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### Raju, C. S. K.

- Unsteady MHD Couette Flow Between Two Parallel Plates with Uniform Suction

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1 Department of Mathematics, JNTU University, Ananthapur, A.P, IN

2 Department of Mathematics, GITAM University, Bangalore, Karnataka, IN

#### Authors

**Affiliations**

1 Department of Mathematics, JNTU University, Ananthapur, A.P, IN

2 Department of Mathematics, GITAM University, Bangalore, Karnataka, IN

#### Source

Research Journal of Science and Technology, Vol 9, No 3 (2017), Pagination: 476-483#### Abstract

In the present paper analysis is carried out to study on an unsteady magnetohydrodynamic flow between two parallel plates with one in uniform motion and the other plate at rest. We also incorporated the uniform suction at stationary plate. The applications of magnetohydrodynamic cover a wide range of engineering areas as power generators, aerodynamics heating, petroleum industry, cooling system, purification of crude oil, separation of matter from fluid, fluid droplets and sprays. We also discussed the physical characteristics of longitudinal and transverse velocity and pressure distributions. The arising set of partial governing differential equations (PDEs) of the flow is solved by similarity transformation. Analytical expression is given for the velocity field and the effects of the various parameters entering into the problem are discussed with the help of graph.#### Keywords

MHD, Parallel Plates, Pressure Gradient, Reynolds Number, Hartmann Number.#### References

- H. a. Attia, N. a. Kotb, MHD flow between two parallel plates with heat transfer, Acta Mech. 117 (1996) 215–220. doi:10.1007/BF01181049.
- Hassanienand M. A. Mansour, unsteady magneto hydrodynamic flow through a porous medium between two infinite parallel plates.Springerlink, January 1990, Volume 16, pp 241–246. doi: 10.1007/BF00655745.
- M. Venkateswarlu, G.V.R. Reddy, D. V Lakshmi, Unsteady MHD flow of a viscous fluid past a vertical porous plate under oscillatory suction velocity, 4 (2013) 52–67.
- .M. Hameed, S. Nadeem, Unsteady MHD flow of a non- Newtonian fluid on a porous plate, J. Math. Anal. Appl. 325 (2007) 724–733. doi:10.1016/j.jmaa.2006.02.002.
- S. Ganesh, S. Krishnambal, Unsteady magneto hydrodynamic stokes flow of viscous fluid between two parallel porous plates, J. Appl. Sci. 7 (2007) 374–379.
- Stamenkovic´ M. Zˇ ivojin, Dragisˇa D. Nikodijevic, Bratislav D. Blagojevic´, Slobodan R. Savic´, MHD flow and heat transfer of two immiscible fluids between moving PLATES, Transactions of the Canadian Society for Mechanical Engineering, Vol. 34, No. 3–4, 2010.
- P.D.Verma and A.K. Mathur ,Magneto hydrodynamics flow between two parallel plates through porous medium with One Plate Moving Uniformly and the Other Plate at Rest with Uniform Suction,1968
- H.A. Attia, Unsteady MHD couette flow and heat transfer of dusty fluid with variable physical properties, Appl. Math. Compute. 177 (2006) 308–318. doi:10.1016/j.amc.2005.11.010.
- Md. Faisal Kabir and Md. Mahmud Alam, Unsteady Casson Fluid Flow through Parallel Plates with Hall Current, Joule Heating and Viscous Dissipation, AMSE JOURNALS –2015-Series: Modelling B; Vol. 84; N 1; pp 1-22.
- D.W. Kiema, W.A. Manyonge, J.K. Bitok, R.K. Adenyah and J.S. Barasa, On the steady MHD couette flow between two infinite parallel plates in a uniform transverse magnetic field, Journal of Applied Mathematics and Bioinformatics, vol.5, no.1, 2015, 87-99.
- V. M. Soundalgekar and A. G. Uplekar, Hall Effects in MHD Couette Flow with Heat Transfer, IEEE transactions on plasma science, vol. PS-14, NO. 5, October 1986,dio: 0093-3813/86/1000-0579.
- A.A. Moniem, W.S. Hassanin, Solution of MHD Flow past a Vertical Porous Plate through a Porous Medium under Oscillatory Suction, 2013 (2013) 694–702.
- D. Bose, U. Basu, MHD Fluctuating Flow of Non-Newtonian Fluid through a Porous Medium Bounded by an Infinite Porous Plate, (2015) 1988–1995. http://www.scirp.org/journal/am , http://dx.doi.org/10.4236/am.2015.612176.
- M. Thamizhsudar, J. Pandurangan, Combined Effects of Radiation and Hall Current on MHD Flow Past an Exponentially Accelerated Vertical Plate in the Presence of, (2014) 7498–7509, 10.15680/ijircce.2014.0212041.
- H.A. Attia, M.E. Sayed-Ahmed, Hall Effect on unsteady MHD Couette flow and heat transfer of a Bingham fluid with suction and injection, Appl. Math. Model. 28 (2004) 1027–1045. doi:10.1016/j.apm.2004.03.008.
- S.K. Karode, Laminar flow in channels with porous walls, revisited, J. Memb. Sci. 191 (2001) 237–241. doi:10.1016/S0376-7388(01)00546-4.
- B.S. Rma, H. Konwar, MHD Flow, Heat and Mass Transfer about a Horizontal Cylinder in Porous Medium, Int. J. Innov. Res. Sci. Eng. Technol. 03 (2014) 16459–16469. doi:10.15680/IJIRSET.2014.0310008.
- E. Kim, Natural convection along a wavy vertical plate to non-Newtonian fluids, Int. J. Heat Mass Transf. 40 (1997) 3069–3078. doi:http://dx.doi.org/10.1016/S0017-9310 (96)00357-2.
- B.B. Singh, An integral treatment for heat and mass transfer along a vertical wall by natural convection in a porous media, compute. Methods Multiphase. Flow IV. 56 (2007) 143–151. doi: 10.2495/Mpf070141.
- A.M. Ismail, S. Ganesh, C.K. Kirubhashankar, Unsteady MHD flow between two parallel plates through porous medium with One Plate Moving Uniformly and the Other Plate at Rest with Uniform Suction, 3 (2014) 6–10.

