Received September 24, 2012; revised October 25, 2012; accepted November 14, 2012

Transcription

1 Open Journal o Fluid Dynamics,,, -9 Published Online December ( Eects o Thermophoresis on Unsteady MHD Free Convective Heat and Mass Transer along an Inclined Porous Plate with Heat Generation in Presence o Magnetic Field Md Alamgir Kabir, Md Abdullah Al Mahbub Department o Natural Sciences, Daodil International University, Dhaka, Bangladesh Department o Mathematics, Comilla University, Comilla, Bangladesh akabir@daodilvarsity.edu.bd Received September 4, ; revised October 5, ; accepted November 4, ABSTRACT An analysis o Thermophoresis eect on unsteady magneto-hydrodynamic ree convection low over an inclined porous plate with time dependent suction in presence o magnetic ield with heat generation has been considered by employing Nachtsheim-Swigert shooting iteration technique along with sixth order Runge-Kutta integration scheme. Resulting non-dimensional velocity, temperature and concentration proiles are then presented graphically or dierent values o the parameters entering into the problem. Finally, the eects o the pertinent parameters on the skin-riction coeicient, the rate o heat transer (Nusselt number) and wall deposition lux (Stanton number), which are o physical interest, are exhibited in tabular orm. Keywords: Heat Generation; Magnetic Field; Nusselt Number; Stanton Number; Thermophoresis. Introduction The ree convection processes involving the combined mechanism o heat and mass transer are encountered in many natural processes, in many industrial applications and in many chemical processing systems. The study o ree convective mass transer low has become the object o extensive research as the eects o heat transer along with mass transer eects are dominant eatures in many engineering applications such as rocket nozzles, cooling o nuclear reactors, high sinks in turbine blades, high speed aircrats and their atmospheric re-entry, chemical devices and process equipments. S. Ostrach [], the initiator o the study o convection low, made a technical note on the similarity solution o transient ree convection low past a semi ininite vertical plate by an integral method. B. C. Sakiadis [] analyzed the boundary layer low over a solid surace moving with a constant velocity. This boundary layer low situation is quite dierent rom the classical Blasius problem o boundary low over a semi-ininite lat plate due to entrainment o ambient luid. L. E. Erickson, L. T. Fan and V. G. Fox [3] extended the work o Sakiadis or suction or injection o a smooth surace. S. L. Goren [4] studied thermophoresis in laminar low over a horizontal lat plate. He ound the deposition o particles on cold plate and particles ree layer thickness in hot plate case. E. M. Sparrow [5] explained a parameter named Rosseland approximation to describe the radiation heat lux in the energy equation in his book. R. S. R. Gorla [6] depicted the application o linearly stretched surace in electrochemistry. G. M. Homsy, F. T. Geyling and K. L. Walker [7] solved Blasius series solution. A. Raptis and C. Perdikis [8] studied numerically ree convection low through a porous medium bounded by a semi-ininite vertical porous plate. M. Epstein, G. M. Hauser and R. E. Henry [9] analyzed the thermophoresis in natural convection or a cold vertical surace. M. A. Alabraba, A. R. Bestman and A. Ogulu [] studied the interaction o mixed convection with thermal radiation in laminar boundary layer low taking into account the binary chemical reaction and Soret-Duour eects. A. Sattar and M. Hossain [] investigated the unsteady ree convective low, with Hall currents and mass transer, past an accelerated vertical porous plate in the presence o a transverse magnetic ield while assuming the plate temperature and concentration to be unctions o time. M. A. Hossain and H. S. Takhar [] analyzed the eect o radiation using the Rosseland diusion approximation that leads to non similar boundary layer equation gov- Copyright SciRes.

