Ames W F Nonlinear Partial Differential Equations in Engineering, Vol. II [Book]. - New York : Academic Press, 1972.

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Acrivos A A Theoretical Analysis of Laminar Natural Convection Heat Transfer to Non-Newtonian Fluids [Journal] // A.I.Ch.E J, vol 6. - 1960. - pp. 584-590. Acrivos A, Shah M H and Petersen E E Momentum and heat transfer in laminar boundary layer flows of non-newtonian fluids past external surfaces [Journal] // A. I. Ch. E. Journal, vol. 6 (2). - 1960. - pp. 312-318. Ames W F Nonlinear Partial Differential Equations in Engineering, Vol. II [Book]. - New York : Academic Press, 1972. Asghar S, Hayat T and Siddiqui A M Moving boundary in a non-newtonian fluid [Journal] // Int. J. Non-Linear Mech. Vol. (37). - 2002. - pp. 75-80. Bachok N, Ishak A and Pop I Unsteady three-dimensional boundary layer flow due to permeable shrinking sheet [Journal] // App. Math.-Engl. Ed. vol. 31. - 2010. - pp. 1421-1428. Bagai S Similarity Solutions of Free Convection Boundary Layers over a Body of Arbitrary Shape in a Porous Medium with Internal Heat Generation [Journal] // Int. Comm. Heat and Mass Transfer, Vol. 30. - 2003. - pp. 997-100. Banks W H Similarity solutions of the boundary layer equations for a stretching wall [Journal] // J. Mecanique Theorique Appliquee, Vol. 2. - 1983. - pp. 375-392. Bird R B, Stewart W E and Lightfoot E M Transport phenomena [Book]. - New York : John Wiley, 1960. - pp. 103,106. Birkeland B Ludwig Sylow's lectures on algebraic equations and substitutions,, 1862 [Book]. - Christiania (Oslo) : Historia Mathematica (23rd edition), 1996. - pp. 182-199. Birkhoff G Hydrodynamics: a Study in Logic, Fact, and Similitude [Book]. - New Jersey : Princeton University Press, 1950. Birkhoff G Mathematics for engineers [Journal] // Electr. Engrg. vol. 67. - 1948. - p. 1185. Page 244

Blasius H Boundary layers in fluids with little viscosity [Journal] // NACA-TM. - 1908. - p. 1256. Bluman G W and Anco S Symmetry and Integration Methods For Differential Equations [Book]. - New York : Springer Verlag, 2002. Bluman G W and Cole J D Similarity Methods for Differential Equations Appl. Math. Sci. No. 13 [Book]. - New York : Springer Verlag, 1974. Bluman G W and Kumai S Similarities and differential equations. [Book]. - New York : Springer Verlag, 1989. Boutros Y Z, Malek M B, El-Awadi I A and El-Mansi S M A Group method for temperature analysis of thermally stagnant lakes [Journal] // Acta Mech. vol. 133. - 1999. - pp. 131-144. Boutros Y Z, Malek M B and Badran N A Group theoretic approach for solving time-independent free-convective boundary layer flow on a non isothermal vertical flat plate [Journal] // Arch. Mech. vol. 42. - 1990. - pp. 377 395. Buckingham E Model experiments and the form of empirical equations [Journal] // Trans. ASME, Vol (37). - 1914. - p. 263. Callahan G D and Marner W J Transient free convection with mass transfer on an isothermal vertical flat plate [Journal] // Int. J.Heat Mass Transfer vol. 19. - 1976. - pp. 165 174. Campbell J E Introductory Treatise on Lie's Theory of Finite Continuous Transformation Groups [Book]. - [s.l.] : Oxford University Press, 1863. Cebeci T and Bradshaw P Physical and computational aspects of convective heat transfer [Book]. - New York : Springer-Verlag, 1988. Chamka A J Similarity Solutions for Buoyancy-Induced Flow of Power-Law Fluids over a Horizontal Surface Immersed in a Porous Medium [Journal] // Int. Comm. Heat and Mass Transfer, Vol. (24). - 1997. - pp. 805-817. Page 245

