Thermophoretic Deposition of Nanoparticles Due Toa Permeable Rotating Disk: Effects of Partial Slip, Magnetic Field, Thermal Radiation, Thermal-Diffusion, and Diffusion-Thermo

The present contribution deals with the thermophoretic deposition of nanoparticles over a rapidly rotating permeable disk in the presence of partial slip, magnetic field, thermal radiation, thermal-diffusion, and diffusion-thermo effects. The governing nonlinear partial differential equations such as continuity, momentum, energy and concentration are transformed into nonlinear ordinary differential equations using similarity analysis, and the solutions are obtained through the very efficient computer algebra software MATLAB. Graphical results for non-dimensional concentration and temperature profiles including thermophoretic deposition velocity and Stanton number (thermophoretic deposition flux) in tabular forms are presented for a range of values of the parameters characterizing the flow field. It is observed that slip mechanism, thermal-diffusion, diffusion-thermo, magnetic field and radiation significantly control the thermophoretic particles deposition rate. The obtained results may be useful to many industrial and engineering applications.

Authors:

• M. M. Rahman

Keywords:

• Boundary layer flows
• convection
• diffusion-thermo
• rotating disk
• thermal-diffusion
• thermophoresis.

References:

[1] S.L. Goren, "Thermophoresis of aerosol particles in laminar boundary
layer on flat plate,"J. Colloid Interface Sci., vol. 61, pp. 77-85, 1977.
[2] L. Talbot, R.K. Cheng, R.W. Schefer, D.R. Wills, "Thermophoresis of
particles in a heated boundary layer,"J. Fluid Mech.,vol. 101, pp. 737-
758, 1980.
[3] G.M. Homsy, F.T. Geyling, K.L. Walker, "Blasius series for
thermophoresis deposition of small particles,"J. Colloid Interface Sci.,
vol. 83, pp. 495-501, 1981.
[4] A.F. Mills, X. Hang, F. Ayazi, "The effect of wall suction and
thermophoresis on aerosol-particle deposition from a laminar boundary
layer on a flat plate," Int. J. Heat Mass Transfer, vol.27, pp. 1110-1114,
1984.
[5] M. Epstein, G.M. Hauser, R.E. Henry, "Thermophoretic deposition of
particles in natural convection flow from a vertical plate,"J. Heat
Transfer, vol.107, pp. 272-276, 1985.
[6] G.K. Batchelor, C. Shen, "Thermophoretic deposition of particles in gas
flowing over cold surface," J. Colloid Interface Sci.,vol.107, pp. 21-37,
1985.
[7] W.W. Nazaroff, G.R. Cass, "Particle deposition from a natural
convection flow onto a vertical isothermal flat plate," J. Aerosol
Sci.,vol.18, pp.445-455, 1987.
[8] G. Jia, J.W. Cipolla, Y. Yener, "Thermophoresis of a radiating aerosol in
laminar boundary layer flow,"J. Thermophys. Heat Transfer,vol. 6,pp.
476-482, 1992.
[9] M.C. Chiou, J.W. Cleaver, "Effect of thermophoresis on submicron
particle deposition from a laminar forced convection boundary layer
flow on to an isothermal cylinder,"J. Aerosol Sci.,vol. 27, pp. 1155-
1167, 1996.
[10] S. Jayaraj, K.K. Dinesh, K.L. Pallai, "Thermophoresis in natural
convection with variable properties,"Heat Mass Transfer, vol.34, pp.
469-475, 1999.
[11] R. Tsai, "A simple approach for evaluating the effect of wall suction and
thermophoresis on aerosol particle deposition from a laminar flow over a
flat plate,"Int. Commun. Heat Mass Transfer, vol. 26, pp. 249-257,
1999.
[12] Y.P. Chang, R. Tsai, F.M. Sui, "The effect of thermophoresis on particle
deposition from a mixed convection flow onto a vertical flat plate," J.
Aerosol Sci., vol. 30, pp. 1363-1378, 1999.
[13] A.J. Chamkha, I. Pop, "Effect of thermophoresis particle deposition in
free convection boundary layer from a vertical flat plate embedded in a
porous medium,"Int. Commun. Heat Mass Transfer, vol.31, pp. 421-
430, 2004.
[14] A.J. Chamkha, A.F. Al-Mudhaf, I. Pop, "Effect of heat generation or
absorption on thermophoretic free convection boundary layer from a
vertical flat plate embedded in a porous medium,"Int. Commun. Heat
Mass Transfer, vol.33, pp. 1096-1102, 2006.
[15] M.A. Seddeek, ÔÇÿInfluence of viscous dissipation and thermophoresis on
Darcy-Forchheimer mixed convection in a fluid saturated porous
media,"J. Colloid Interface Sci.,vol. 293, pp. 137-142, 2006.
[16] A. Postelnicu, "Effects of thermophoresis particle deposition in free
convection boundary layer from a horizontal flat plate embedded in a
porous medium,"Int. J. Heat Mass Transfer,vol. 50, pp. 2981-2985,
2007.