2 MD A. KABIR, MD A. AL MAHBUB erning the mixed convection low o an optically dense viscous incompressible luid past heated vertical plate with a ree uniorm stream velocity and surace temperature. In recent years, it is ound that the thermophoresis phenomenon has many practical applications in removing small particles rom gas streams, in determining exhaust gas particle trajectories rom combustion devices, and in studying the particulate material deposition on turbine blades. It has been ound that thermophoresis is the dominant mass transer mechanism in the modiied chemical vapor deposition (MCVD) process as currently used in the abrication o optical iber perorms. Thermophoretic deposition o radioactive particles is considered to be one o the important actors causing accidents in nuclear reactors. J.-S. Lin, C.-J. Tsai and C.-P. Chang [3] investigated the suppression o particle deposition rom low through a tube with circular cross-section when the wall temperature exceeds that o the gas. M. A. Seddek [4] investigated inite element method or the eects o thermophoresis and chemical reaction on a boundary layer hydro magnetic low with heat and mass transer over a heat surace and ound that the velocity, temperature and concentration proiles reduce with the increase o thermophoretic parameter. M. S. Alam, M. M. Rahman and M. A. Sattar [5] considered the eects o heat generation and thermophoresis on steady, laminar, hydromagnetic, two-dimensional low with heat and mass transer along a semi-ininite, permeable inclined lat surace. M. A. Samad and M. E. Karim [6] considered an unsteady two dimensional MHD low o a viscous incompressible and electrically conducting luid along a vertical plate with time dependent suction under the inluence o a uniorm magnetic ield. M. A. A. Mahmoud [7] made a report on the eects o thermal radiation and variable viscosity on the unsteady hydromagnetic low o an electrically conducting luid past an ininite vertical porous plate in the presence o viscous dissipation and time dependent suction. M. A. Samad, M. E. Karim and D. Mohammad [8] calculated numerically the eect o thermal radiation on steady MHD ree convectoin low taking into account the Rosseland diusion approximaion. P. Loganathan and P. P. Arasu [9] analyzed the eects o thermophoresis particle deposition on non-darcy MHD mixed convective heat and mass transer past a porous wedge in the presence o suction or injection. M. Ferdows, Nazmul and M. OTA [] descried that in the presence o uniorm magnetic ield with viscous dissipation at the wall, the thermophoretic parameter is one o the most useul parameter to control the boundary layer o the luid. O. D. Makinde and P. O. Olanrewaju [] investigated unsteady mixed convection with the thermo-diusion and diusion-thermal eects past a vertical porous plate moving through a binary mixture in the presence o radiative heat transer and n-th order Arrhenius-type chemical reaction. N. Ghara, S. L. Maji, S. Das, R. Jana and S. K. Ghosh [] analyzed the unsteady MHD Couette low o a viscous luid between two ininite non-conducting horizontal porous plates with the consideration o both Hall currents and ion-slip. The present paper is the investigation o the thermophoretic eects o an electrically conducting viscous incompressible luid interaction with heat generation on the low over an inclined porous plate in the presence o heat and mass transer permitted by a transversely applied uniorm magnetic ield taking into account the Rosseland diusion approximation. The investigation is based on known similarity analysis and the local similarity solutions are obtained numerically.. Mathematical Analysis In this work we considered an unsteady two-dimensional MHD low o a viscous incompressible and electrically conducting luid past an inclined porous plate with an angle to the vertical embedded in a porous medium under the inluence o a uniorm magnetic ield. Initially the low is assumed to be in the x-direction, which is chosen along the plate in the upward direction and y-axis normal to it. The plate and the luid are at a constant temperature T in a stationary condition with concentration level C at all points. At time t > the plate is assumed to be moving in the upward direction with the velocity Ut and there is a suction velocity v t taken to be a unction o time, the temperature o the plate raised to T t and the concentration level at the plate is raised to C t where T t T and C t > C. The plate is considered to be o ininite length, all derivatives with respect to x vanish and so the physical variables are unctions o y and t only. The low coniguration and the coordinate system are shown in the Figure. The luid is assumed to have constant properties except that the inluence o the density variations with temperature and concentration, which are considered only in the body orce term, and is considered to be gray, absorbing emitting radiation but non-scattering medium, and the Rosseland approximation is used to describe the radioactive heat lux in the energy equation. A uniorm magnetic ield o strength B is applied normal to the plate parallel to y-direction. Under the usual boundary layer and Boussinesq approximation and using the Darcy-Forchhemier model, the low and heat transer in the presence o radiation are governed by the ollowing equations. Continuity Equation v y () Copyright SciRes.