Chaudhary M A, Merkin J H and Pop I Similarity solutions in the free convection boundary-layer flows adjacent to vertical permeable surfaces in porous media. I. Prescribed surface temperature [Journal] // Euro. J. Mech.-B/Fluid, vol. 14. - 1995. - pp. 217-237. Chen C L, Chen C K and Yang Y T Unsteady unidirectional flow of an Oldroyd-B fluid in a circular duct with different given volume flow rate conditions [Journal] // Heat Mass Transf. Vol. (40). - 2004. - pp. 203-209. Chen C L, Chen C K and Yang Y T Unsteady unidirectional flow of second grade fluid between the parallel plates with different given volume flow rate conditions [Journal] // Appl. Math. Comp. Vol. (137). - 2003. - pp. 437-450. Chen H T and Chen C K Free Convection Flows of non-newtonian Fluids Along a Vertical Plate Embedded in a Porous Medium [Journal] // ASME J. Heat Transfer, Vol. 110. - 1988. - pp.,257-259. Chen H T and Chen C K Natural convection of non-newtonian fluids about a horizontal surface in a porous medium [Journal] // Journal of Energy Resources Technology, Vol. 109. - 1987. - pp. 119-123. Chen T S and Strobel F A Buoyancy effects in boundary layer adjacent to a continuous moving horizontal plate [Journal] // J. Heat Transfer vol. 102. - 1980. - pp. 170 172. Cohen A An introduction to Lie Theory of one parameter groups (with application to the solution of differential equations) (Reprinted 1931) [Book]. - New york : G. E. Stechert & Co., 1911. Crane L J Flow past a stretching plate [Journal] // Z Angew. Math. Phys., Vol. 21. - 1970. - pp. 645-647. Currie I G Fundamental Mechanics of Fluids [Book]. - ISBN 0070150001 : McGraw-Hill, Inc, 1974. Desai M I and Timol M G Magnetohydrodynamic of viscous non-newtonian fluids [Journal] // Indian J. Eng. Mater. Sci. Vol. (5), No. 6. - 1988. - pp. 457-464. Page 246

Dodge D W and Metzner A B Turbulent Flow of Non-Newtonian Systems [Journal] // A. I. Ch. E Journal, vol. 5. - 1959. - pp. 189-204. Drachner Application of Lie's theory of ordinary and partial differential equations [Book]. - UK : I. O. P. Bristol, 1999. Eisenhart L P Continuous Group of Transformations [Book]. - New York : Dover, 1961. Falkovich and Gregory Fluid Mechanics [Book]. - ISBN 978-1-107-00575-4 : Cambridge University Press, 2011. Fang T and Zhang J Closed-form exact solutions of MHD viscous flow over a shrinking sheet [Journal] // Commun. Nonlinear Sci. Numer. Simulat., vol. 14. - 2009. - pp. 2853-2857. Fang T and Zhang J Thermal boundary layers over a shrinking sheet: an analytical solution [Journal] // Acta Meek, vol. 209. - 2010. - pp. 325-343. Fang T Boundary layer flow over a shrinking sheet with power-law velocity [Journal] // Int. J. Heat Mass Transfer, vol. 51. - 2008. - pp. 5838-5843. Fetecau C and Fetecau C Decay of a potential vortex in a Maxwell fluid. [Journal] // Int. J. Eng. Sci. Vol. (43). - 2005. - pp. 781-789. Fetecau C and Fetecau C The Rayleigh Stokes problem for a fluid of Maxwellian type [Journal] // Int. J. Non-Linear Mech. Vol. (38). - 2003. - pp. 603 607. Fox R W and McDonald A T Introduction to fluid mechanics [Book]. - New York : John Wiley, Third edition, 1985. Fredrickson A G and Bird R B Non-Newtonian flow in annuli [Journal] // Ind. Eng. Chem. vol. 50. - 1958. - pp. 347 352. Fushchich W L, Shtelen W M and Serov N L Symmetry analysis and exact solutions of equations of nonlinear mathematical physics [Book]. - [s.l.] : Kluwer Academic Pub., 1989. Page 247