- Blasius and Sakiadis Flow of Magneto Hydrodynamic Tangent Hyperbolic Fluid with Exponentially Decaying Heat Source or Sink

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1 Department of Mathematics, Sri Shakthi Institute of Engineering and Technology, Coimbatore-641 005, IN

2 Department of Mathematics, GITAM University, Bangalore-562123, IN

#### Authors

**Affiliations**

1 Department of Mathematics, Sri Shakthi Institute of Engineering and Technology, Coimbatore-641 005, IN

2 Department of Mathematics, GITAM University, Bangalore-562123, IN

#### Source

Research Journal of Science and Technology, Vol 9, No 3 (2017), Pagination: 484-488#### Abstract

In this article, we have studied the flow and heat transfer in magneto hydrodynamic Tangent hyperbolic fluid with exponentially heat source/sink. The partial differential equations governing the problem have been reduced by similarity transformations into the ordinary differential equations. Numerical solutions are transferred out by using Runge-Kutta Shooting technique. The effects of various governing parameters on the flow quantities are demonstrated graphically. The solution depends on various interesting parameters including the friction factor coefficient and local Nusselt numbers for the Sakiadis and Blasius flow cases. It is determined that the rate of heat transfer is extremely high in Blasius flow case when compared with Sakiadis flow case.#### Keywords

MHD, Blasisus and Sakiadis Flow, Tangent Fluid, Exponential Decaying Heat Source/Sink.#### References