3 MD A. KABIR, MD A. AL MAHBUB Ut v t T x T U Figure. Flow coniguration and coordinate system. Momentum Equation u u u v gt T cos t y y B b CC cos u u u k k Energy Equation T T T v T t y cp y cp Concentration Equation y Q g u v () T (3) C C C v Dm VT CC (4) t y y y where u and v are the velocity components along x- and y-directions respectively, υ is the kinematic viscosity, ρ is the density o the luid, g is the acceleration due to gravity, β is the coeicient o volume expansion, β * is the volumetric coeicient o expansion with concentration, α is the inclination o the plate, σ is the electric conductivity, B is the uniorm magnetic ield strength (magnetic induction), k is the Darcy permeability, b is the empirical constant, c p is the speciic heat at constant pressure, T and T are the luid temperature within the boundary layer and in the ree-stream respectively, while C and C are the corresponding concentrations. Also Q is the heat generation, D m is the coeicient o mass diusivity and V T is the thermophoretic velocity. The eects o thermophoresis are being taken into account to help in the understanding o the mass deposition variation on the surace. We urther assume that ) the mass lux o particles is suiciently small so that the main stream velocity and temperature ields are not aected by the thermo-physical processes experienced by the relatively small number o particles; ) due to the boundary layer behavior the temperature gradient in the y-direction is much larger than that in the x-direction and hence only the thermophoretic velocity component which is normal to the surace is o importance; 3) the luid has constant kinematic viscosity and thermal diusivity, and that the Boussinesq approximation may be adopted or unsteady laminar low; 4) the particle diusivity is assumed to be constant, and the concentration o particles is suiciently dilute to assume that particle coagulation in the boundary layer is negligible; and 5) the magnetic Reynolds number is assumed to be small so that the induced magnetic ield is negligible in comparison to the applied magnetic ield. Initially (t = ) the luid and the plate are at rest. Thus the no slip boundary conditions at the surace o the plate or the above problem or t > are: u U t, vv t, T T t, C C t at y (5) u, T T, C C as y The eect o thermophoresis is usually prescribed by means o an average velocity that a particle will acquire when exposed to a temperature gradient. For boundary layer analysis it is ound that the temperature gradient along the plate is much lower than the temperature gra- T dient normal to the surace, i.e., T. So the y x component o thermophoretic velocity along the plate is negligible compared to the component o its normal to the surace. As a result, the thermophoretic velocity V T which appears in Equation (4) can be written as T K T VT K T T y, (6) re where K is the thermophoretic coeicient which ranges in value rom to. as indicated by G. K. Batchelor and C. Shen [3] and is deined rom the theory o L. Talbot, R. K. Cheng, A. W. Scheer and D. R. Wills [4] by: C3 Kn 3Cm Kng p Ct Kn Cs g p Ct Kn Kn C C e K re, (7) where C, C, C 3, C m, C s and C t are constants, g and p are the thermal conductivities o the luid and diused particles, respectively and Kn is the Knudsen number. A thermophoretic parameter can be deined (see A. F. Mills, X. Hang and F. Ayazi [5] and R. Tsai [6] as ollows: re K T T. (8) T Typical values o are.,. and. corre- K T equal sponding to approximate values o T Copyright SciRes.