Gabbert C H Similarity for unsteady compressible boundary layer [Journal] // AIAA. J. vol. 5. - 1967. - pp. 1198-1200. Gaggioli R A and Moran M J Group theoretic technique for the similarity solution of the systems of partial diffeerential equations with auxiliary conditions [Report] : Technical Summary Report No. 693. - [s.l.] : Mathematics Research Center, U.S. Army, University of Wisconsin, 1966. Gebhart B, Jaluria Y, Mahajan R L and Samm B Buoyancy-Induced Flows and Transport [Book]. - [s.l.] : Hemisphere Publishing Corporation, 1988. - p. Zbl 699.76001. Gebhart B and Pera L The nature of vertical natural convection flows resulting from the combined buoyancy effects of thermal and mass diffusion [Journal] // Int. J. Heat Mass Transfer, Vol. 14. - 1971. - pp. 2025 2049. Gebhart B Transient natural convection from vertical elements [Journal] // Trans. ASME. J. Heat Transfer, vol. 83. - 1961. - pp. 61 70. Georgantopoulos G A, Kafousias N G and Nanousis N D Free convection and mass transfer effects on the oscillatory flow of a dissipative fluid past an infinite vertical porous plate II [Journal] // Czechoslovac. Jour. Of Phy., B31. - 1981. - pp. 876-884. Hansen A G and Herzig H Z On Possible Similarity Solutions for Three- Dimensional Incompressible Laminar Boundary Layers. I - Similarity with Respect to Stationary Rectangular Coordinates, [Journal] // NACA-TN 3768. - 1956. Hansen A G and Na T Y Similarity solutions of laminar incompressible boundary layer equations of non-newtonian fluids [Journal] // ASME J. basic eng.. - 1968. - pp. 71-74. Hansen A G Similarity analysis in engineering boundary value problems [Book]. - New york : Prentice- Hall., 1964. Hardee H C and Nilson P H Natural convection in porous media with heat generation [Journal] //. Nuclear Sci. Engng., Vol. (63). - 1977. - pp. 119-132. Page 248

Hayat T and Kara A H A variational analysis of a non-newtonian flow in a rotating system [Journal] // Int. J.Comp. Fluid Dyn. Vol (20). - 2006. - pp. 157 162. Hayat T, Abbas Z and Sajid M On the analytic solution of magnetohydrodynamic flow of a second grade fluid over a shrinking sheet [Journal] // J. App. Mech., vol. 74. - 2007. - pp. 1165-1171. Hayat T, Wang Y and Hutter K Hall effects on the unsteady hydromagnetic oscillatory flow of a second grade fluid [Journal] // Int. J. Non-Linear Mech. Vol. (39). - 2004. - pp. 1027 1037. Hellums J D and Churchill S W Transient and steady state free and natural convection, numerical solutions [Journal] //, A.I.Ch.E. J. vol. 8. - 1962. - pp. 690 695. Helmholtz H Uber discontinuierliche flussigkeitsbewegungen [Journal] // Montasber Berlin, AKADA. - 1873. - p. 215. Helmy K A Solution of the boundary layer equation for a power law fluid in magneto-hydrodynamics [Journal] // Acta Mech., vol. 102. - 1994. - pp. 25-37. Herzig H Z and Hansen A G On Possible Similarity Solutions for Three- Dimensional Incompressible Laminar Boundary Layers. II - Similarity with Respect to Stationary Polar Coordinates [Journal] // NACA-TN 3832. - 1956a. Horvat A, Kljenak I and Marn J Two-dimensional large eddy simulation of turbulent natural convection due to internal heat generation [Journal] // Int. J. Heat Mass Transfer, Vol. (44). - 2001. - pp. 3985-3995. Horvat A, Kljenak L and Marn J Two-dimensional large eddy simulation of turbulent natural convection due to internal heat generation [Journal] // Int. J. Heat Mass Transfer, Vol. 44. - 2001. - pp. 3985-3995. Hsiao K Heat and mass mixed convection for MHD viscoelastic fluid past a stretching sheet with ohmic dissipation [Journal] // Comm. Nonlinear Sci. Numer. Simulat. vol. 15. - 2010. - pp. 1803-1812. Page 249