- H. Blasius, Grenzschichten in Flüssigkeiten mit kleiner Reibung, Z. Math. Phys. 1908; 56: 1–37.
- B.C. Sakiadis, Boundary-layer behaviour on continuous solid surfaces: I. Boundary-layer equations for two-dimensional and axisymmetric flow, AIChE J.1961; 7: 26–28.
- F.K. Tsou, E.M. Sparrow, R.J. Goldstein, Flow and heat transfer in the boundary layer on a continuous moving surface, Int. J. Heat Mass Transfer. 1967; 10: 1 281–288.
- C.H. Chen, Forced convection over a continuous sheet with suction or injection moving in a flowing fluid, Acta Mech. 1999; 138: 1–11.
- E.M. Sparrow, R. Eichhorn, J.L. Grigg, Combined forced and free convection in a boundary layer, Phys. Fluids 1959; 2: 319– 320.
- L.E. Erickson, L.T. Fan, V.G. Fox, Heat and mass transfer on a moving continuous flat plate with suction or injection , Ind. Eng. Chem. vol. 1966; 5: 19-25.
- S. Sandeep and C. Sulochana, Dual solutions of radiative MHD nanofluid flow over an exponentially stretching sheet with heat generation/absorption, Applied Nanoscience. 2016; 1: 131-139.
- M.Qasim and S.Noreen, Falkner-Skan flow of a Maxwell fluid with heat transfer and magnetic field, International journal of Engineering Mathematics, 2013; 7: 13-20.
- S. A. Gaffar, V. Ramachandra Prasad and E. Keshava Reddy, Computational study of non-Newtonian Eyring-powell fluid from a horizontal circular cylinder with Biot number effects, Int. J. Math. Archv. 2015; 6: 114-132.
- W.A. Khan, R. Culham and O.D. Makinde, Hydromagnetic blasius flow of power‐ law nano-fluids over a convectively heated vertical plate, The Canadian Journal of Chemical Engineering, 2015; 93(10): 1830-1837.
- C.S.K. Raju, N.Sandeep, Heat and mass transfer in MHD non-Newtonian bioconvection flow over a rotating cone/plate with cross diffusion, Journal of Molecular Liquids, 2016; 215: 115-126.
- C.S.K. Raju, N.Sandeep, A comparative study on heat and mass transfer of the Blasius and Falkner-Skan flow of a bio-convective Casson fluid past a wedge, European Physical Journal Plus, 2011; 131: 405-411.
- K. Gangadhar, Radiation, Heat Generation and Viscous Dissipation Effects on MHD Boundary Layer Flow for the Blasius and Sakiadis Flows with a Convective Surface Boundary Condition, Journal of Applied Fluid Mechanics, 2015; 5598(3): 562 -570.
- K. R. Sekhar, G. Viswanatha Reddy and S. V. K. Varma, Mixed convection coquette flow of a nano-fluid through a vertical channel, Elixir International Journal, 2016; 99: 43237-43241.
- C.S.K. Raju, K. R. Sekhar, S. M. Ibrahim, G. Lorenzini, G. Viswanatha Reddy and E. Lorenzini, Variable viscosity on unsteady dissipative Carreau fluid over a truncated cone filled with titanium alloy nano-particles, Continuum Mech.Thermodyn., 2017; DOI 10.1007/s00161-016-0552-8.

- Heat Source or Sink on MHD Tangent Hyperbolic Dusty Fluid in Suspension of Convective Conditions

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1 Department of BS&H (Mathematics), Sree Vidyanikethan Engineering College (Autonomous), A. Rangampet, Tirupati-517102, (A.P), IN

2 Dept. of Mathematics, SRM University, Kattankulathur (T.N), IN

3 SAS, VIT University, Vellore (T.N), IN

4 Dept. of Mathematics, S.V. University, Tirupati (A.P), IN

5 Dept. Of Mathematics, GITAM University, Bangalore (K.A), IN

#### Authors

P. Durga Prasad

^{1}, N. Sivakumar^{2}, B. Rushi Kumar^{3}, S. V. K. Varma^{4}, C. S. K. Raju^{5}**Affiliations**

1 Department of BS&H (Mathematics), Sree Vidyanikethan Engineering College (Autonomous), A. Rangampet, Tirupati-517102, (A.P), IN

2 Dept. of Mathematics, SRM University, Kattankulathur (T.N), IN

3 SAS, VIT University, Vellore (T.N), IN

4 Dept. of Mathematics, S.V. University, Tirupati (A.P), IN

5 Dept. Of Mathematics, GITAM University, Bangalore (K.A), IN

#### Source

Research Journal of Science and Technology, Vol 9, No 4 (2017), Pagination: 561-568#### Abstract

This paper comprehensively analyses the momentum, heat and mass transfer behavior of a heat source or sink on magnetohydrodynamic tangent hyperbolic dusty fluid in suspension of convective conditions. The governing partial differential equations of the flow, heat transfer are transformed into non-linear ordinary differential equations by using self-similarity transformations, which are further solved numerically using the Runge-Kutta and Newton’s method. The effects of various non-dimensional governing parameters on velocity and temperature distributions are discussed with the help of graphs. Furthermore, the effects of these parameters on local friction factor coefficient and heat transfer rate are also discussed and presented through tables.#### Keywords

Heat Source, Convective Conditions, Dusty Fluid, Hyperbolic Tangent Fluid.#### References

