.

ANDERSSON, H.I. and de KORTE, E. (2002). MHD flow of a power law fluid over a rotating disk. European J. Mech. B./Fluids, 21: 317-324.

ARIKOGLU, A. and OZKOL, I. 2006. On the MHD and slip flow over a rotating disk with heat transfer. Int. J. Numer Methods Heat Fluid Flow, 28: 172-184.

ATTIA, H.A. 1998. Unsteady MHD flow near a rotating porous disk with uniform suction or injection. Fluid Dyn. Res., 23: 283-290.

ATTIA, H.A. 2006. Unsteady flow and heat transfer of viscous incompressible fluid with temperature-dependent

viscosity due to a rotating disc in a porous medium. J. Phys. A, Math. Gen., 39: 979-991.

BENTON, E.R. 1965. On the flow due to a rotating disc. J. Fluid Mech., 24: 781-800.

COCHRAN, W.G. 1934. The flow due to a rotating disc. Proc. Cambridge Phil. Soc. 30: 365-375.

EL-MISTIKAWY, T.M.A., ATTIA, H.A. and MEGAHED, A.A. 1991. The rotating disk flow in the presence of weak magnetic field. Proc. Fourth Conf. Theoret. Appl. Mech., Cairo, Egypt, 5–7 November 1991, pp. 69-82.

EL-MISTIKAWY, T.M.A. and ATTIA, H.A. 1990. The rotating disk flow in the presence of strong magnetic field. Proc. Third int. Cong. Fluid Mech., Cairo, Egypt, 2-4 January 1990, 3: 1211-1222.

GAD-EL-HAK, M. 1999. The fluid mechanics of micro devices-the free scholar lecture. J. Fluid Eng-T. Asme., 121: 5-33.

HERRERO, J., HUMPHREY, J.A.C. and GIRALT, F. 1994. Comparative analysis of coupled flow and heat transfer between co-rotating discs in rotating and fixed cylindrical enclosures, Am. Soc. Mech. Eng., Heat Transfer Div. 300: 111-121.

HERWIG, H. and KLEMP, K. 1988. Variable property effects of fully developed laminar flow in concentric annuli. ASME J. Heat Trans., 110: 314-320.

JAYARAJ, S. 1995. Thermophoresis in laminar flow over cold inclined plates with variable properties. Heat Mass Trans., 40: 167-174.

KELSON, N. and DESSEAUX, A. 2000. Note on porous rotating disk flow. ANZIAM J. 42(E): C837-C855.

KUIKEN, H.K. 1971. The effect of normal blowing on the flow near a rotating disk of infinite extent. J. Fluid Mech., 47: 789-798.

MALEQUE, A.K. and SATTAR, A.M. 2005a. Steady laminar convective flow with variable properties due to a porous rotating disk. J. Heat Trans., 127: 1406-1409.

MALEQUE, A.K. and SATTAR, A.M. 2005b. The effects of variable properties and Hall current on steady MHD laminar convective fluid flow due to a porous rotating disk. Int. J. Heat Mass Trans., 48: 4963-4972.

MIKLAVCIC, M. and WANG, C.Y. 2004. The flow due to a rough rotating disk. Z. Angew. Math. Phys., 55: 235-246.

NACHTSHEIM, P.R. and SWIGERT, P. 1965. Satisfaction of asymptotic boundary conditions in numerical solution of system of nonlinear of boundary layer type. NASA TN-D3004.

OSALUSI, E., SIDE, J. and HARRIS, R. 2008. Thermal-diffusion and diffusion-thermo effects on combined heat and mass transfer of a steady MHD convective and slip flow due to a rotating disk with viscous dissipation and Ohmic heating. Int. Commu. Heat Mass Trans., 35: 908-915.

OSALUSI, E. and SIBANDA, P. 2006. On v ariable laminar convective flow properties due to a porous rotating disk in a magnetic field. Rom. J. Phys., 51: 933-944.

OWEN, J.M. and ROGERS, R.H. 1989. Flow and heat transfer in rotating disc system, Rotor–Stator Systems, vol. 1, Research Studies Press, Taunton, UK and John Wiley, NY.

ROGER, M.G. and LANCE, G.N. 1960. The rotationally symmetric flow of a viscous fluid in presence of infinite rotating disc. J. Fluid Mech., 7: 617-631.

SPARROW, E.M., BEAVERS, G.S. and HUNG, L.Y. 1971. Flow about a porous-surface rotating disk. Int. J. Heat Mas Tranfer., 14: 993-996.

TAKHAR, H.S., SINGH, A.K. and NATH, G. (2002). Unsteady MHD flow and heat transfer on a rotating disk in an ambient fluid. Int. J. Therm. Sci., 41: 147-155.

VON KARMAN, T. 1921. Uber laminare und turbulente reibung. ZAMM, 1: 233-255.

ZAKERULLAH, M. and ACKROYD, J.A.D. 1979. Laminar natural convection boundary layers on horizontal circular discs. J. Appl. Math. Phys., 30: 427- 435.