Hsiao K Heat and mass transfer for micropolar flow with radiation effect past a nonlinearly stretching sheet [Journal] // Heat Mass Transfer, vol. 64. - 2010a. - pp. 413-419. Hsiao K MHD mixed convection for viscoelastic fluid past a porous wedge [Journal] // Int. J. Non-Linear Mech. vol. 46. - 2011. - pp. 1-8. Illingworth C R Unsteady laminar flow of gas near an infnite flat plate [Journal] // Proc. Camb. Philos. Soc. Vol. 46. - 1950. - pp. 603 613. Ingham D B and Pop I Transport Phenomena in Porous Media, vol I and vol. II [Book]. - [s.l.] : Pergamon, Oxford, 1998; 2002. Ishak A, Jafar k, Nazar R and Pop I MHD stagnation point flow towards a stretching sheet [Journal] // Physica A, vol. 388. - 2009. - pp. 3377-3383. Ishak A, Lok Y and Pop I Stagnation-point flow over a shrinking sheet in a micropolar fluid [Journal] // Chem. Eng. Commun., 197,. - 2010. - pp. 1417 1427. Ishak A, Nazar R and Pop I Hydromagnetic flow and heat transfer adjacent to a stretching vertical sheet [Journal] // Heat Mass Transfer, vol. 44. - 2008. - pp. 921-927. Jahn M and Reinke H H Free convection heat transfer with internal energies sources: calculation and measurements [Conference] // Paper NC 2.8. - Tokyo, Japan : Proceedings of the 5th Int. Heat Transfer Conference, 1974. - pp. 74-78. Kafousias G MHD thermal-diffusion effects on free convective and mass transfer flow over an infinite vertical moving plate, [Journal] // Astro.Phy.Space Sci, Vol. (192). - 1992. - pp. 11-19. Kumari M, Slaouti A, Takhar H S and Nakamur S Unsteady free convection flow over a continuous moving vertical surface [Journal] // Acta Mech. vol. 116. - 1996. - pp. 75 82. Lee S L and Tsai J S Cooling of a continuous moving sheet of infinite thickness in the presence of natural convection [Journal] // Int. J. Heat Mass Transfer, vol. 33. - 1990. - pp. 457 464. Page 250

Lee S Y and Ames W F Similarity solutions for non-newtonian fluids [Journal] // A.I.Ch. E. J. Vol. (12). - 1966. - pp. 700 708. Lie S and Engel F Theorie der Transformations- gruppen [Journal] // Teubner, Leipzig, Vols. (1-3). - 1890. Lie S and Scheffers G Vorlesungen uber Differential-gleichungen mitbekannten infinitesimalen Transformationen [Journal] // Teubner, Leipzig. - 1891. Lie S Math. Annalen,Vol. (8) [Journal] // Math. Annalen, Vol. (8). - 1875. - p. 220. Mahapatra T R, Nandy S K and Gupta A S Magnetohydrodynamic stagnationpoint flow of a power-law fluid towards a stretching surface [Journal] // Int.J. Non- Linear Mech., vol. 44. - 2009. - pp. 124-129. Mahapatra T R and Gupta A S Heat transfer in stagnation-point flow towards a stretching sheet [Journal] // Heat Mass Transfer, vol. 38. - 2002. - pp. 517-521. Malek M B and Badran N A Group method analysis of steady free-convective laminar boundary-layer flow on a non-isothermal vertical circular cylinder [Journal] // J. Comput. Appl. Math. Vol. (36). - 1991. - pp. 227 238. Malek M B and Badran N A Group method analysis of unsteady free convective boundary-layer flow on a non isothermal vertical flat plate [Journal] // J. Eng. Math. vol. 24. - 1990. - pp. 343-368. Malek M B and Badran N A Group method analysis of unsteady free-convective laminar boundary-layer flow on a non-isothermal vertical circular cylinder [Journal] // Acta Mech. Vol. (85). - 1990. - pp. 193 206. Malek M B and Helal M M Group method solution for solving nonlinear heat diffusion problems [Journal] // Applied Mathematical Modeling Vol. (30). - 2006. - pp. 930 940. Malek M B and Helal M M Similarity solutions for magneto-forced-unsteady free convective laminar boundary-layer flow [Journal] // Journal of Computational and Applied Mathematics vol. (218). - 2008. - pp. 202 214. Page 251