[17] M.S. Alam, M.M. Rahman, M.A. Sattar, "Effects of variable suction and
thermophoresis on steady MHD combined free-forced convective heat
and mass transfer flow over a semi-infinite permeable inclined plate in
the presence of thermal radiation,"Int. J. Thermal Sci., vol.47, pp. 758-
765, 2008.
[18] M.S. Alam, M.M. Rahman, M.A. Sattar,"Effects of chemical reaction,
thermophoresis and heat generation/absorption on steady MHD mixed
convective heat and mass transfer flow along a semi-infinite inclined
porous flat plate with viscous dissipation and joule heating,"Canadian J.
Phys., vol.86, pp.1057-1066, 2008.
[19] M.S. Alam, M.M. Rahman, M.A. Sattar,"On the effectiveness of viscous
dissipation and Joule heating on steady Magnetohydrodynamic heat and
mass transfer flow over an inclined radiate isothermal permeable surface
in the presence of thermophoresis,"Commun. Nonlinear. Sci. Numer.
Simulat,vol. 14, pp. 2132-2143, 2009.
[20] M.S. Alam, M.M. Rahman, M.A. Sattar,"Transient
magnetohydrodynamic free convective heat and mass transfer flow with
thermophoresis past a radiate inclined permeable plate in the presence of
variable chemical reaction and temperature dependent viscosity,"Nonlin.
Analy. Model. Control,vol.14, pp. 3-20, 2009.
[21] N.F.M. Noor, S. Abbasbandy, I. Hashim, "Heat and mass transfer of
thermophoretic MHD flow over an inclined radiate isothermal
permeable surface in the presence of heat source/sink,"Int. J. Heat Mass
Transfer,vol. 55, pp. 2122-2128, 2012.
[22] A. Postelnicu, "Thermophoresis particle deposition in natural convection
over inclined surfaces in porous media,"Int. J. Heat Mass Transfer, vol.
55, pp. 2087-2094, 2012.
[23] T.von Karman, "Uberlaminare und turbulentereibung,"ZAMM,.vol.1,
pp.233-255, 1921.
[24] N. Kelson, A. Desseaux, "Note on porous rotating disk flow", ANZIAM
J., vol.42(E), pp. C837-C855, 2000.
[25] H.I. Andersson, E. de Korte, "MHD flow of a power law fluid over a
rotating disk,"European J. Mech. B. Fluids, vol.21, pp. 317-324, 2002.
[26] H.S. Takhar, A.K. Singh, G. Nath, "Unsteady MHD flow and heat
transfer on a rotating disk in an ambient fluid,"Int. J. Therm. Sci., vol.41,
pp.147-155, 2002.
[27] M. Miklavcic, C.Y. Wang, "The flow due to a rough rotating disk", Z.
Angew. Math. Phys., vol.55,pp. 235-246, 2004.
[28] K.A. Maleque, M.A. Sattar, "Steady laminar convective flow with
variable properties due to a porous rotating disk,"J. Heat Trans.,
vol.127, pp.1406-1409, 2005.
[29] K.A. Maleque, M.A. Sattar, "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 Transfer, vol.48, pp. 4963-4972, 2005.
[30] A. Arikoglu, I. Ozkol, "On the MHD and slip flow over a rotating disk
with heat transfer,"Int. J. Numer Methods Heat Fluid Flow,vol.28,
pp.172-184, 2006.
[31] E. Osalusi, P. Sibanda, "On variable laminar convective flow properties
due to a porous rotating disk in a magnetic field,"Romanian J. Phys.,
vol.51, pp. 933-944, 2006.
[32] E. Osalusi, J. Side, R. Harris, "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 Transfer,vol.35, pp.908-915, 2008.
[33] M.M. Rahman, "Convective hydromagnetic slip flow with variable
properties due to a porous rotating disk,"SQU J. Sci.,vol.15, pp. 55-79,
2010.
[34] C.-G. Song, J. Hwang, "Particle deposition on a rotating disk in
application to vapor axial deposition (VAD) process,"J. Aerosol Sci.,
vol. 29, pp. 99-114, 1998.
[35] C.C. Wang, "Combined effects of inertia and thermophoresis on particle
deposition onto a wafer with wavy surface,"Int. J. Heat Mass
Transfer,vol.49, pp.1395-1402, 2006.
[36] C.L. Chen, K.C. Chan, "Combined effects of thermophoresis and
electrophoresis on particle deposition onto a wavy surface disk,"Int. J.
Heat Mass Transfer,vol.51, pp. 2657-2664, 2008.
[37] M.M. Rahman, A. Postelnicu, "Effects of thermophoresis on the forced
convective laminar flow of a viscous incompressible fluid over a
rotating disk,"Mech. Res. Commun.,vol. 37, pp. 598-603, 2010.
[38] M. Gad-el-Hak, "The fluid mechanics of microdevices-the freeman
scholar lecture,"J. Fluids Eng., vol. 121, pp. 5-33, 1999.
[39] J.-S. Lin, C.J. Tsai, C.P. Chang, "Suppression of particle deposition in
tube flow by thermophoresis,"Aerosol Sci., vol. 35, pp. 1235-1250,
2004.
[40] M.M. Rahman, M.A. Lawatia, I.A. Eltayeb, N. Al-Salti,
"Hydromagnetic slip flow of water based nanofluids past a wedge with
convective surface in the presence of heat generation (or)
absorption,"Int. J. Thermal Sci., vol. 57, pp.172-182, 2012.