- Crane L. Flow past a stretching plate, Z. Angew. Math. Phy, 1970; 21:p.645-647.
- Cortell R. Flow and Heat transfer of fluid through a pours medium over a stretching sheet with internal heat generation/absorption suction/blowing, Fluid Dyn. Res. 2005; 37:p.231-245.
- IbrahimW. Makinde O. D. Magnetohydrodynamic stagnation point flow and heat transfer of Casson nanofluid past a stretching sheet with slip and convective boundary condition. Journal of Aerospace Engineering, 2016; 29: 04015037.
- Ibrahim W. Makinde O.D. Magnetohydrodynamic stagnation point flow of a power-law nanofluid towards a convectively heated stretching sheet with slip. Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering. 2016; 230: p. 345-354.
- Nadeem S. Akram S. Peristaltic transport of a hyperbolic tangent fluid model in an asymmetric channel, Z. Naturforsch. 2009; 64: p. 559–567.
- Nadeem S. Akram S. Effects of partial slip on the peristaltic transport of a hyperbolic tangent fluid model in an asymmetric channel, Int. J. Numer. Methods Fluids. 2010; 63:p. 374-394.
- Nadeem S. Rehman A. Lee C. LeeJ. Boundary layer flow of second grade fluid in a cylinder with heat transfer, Math. Prob. Eng. 2012; 212:doi.org/10.1155/2012/640289.
- Nadeem S. Rehman A. Vajravelu K. Lee J. Lee C. Axisymmetric stagnation flow of a micropolar nanofluid in a moving cylinder, Math. Prob. Eng. 2012: 2012: doi.org/10.1155/2012/378259.
- Gireesha BJ. Roopa GS. Lokesh HJ. Bajewadi CS. MHD flow and heat transfer of a dusty fluid over a stretching sheet. Int. J. Phys. Math. Sci. 2012; 3:p.171-82.
- Abu BakarNA. Zaimi K. HamidRA. MHD boundary layer flow of a Maxwell nanofluid over a permeable vertical surface. AIP Conf. Proc. 2014; p. 422-7.
- Nadeem S. Saleem S. Series solution of unsteady Eyring Powell nanofluid flow on a rotating cone. Ind. J. Pure Appl. Phys. 2014; 52:p. 725-37.
- Ramesh GK. Numerical study of the influence of heat source on stagnation point flow towards a stretching surface of a Jeffery nanoliquid. J. Eng. 2015; 2015: 382061.
- Gorla RSR. Gireesha BJ. Singh B. MHD flow and heat transfer of dusty nanofluid embedded in porous medium over an exponentially stretching sheet. J. Nanofluids.2015; 4:p. 1-12.
- Ramana Reddy J. V. Sugunamma V. Sandeep N. Raju C.S.K. Chemically Reacting MHD Dusty Nanofluid Flow over a Vertical Cone with Non-Uniform Heat Source/Sink, Engineering and Physical Sciences, Walailak J Sci & Tech. 2017; 14(2): p.141-156.
- Gireesha B.J. Ramesh G.K. Bagewadi C.S. Heat transfer in MHD flow of a dusty fluid over a stretching sheet with viscous dissipation, Advances in Applied Science Research, 2012: 3 (4):p.2392-2401.
- Sandeep N. Sulochana C. MHD flow of dusty nanofluid over a stretching surface with volume fraction of dust particles. Ain Shams Eng. J. 2016; 7:p.709-16.
- Prasannakumaraa BC. Gireeshac BJ. Manjunatha PT. Melting phenomenon in MHD stagnation point flow of dusty fluid over a stretching sheet in the presence of thermal radiation and non-uniform heat source/sink, International Journal for Computational Methods in Engineering Science and Mechanics. DOI: 10.1080/15502287.2015.1047056
- Naseer M. Malik MY. Rehman A. Numerical study of convective heat transfer on the power law fluid over a vertical exponentially stretching cylinder, Applied and Computational Mathematics. 2015; 4(5): 346-350, doi: 10.11648/j.acm.20150405.13.
- NaseerM. Yousaf Malik M. Nadeem, S. Rehman A. The boundary layer flow of hyperbolic tangent fluid over a vertical exponentially stretching cylinder, Alexandria Engineering Journal. 2014; 53:p.747-750.
- Mamatha S. Upadhay, Mahesha, Raju C.S.K. Cattaneo-Christov on heat and mass transfer of unsteady Eyring Powell dusty nanofluid over sheet with heat and mass flux conditions. Informatics in Medicine unlocked.2017; 9:76-85.