Malek M B and Mekky M L Similarity solutions for unsteady free-convection flow from a continuous moving vertical surface [Journal] // J. Comput. Appl. Math. vol. 164. - 2004. - pp. 11-24. Malek M B, Boutros Y Z and Badran N A Group method analysis of unsteady freeconvective boundary-layer flow on a non isothermal vertical flat plate [Journal] // J. Eng. Math. vol. 24. - 1990. - pp. 343 368. Malek M B, Kassem M M and Mekky M I Similarity solutions for unsteady freeconvection flow from a continuous moving vertical surface [Journal] // Journal of Computational and Applied Mathematics, Vol. (11), No. 24. - 2004. - pp. 164 165. Massey B and Ward-Smith J Mechanics of Fluids (8th ed.) [Book]. - ISBN 978-0- 415-36206-1 : Taylor & Francis, 2005. Mehta K N and Rao K N Buoyancy-induced flow of non-newtonian fluids in a porous medium past a vertical flat plate with non-uniform surface heat flux [Journal] // Int. J. Engng. Sci. - 1984. - pp. 297-302. Menold E R and Yang K T Asymptotic solutions for unsteady laminar free convection on a vertical plate [Journal] // Trans. ASME. J. Appl. Mech. vol. 29. - 1962. - pp., 124 126. Metzner A B [Book Section] // Advances in Chemical Engineering, Vol. 1 / book auth. Drew T B and Hoopes Jr. J V. - Academic Press : New York, 1956. Metzner A B and Friend W L Heat Transfer to Turbulent Non-Newtonian Fluids [Journal] // Ind. Eng. Chem. vol. 51. - 1959. - pp. 879-882. Michal A D Differential invariance and invariant partial differential equations under continuous transformation groups in normed linear space [Journal] // Proc. Natn. Acad. Sci. U.S.A., Vol. (37). - 1952. - pp. 623-627. Miklavcic M and Wang C Y Viscous flow due to a shrinking sheet [Journal] // Quart. Appl. Math., vol. 64. - 2006. - pp. 283-290. Molla M M and Yao L S The flow of non-newtonian fluids on a flat plate a uniform heat flux [Journal] // ASME J. Heat Transfer. Vol. 131. - 2009. - pp. 011702 1-6. Page 252