4 MD A. KABIR, MD A. AL MAHBUB 3 to 3, 3 and 3 K or a reerence temperature o T re = 3 K. In order to obtain a local similarity solution in time o the problem under consideration, we introduce a time dependent length scale as δ δ t. (9) With this similarity parameter, a similarity variable is then introduced as y () δ In terms o this length scale, a convenient solution o the Equation () can be taken as v v t v () δ where v is the mass transer parameter, which is positive or suction and negative or injection. Following M. M. A. Samad and M. M. Rahman [7], we see that Ut, T t and C t are now considered to have the ollowing orm: n Uδ δ U t n T t T T T n C t C C C δ () where n is a non-negative integer and, U, T and C are respectively the ree stream velocity, mean temperature δ and concentration. Here δ δ, δ is the value o at t = t. Now to make the Equations ()-(4) dimensionless, we introduce the ollowing transormations: n δ n δ n δ u U t t U T T T T C C C C (3) Now introducing all the above similarity variables in Equations () and (3) we have the ollowing dimensionless ordinary non-linear dierential equations v Grcos Gmcos Fs 4n4M Da Da v Q n (4) Pr Pr 4 (5) v Sc Sc 4nSc Sc (6) where gtδ Gr is the local Grasho number, U g* Tδ Gm is the modiied Grasho number, U B δ M is the local magnetic ield parameter, b Fs is the Forchhemier number and δ n Uδ b δ Fs is the modiied Forchhemier δδ k c p number, Da is the Darcy number, Pr is δ Q the Prandtl number, Q δ is the heat generation, cp Sc is the Schmidt number and Dm T T δ n is the Thermophoresis parameter. T re As a result the corresponding boundary conditions or t > take the orm,, at,, as Skin-Friction Coeicient, Nusselt Number and Stanton Number (7) The parameters o engineering interest or the present problem are the skin-riction coeicient, local Nusselt number and the local Stanton number which indicate physically wall shear stress, rate o heat transer and wall deposition lux respectively. The skin-riction coeicient is given by Rex C, (8) the local Nusselt number may be written as Nux Rex and the Stanton number can be written as i.e., Rex Stx Sc J s UC C Js Dm y y, (9) () Thus the values proportional to the skin-riction coeicient, Nusselt number and the Stanton number are Copyright SciRes.

5 4 MD A. KABIR, MD A. AL MAHBUB, and respectively. 3. Numerical Computation The numerical solutions o the nonlinear dierential Equations (4)-(6) under the boundary condition (7) have been perormed by applying a shooting method namely P. R. Nachtsheim and P. Swigert [8] iteration technique (guessing the missing value) along with sixth order Runge-Kutta integration scheme. We have chosen a step size o =. to satisy the convergence criterion o 6 in all cases. The value o was ound to each iteration loop by = +. The maximum value o to each group o parameters v, Gr, Gm, α, M, Da, Fs, n, Pr, Q, Sc and τ determined when the value o the unknown boundary conditions at = not change to successul loop with error less than 6. In order to veriy the eects o the step size () we ran the code or our model with three dierent step sizes as =., =.5, =. and in each case we ound excellent agreement among them. Figures -4 show the velocity, temperature and concentration proiles or dierent step sizes respectively considering v =., Gr =, Gm =, α = 3, M =, Da =., Fs =., n =, Pr =, Q = 5., Sc = and τ =. 4. Results and Discussion For the purpose o discussing the results, the numerical calculations are presented in the orm o non-dimensional velocity and temperature proiles. Numerical computations have been carried out or dierent values o the suction parameter (v ), Grasho number (Gr), modiied Grasho number (Gm), angle o the inclination, magnetic ield parameter (M), Darcy number (Da), modiied Forchhemier number (Fs ), constant parameter (n), Prandtl number (Pr), heat generation (Q), Schmidt number (Sc) and the thermophoresis parameter (τ). The values o Grasho number (Gr) are taken be large rom.6.3. Curves 3 Figure. Velocity proiles or dierent values o Curves 3 Figure 3. Temperature proiles or dierent values o Curves 3 Figure 4. Concentration proiles or dierent values o. the physical point o view. The large Grasho number values correspond to ree convection problem. Figures 5-7 display the eects o the suction parameter v on the velocity, temperature and concentration proiles respectively. It is observed that, when suction v increases, all the proiles decrease. The eects on velocity and temperature proiles are signiicant but on concentration are small. The decreasing suction restrains the heat transer coeicient. We take α =, 3, 4 and 6 as the values o the angle o the inclination o the plate to explain the eect o α. As α increases, the eect o the buoyancy orce decreases because o the multiplication actor cosα and hence the velocities decrease with the increase o α switly shown in Figure 8. Figure 9 explains that the temperatures as well as the concentration proiles are completely beyond the inluence o the inclination o the plate. M =,,.,. are taken to examine the eect o the magnetic ield parameter M on the velocity, temperature and concentration ields shown in Figures Copyright SciRes.