Mooney M and Black S A A Generalized Fluidity Power Law and Laws of Extrusion [Journal] // J. Colloid Sci. vol. 7. - 1952. - p. 204. Moran M J A unification of dimensional and similarity analysis via group theory, Doctoral dissertation [Book]. - Medison : University of Wisconsin, 1967. Moran M J and Gaggioli R A Reduction of the number of variables in system of partial differential equations with auxiliary conditions [Journal] // SIAM J. Appl. Math., vol(16),. - 1968. - pp. 202-215. Moran M J and Gaggioli R A A new systematic formalism for similarity analysis, with application to boundary layer flow [Report] : Technical Summary Report No. 918. - [s.l.] : U.S. Army Mathematics Research Center, 1968b. Moran M J and Gaggioli R A Similarity analysis of compressible boundary layer flows via group theory, [Report] : Technical Summary Report No. 838,. - Wisconsin : U.S. Army Mathematics Research Center, Madison, 1967. Moran M J and Gaggioli R A Similarity analysis via group theory [Journal] // AIAA J. Vol. (6). - 1968a. - pp. 2014 2016. Morgan A J A The reduction by one of the number of independent variables in some systems of nonlinear partial differential equations [Journal] // Quart. J. Math. Oxford, Vol (3). - 1952. - pp. 250 259. Moutsolglou A and Chen T S Buoyancy effects in boundary layer on inclined continuous moving sheets [Journal] // J. Heat Transfer, vol. 102. - 1980. - pp. 371 373. Myers T G The application of non-newtonian models to thin film flow, Phys.Rev. E 72 [Journal] // doi:10.1103/physreve.72.066302. - 2005. - pp. 066302-1 066302-11. Na T Y and Hansen A G Possible similarity solution of laminar natural convection flow of non-netonian fluids [Journal] // Int. J of heat and mass transfer, vol. 9. - 1966. - p. 261. Page 253

Na T Y and Hansen A G Similarity solutions of a class of laminar three-dimensional boundary layer equations of power-law fluids [Journal] // Int. J. Non-linear Mech., vol. (2). - 1967a. - pp. 373-385. Na T Y Boundary layer flow of Reiner-Philippoff fluids [Journal] // Int. J. Non- Linear Mechanics, 29, Vol. (6). - 1994. - pp. 871-877. Na T Y Computational Methods in Engineering Boundary Value Problems [Book]. - New York : Academic Press, 1979. Na T Y, Abbott D E and Hansen A G Similarity Analysis of Partial Differential Equations [Report] : Contract No. NAS 8-20065. - Dearborn : The University of Michigan, 1967. Nakayama A and Koyama H Bouyancy-induced flow of non-newtonian fluids over a non-isothermal body of arbitrary shape in a fluid saturated porous medium [Journal] // Appl. Sci. Res., Vol. 48. - 1991. - pp. 55-70. Nakayama A and Shenoy A V Combined Forced and Free Convection Heat Transfer in Power-Law Fluid-Saturated Porous Media [Journal] // Appl. Sci. Res., Vol (50). - 1993. - pp. 83-95. Oosthuizen P H An introduction to convective Heat Transfer Analysis [Book]. - New York : McGraw-Hill, 1999. Ovsiannikov L V Group Analysis in Differential Equations [Book]. - New York : Academic Press (English translation edited by Ames W F), 1982. Pakdemirli M and Boyaci H Effect of non-ideal boundary conditions on the vibrations of continuous systems [Journal] // Journal of Sound and Vibration, Vol. (249), No. 4. - 2002. - pp. 815 823. Pakdemirli M and Yurusoy M Equivalence transformations applied to exterior calculus approach for finding symmetries: an example of non-newtonian fluid flow [Journal] // Int. J. of Engineering Science, Vol. (37). - 1999. - pp. 25-32. Page 254