6 MD A. KABIR, MD A. AL MAHBUB 5..6 v=.,,,..6 =,3,45, Figure 5. Velocity proiles or dierent values o v. 3 4 Figure 8. Velocity proiles or dierent values o..6 v=.,,, Temperature proiles Concentration proiles =,3,45,6.5 Figure 6. Temperature proiles or dierent values o v..6 v=.,,, Figure 7. Concentration proiles or dierent values o v. and. Figure 8 states that the velocity increases aintly with the increase o M. In Figure there is no outcome on the temperature and concentration proiles due the distinction o the values o M. We chose Da =.,., 3., 4. to analyze the eect 3 4 Figure 9. Temperature and concentration proiles or dierent values o M=,,., Figure. Velocity proiles or dierent values o M. o the Darcy number Da on the velocity, temperature and concentration ields shown in Figures and 3 expressing that the velocity increases slightly with the increase o Da but no eect is shown on the temperature Copyright SciRes.

7 6 MD A. KABIR, MD A. AL MAHBUB.6 Concentration proiles Temperature proiles M=,,.,. 4-6 represent the control o the constant parameter n to all the proiles. All the proiles decrease with the increase o n. The eects o n are very signiicant and smooth on the distributions. We have illustrated non-dimensional velocity, tem Figure. Temperature and concentration proiles or dierent values o M...6 n =,,3, Da=.,., 3., 4. Figure 4. Velocity proiles or dierent values o n Figure. Velocity proiles or dierent values o Da Concentration proiles Temperature proiles Da=.,., 3., Figure 3. Temperature and concentration proiles or dierent values o Da. and concentration proiles due the distinction o the values o Da. Here n =,, 3, 5 are considered to demonstrate the eect o the nonlinearity constant parameter. Figures.6 n =,,3, Figure 5. Temperature proiles or dierent values o n..6 n =,,3, Figure 6. Concentration proiles or dierent values o n. Copyright SciRes.

8 MD A. KABIR, MD A. AL MAHBUB 7 p erature and concentration proiles against or some representative values o the heat source parameter Q =, 3, 5, 7 in Figures 7 and 8. The positive value o Q represents source i.e. heat generation in the luid. From Figure 7, it is observed that due to the generation o heat the buoyancy orce increases which in turn gives higher velocity in the boundary layer. This is corroborated by Figure 8 where it is seen that the temperatures indicated by solid lines do indeed rapidly increase as Q increases and there are very tiny luctuations in the concentration proiles pointed out by dashed lines. In Figures 9 and we have plotted the dimen- sionless velocity, temperature and concentration proiles showing the eect o thermophoretic parameter τ. The dropping eect o τ on velocity is seen in Figure 9. There is no eect on temperature proiles marked by solid line or the variation o the values o τ in Figure. We also observe rom Figure speciied by the dashed lines that the thermophoretic parameter τ aects the concentration proiles very considerably. The concentration proiles decrease with the increase o τ. Finally, the eects o various parameters on the skin riction C, local Nusselt number Nu and local Sherwood number Sh are shown in Tables Conclusions In this paper we have studied the thermal radiation interaction with unsteady MHD boundary layer low past a continuously moving vertical plate with suction. From the present study we can make the ollowing conclu- sions: Using suction boundary layer growth can be controlled. Suction stabilizes the hydrodynamic, thermal..6 =,.5,3, Q=,3,5,7 3 4 Figure 9. Velocity proiles or dierent values o τ..3. Temperature proiles Concentration proiles 3 4 Figure 7. Velocity proiles or dierent values o Q Q=,3,5,7 Temperature proiles Concentration proiles 3 Figure 8. Temperature and concentration proiles or dierent values o Q..6 =,.5,3, Figure. Temperature and concentration proiles or dierent values o τ. Table. C, Nu and Sh or dierent values o α. α C Nu Sh Copyright SciRes.