Pakdemirli M and Yurusoy M Symmetry reduction o unsteady three-dimensional boundary layers of some non-newtonian fluids [Journal] // Int. J. Engng Sci. Vol. (35), No. 8. - 1997. - pp. 731-740. Pakdemirli M Boundary layer flow of power-law fluids past arbitrary profiles [Journal] // IMA J. Appl. Math. Vol. (50). - 1993. - pp. 133-148. Pakdemirli M Similarity analysis of boundary layer equations of a class of non- Newtonian fluids [Journal] //. Int. J. Non-Linear Mech. Vol. (29). - 1994. - pp. 187-196. Pakdemirli M The boundary layer equations of third grade fluids [Journal] // Int. J. Non- Linear Mech. Vol. (27). - 1992. - pp. 785-793. Patel M and Timol M G The Stress Strain Relationship For Visco-Inelastic Non- Newtonian Fluids [Journal] // Int. J. of Appl. Math and Mech. Vol. (6), No. 12. - 2010. - pp. 79-93. Patel M and Timol M G Similarity solutions for three-dimensional boundary layer small-cross flow of Power-law fluids [Journal] // International Journal of Mathematical Sciences and Engineering Application (IJMSEA) Vol. (2), No. 1. - 2008. - pp. 167-174. Pearson J R A and Tardy M J Models for flow of Non-Newtonian and complex fluids through porous media [Journal] // J. Non-Newtonian Fluid Mech. Vol. 102. - 2002. - pp. 447 473. Pop I and Ingham D B Convective Heat Transfer: Mathematical and Computational Viscous Fluids and Porous Media [Book]. - [s.l.] : Pergamon, Oxford, 2001. Postelnicu A and Pop I Similarity solutions of boundary layer free convection flows with internal heat generation about vertical and horizontal surfaces in porous media [Journal] // Int. Comm. Heat Mass Transfer, Vol. 26. - 1999. - pp. 1183-1191. Postelnicu A, Grosan T and Pop I The effect of variable viscosity on forced convection over a horizontal flat plate in a porous medium with internal heat generation [Journal] // Mech. Res. Communications, Vol. 28. - 2001. - pp. 331-337. Page 255

Postelnicu A, Pop I and Grosan D Free convection boundary-layer flows over a vertical permeable flat plate in porous media with internal heat generation [Journal] // Int. Comm. Heat Mass Transfer,Vol. 27. - 2000. - pp. 729-738. Rajagopal K R and Gupta A S An exact solution for flow of a non-newtonian fluid past an infinite plate [Journal] // Meccanica, Vol. (19). - 1984. - pp. 158-160.. Rajagopal K R A note on unsteady unidirectional flows of non-newtonian fluid [Journal] // Int. J. Non-Linear Mech. Vol. (17). - 1982. - pp. 369-373. Rajagopal K R, Gupta A S and Na T Y A note on the Falkner-Skan flows of a non- Newtonian fluid [Journal] // Int. j. non-linear Mechanics, vol (18), No. 4. - 1983. - pp. 313-320. Ramachandran N, Armaly B F and Chen T S Correlation for laminar mixed convection on boundary layers adjacent to inclined continuous moving sheets [Journal] // Int. J. Heat Mass Transfer, vol. 30. - 1987. - pp. 2196 2199. Reiner M A mathematical theory of dilataney [Journal] // American J. Math. vol. 67. - 1945. - pp. 350-362. Revankar S T Natural convection effects on MHD flow past an impulsively started permeable vertical plate [Journal] // Ind. J. Pure and Appl. Maths, Vol. (14), No. 4. - 1983. - pp. 530-539. Reynolds O On the dynamical theory of incompressible viscous fluids and the determination of the criterion [Journal] // Philos. Trans. R. Soc. vol (186). - 1895. - pp. 123-164. Rivlin R S The Hydrodynamics of non-newtonian fluids [Conference] // Proc. Roy. Soc. A193. - London : [s.n.], 1948. - pp. 260-281. Rogers C and Ames W F Non linear boundary value problems in science and engineering [Book]. - London : Academic press, inc., 1989. Rogers C, Stallybrass M P and Clement D L On two phase filtration under gravity and with boundary infiltration: Application of Bäcklund transformation [Journal] // Nonlinear Anal. Theory. Methods Appl. vol. 7. - 1093. - pp. 785-799. Page 256