9 8 MD A. KABIR, MD A. AL MAHBUB Q Table. C, Nu an d Sh or dierent values o Q. C Nu Sh Table 3. C, Nu and Sh or dierent values o n. n C Nu Sh Table 4. C, Nu and Sh or dierent values o Da. Da C Nu Sh Table 5. C, Nu and Sh or dierent values o τ. τ C Nu Sh as well as concentration boundary layers growth. The velocity proiles increase whereas tempera ture proiles decrease with an increase o the ree convection current. Magnetic ield has signiicant eect on velocity ield and retards the motion o the luid. Velocity proiles increase with the increase o Darcy number. Thermophoretic number τ has considerable eect on concentration proiles. REFERENCES [] S. Ostrach, An Analysis o Lamina r Free-Convection Flow and Heat Transer about a Flat Plate Parallel to the Direction o the Generating Body Force, Technical Note, NACA Report, Washington, 95. [] B. C. Sakiadis, Boundary-Layer Behavior on Continuous Solid Suraces: I. Boundary-Layer Equations or Two- Dimensional and Axisymmetric Flow, AIChE Journal, Vol. 7, No., 96, pp doi:./aic.6978 [3] L. E. Erickson, L. T. Fan and V. G. Fox, Heat and Mass Transer on a Moving Continuous Flat Plate with Suction or Injection, Industrial Engineering and Chemical Fundamentals, Vol. 5, No., 966, pp doi:./i67a4 [4] S. L. Goren, Thermophoresis o Aerosol Particles in Laminar Boundary Layer on Flat Plate, Journal o Colloid Interace Science, Vol. 6, No., 977, pp doi:.6/-9797(77)946-7 [5] E. M. Sparrow, Radiation Heat Transer, Augmented Edition, Hemisphere Publishing Corp., Washington DC, 978. [6] R. S. R. Gorla, Unsteady Mass Transer in the Boundary Layer on a Continuous Moving Sheet Electrod, Journal o the Electrochemical Society, Vol. 5, No. 6, 978, pp doi:9/.3569 [7] G. M. Homsy, F. T. Geyling and K. L. Walker, Blasius Series or Thermophoretic Deposition o Small Particles, Journal o Colloid Interace Science, Vol. 83, No., 98, pp doi:.6/-9797(8) [8] A. Raptis and C. Perdikis, Unsteady Flow through a Porous Medium in the Presence o Free Convection, International Communications in Heat and Mass Transer, Vol., No. 6, 985, pp doi:.6/ (85)9-3 [9] M. Epstein, G. M. Hauser and R. E. Henry, Thermophoretic Deposition o Particles In Natural Convection Flow rom a Vertical Plate, Journal o Heat Transer, Vol. 7, No., 985, pp doi:/.3474 [] M. A. Alabraba, A. R. Bestman and A. Ogulu, Laminar Convection in Binary Mixed o Hydromagnetic Flow with Radiative Heat Transer-I, II, Astrophysics and Space Science, Vol. 95, No., 99, pp , doi:.7/bf [] A. Sattar and M. Hossain, Unsteady Hydromagnetic Free Convection Flow with Hall Current and Mass Transer along an Accelerated Porous Plate with Time Dependent Temperature and Concentration, Canadian Journal o Physics, Vol. 7, No. 5, 99, pp doi:.39/p9-6 [] M. A. Hossain and H. S. Takhar, Radiation Eect on Mixed Convection along a Vertical Plate with Uniorm Surace Temperature, Heat and Mass Transer, Vol. 3, No. 4, 996, pp doi:.7/bf3866 [3] J.-S. Lin, C.-J. Tsai and C.-P. Chang, Suppression o Particle Deposition in Tube Flow by Thermophoresis, Journal o Aerosol Science, Vol. 35, No. 4, pp doi:.6/j.jaerosci [4] M. A. Seddek, Finite-Element Method or the Eects o Chemical Reaction, Variable Viscosity, Thermophoresis and Heat Generation/Absorption on a Boundary-Layer Hydromagnetic Flow with Heat and Mass Transer over a Heat Surace, Journal o Acta Machanica, Vol. 77, 5, pp. -8. Copyright SciRes.

10 MD A. KABIR, MD A. AL MAHBUB 9 [5] M. S. Alam, M. M. Rahman and M. A. Sattar, Similarity Solutions or Hydromagnetic Free Convective Heat and Mass Transer Flow along a Semi-Ininite Permeable Inclined Flat Plate with Heat Generation and Thermophoresis, Nonlinear Analysis: Modelling and Control, Vol., No. 4, 7, pp [6] M. A. Samad and M. E. Karim, Thermal Radiation Interaction with Unsteady MHD Flow past a Vertical Flat Plate with Time Dependent Suction, Dhaka University Journal o Science, Vol. 57, No., 9, pp [7] M. A. A. Mahmoud, Thermal Radiation Eect on Unsteady MHD Free Convection Flow Past a Vertical Plate with Temperature Dependent Viscosity, Canadian Journal o Chemical Engineering, Vol. 87, No., 9, pp doi:./cjce.35 [8] M. A. Samad, M. E. Karim and D. Mohammad, Free Convection Flow through a Porous Medium with Thermal Radiation, Viscous Dissipation and Variable Suction in Presence o Magnetic Field, Bangladesh Journal o Scientiic Research, Vol. 3, No.,, pp [9] P. Loganathan and P. P. Arasu, Thermophoresis Eects on Non-Darcy MHD Mixed Convective Heat and Mass Transer past a Porous Wedge in The Presence o Suction/Injection, Theoretic Applied Mechanics, Vol. 37, No. 3,, pp doi:98/tam33l [] M. Ferdows, Nazmul and M. Ota, Thermophoresis and Chemical Reaction Eects on MHD Natural Convective Heat and Mass Transer Flow in a Rotating Fluid Considering Heat and Mass Fluxes, Canadian Journal on Science and Engineering Mathematics, Vol., No. 3,, pp [] O. D. Makinde and P. O. Olanrewaju, Unsteady Mixed Convection with Soret and Duour Eects past a Porous Plate Moving through a Binary Mixture o Chemical Reacting Fluid, Chemical Engineering Communications, Vol. 98, No. 7,, pp doi:.8/ [] N. Ghara, S. L. Maji, S. Das, R. Jana and S. K. Ghosh, Eects o Hall Current and Ion-Slip on Unsteady MHD Couette Flow, Open Journal o Fluid Dynamics, Vol., No.,, pp. -3. doi:36/ojd.. [3] G. K. Batchelor and C. Shen, Thermophoretic Deposition o Particles in Gas lowing over Cold Surace, Journal o Colloid Interace Science, Vol. 7, No., 985, pp doi:.6/-9797(85)945-6 [4] L. Talbot, R. K. Cheng, A. W. Scheer and D. R. Wills, Thermophoresis o Particles in a Heated Boundary Layer, Journal o Fluid Mechanics, Vol., No. 4, 98, pp doi:.7/s895 [5] A. F. Mills, X. Hang and F. Ayazi, The Eect o Wall Suction and Thermophoresis on Aerosol-Particle Deposition rom a Laminar Boundary Layer on a lat Plate, International Jornal o Heat and Mass Transer, Vol. 7, No. 7, 984, pp. -4. doi:.6/7-93(84)97-3 [6] R. Tsai, A Simple Approach or Evaluating the Eect o Wall Suction and Thermophoresis on Aerosol Particle Deposition Froma Laminar Flow over Alat Plate, International Communications in Heat and Mass Transer, Vol. 6, No., 999, pp doi:.6/s (99)- [7] M. A. Samad and M. M. Rahman, Thermal Radiation Interaction with Unsteady MHD Flow past a Vertical Porous Plate Immersed in a Porous Medium, Journal o Naval Architechture and Marine Engineering, Vol. 3, No., 6, pp [8] P. R. Nachtsheim and P. Swigert, Satisaction o the Asymptotic Boundary Conditions in Numerical Solution o the Systems o Non-Linear Equations o Boundary Layer Type, Ph.D. Thesis, NASA TN D-34, Washington DC, 965. Copyright SciRes.