Scheidegger A E Physics of flow through porous media [Book]. - [s.l.] : Toranto press, 1974. Sedov L I Similarity and dimensional Methods in Mechanics [Book]. - New york : Academic Press. Inc., 1959. Seshadri R and Na T Y Group invariance in engineering boundary value problems. [Book]. - New York : Springer Verlag, 1985. Siegel R Transient free convection from a vertical flat plate [Journal] // Trans. A.S.M.E. C. J. Heat Transfer, vol. 80. - 1958. - pp. 347 359. Sirohi V, Timol M G and Kalthia N L Powell-Eyring model flow near an accelerated plate [Journal] // Fluid Dy. Res. Vol (2), No.3. - 1987. - pp. 193-204. Sisko A W The flow of lubricating greases [Journal] // Ind. Eng. Chem. Vol. (50). - 1958. - pp. 1789 1792. Skelland A H P Non-Newtonian flow and heat transfer [Book]. - New York : John Wiley, 1967. Slater L J Confluent hypergeometric functions [Book]. - London : Cambridge Univ. Press, 1960. Sneddon I N Elements of partial differential equations [Book]. - New York : McGraw-Hill, 1957. Soundalgekar V M Free convection effects on the oscillatory flow Past an infinite, vertical porous plate with constant suction II [Conference] // Proc. R.Soc., Vol. A333. - London : [s.n.], 1973. - pp. 37-50. Soundalgekar V M Free convection effects on the Stokes problem for an infinite vertical plate [Journal] // J. Heat transfer, Trans. ASME, Vol. (99). - 1977. - pp. 499-501. Sparrow E M and Gregg J L Similar solution for free convection from a nonisothermal vertical plate [Journal] // Trans. ASME C: J. Heat transfer, vol. 80. - 1958. - pp. 379-386. Page 257

Stewart W E and Dona C L G Free convection in a heat-generating porous medium in a finite vertical cylinder [Journal] // ASME Journal of Heat Transfer, Vol. 110. - 1988. - pp. 517-520. Tan W C and Masuoka T Stokes first problem for an Oldroyd-B fluid in a porous half space [Journal] // Phys.Fluid. vol. (17). - 2005b. - pp. 023101 023107. Tan W C and Masuoka T Stokes first problem for second grade fluid in a porous half space [Journal] // Int. J.Non-Linear Mech. vol. (40). - 2005a. - pp. 515 522. Timol M G and Kalthia N L Similarity solutions of three dimensional boundary layer equations of non-newtonian fluids [Journal] // Int. J. Non-Linear Mech. Vol. (21). - 1986. - pp. 475-481. Timol M G and Patel M Numerical treatment of Powell Eyring fluid flow using Method of Satisfaction of Asymptotic Boundary Conditions (MSABC) [Journal] // Applied Numerical Mathematics Vol. (59), Elsevier, North- Holland. - 2009. - pp. 2584 2592. Timol M G and Patel M On the class of similarity solutions for three dimensional boundary layer flows of non-newtonian fluids [Journal] // J. of Veer Narmad South Gujarat University, II-B. - 2007. - pp. 103-109. Timol M G and Timol A G Three dimensional Magnetofluiddynamic flow with pressure gradient and fluid injection [Journal] // Ind. J. Pure and Appl. Maths, Vol. (19). - 1988. - pp. 208-216. Vafai K Handbook of Porous Media [Book]. - New York : Marcel Dekker, 2000. Wafo C Invariant solutions of the unidirectional flow of an electrically charged power law non-newtonian fluid over a flat plate in presence of a transverse magnetic field [Journal] // Comm. in Nonlinear Science and Numerical Simulation, Vol. (10). - 2005. - pp. 537-548. Wang C and Tu C Boundary-layer flow and heat transfer of non-newtonian fluids in porous media [Journal] // Int. J. Heat Mass Transfer, Vol. 10. - 1989. - pp. 160-165. Page 258

Wang C Y Stagnation flow towards a shrinking sheet [Journal] // Int. J. Non-Linear Mech., vol. 43. - 2008. - pp. 377-382. Wilkinsion W L Non-Newtonian fluids [Book]. - New York : Pergamon press, 1960. Williams J C, Mulligan J C and Rhyne T B Semi similar solution for unsteady freeconvective boundary layer-flow on a vertical plat plate [Journal] // J. Fluid Mech. vol. 175. - 1987. - pp. 309 332. Yao L S and Molla M M Forced convection of non-newtonian fluids on a heated flat plate [Journal] // Int. J. Heat Mass Transfer. Vol. 51. - 2008. - pp. 5154 5159. Page 259