- Convective Conditions on Magnetohydrodynamic Flow Over Stretched Cylinder with Time and Space Dependent Heat Source or Sink

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1 Higher College of Technology, Muscat -105, OM

2 Department of Mathematics, S.P.M.V.V, Tirupati, A.P., IN

3 Department of Mathematics, GITAM University, Bangalore Campus, K.A., IN

4 Dept. of Mechanical Engineering, NIT Warangal, Warangal (Telangana), IN

#### Authors

B. Madhusudhana Rao

^{1}, V. Nagendramma^{2}, C. S. K. Raju^{3}, A. Leelaratnam^{2}, P. Prakash^{4}**Affiliations**

1 Higher College of Technology, Muscat -105, OM

2 Department of Mathematics, S.P.M.V.V, Tirupati, A.P., IN

3 Department of Mathematics, GITAM University, Bangalore Campus, K.A., IN

4 Dept. of Mechanical Engineering, NIT Warangal, Warangal (Telangana), IN

#### Source

Research Journal of Science and Technology, Vol 9, No 4 (2017), Pagination: 569-575#### Abstract

The present study emphases steady boundary layer flow and heat transfer of a hyperbolic tangent fluid flowing over a vertical exponentially stretching cylinder in its axial directionwith non-uniform heat source/sink. Proposed mathematical model has a tendency to characterize the effect of the non-uniform heat source/sink. The non-linear ordinary differential equations are solved using the Runge-Kutta Feldberg (RKF) integration method. The characteristics of velocity and temperature boundary layers in the presence of Weissennberg number We are presented for different physical parameters such as heat source/ sink parameter, Reynolds number Re, the Prandtl number Pr , the Weissennberg number We and the natural convection parameter λ , magnetic field parameter and porosity parameter K . Moreover, the friction factor coefficients, Nusselt number are also estimated and discussed for aforesaid physical parameters. In addition, the rate of heat transfer rate is higher in case of We = 0.5 compared toWe = 0 with n = 0.2 .#### Keywords

Weissennberg Number, Stretching Cylinder, Non-Uniform Heat Source/Sink, Non-Newtonian Fluid.#### References

- Ahmad K. Hanouf Z. Ishak A. Mixed convection Jeffrey fluid flow over an exponentially stretching sheet with magnetohydrodynamic effect. AIP Advances. 2016;6: 035024.
- Ramzan M. Farooq M. Alhothuali S. Malaikah HM. Cui W. Hayat T. Three dimensional flow of an Oldroyd-B fluid with Newtonian heating. International Journal of Numerical Methods for Heat and Fluid Flow. 2015; 25(1): p.68-85.
- Crane L. Flow past a stretching plate. Angew Z. Math. Phy.1970; 21: p. 645-647.
- Cortell R. Flow and Heat transfer of fluid through a pours medium over a stretching sheet with internal heat generation /absorption suction blowing. Fluid Dyn. Res. 2005:37:p.231-245.
- Makinde OD. Animasaun IL. Bioconvection in MHD nanofluid flow with nonlinear thermal radiation and quartic autocatalysis chemical reaction past an upper surface of a paraboloid of revolution. International Journal of Thermal Sciences.2016; 109:p. 159-171.
- Das S. Ali A. Jana RN. Makinde OD. Magnetohydrodynamic boundary layer slip flow of radiating and chemically reactive nanofluid over a stretching sheet with Newtonian heating. Journal of Nanofluids. 2016; 5(4):p. 606-616.
- Ibrahim W. Makinde OD. Magnetohydrodynamic stagnation point flow and heat transfer of Casson nanofluid past a stretching sheet with slip and convective boundary condition. Journal of Aerospace Engineering.2016; 29(2):04015037.
- Ibrahim W. Makinde OD. Magnetohydrodynamic stagnation point flow of a power-law nanofluid towards a convectively heated stretching sheet with slip. Proceedings of the Institution of Mechanical Engineers. Part E: Journal of Process Mechanical Engineering, 2016; 230(5):p. 345-354.
- Eegunjobi AS. Makinde OD.Second law analysis for MHD permeable channel flow with variable electrical conductivity and asymmetric Navier slips. Open Physics. 2015; 13:p.100-110.
- Wang TY. Mixed convection heat transfer from a vertical plate to non-Newtonian fluids, Int. J. Heat Fluid Flow. 1995; 16: p.56-61.
- Xu H. Liao SJ. Pop I. Series solution of unsteady boundary layer flows of non-Newtonian fluids near a forward stagnation point, J. NonNewtonian Fluid Mech. 2006;139:p.31-43.
- Friedman AJ. Dyke SJ. Phillips BM. Over-driven control for large-scale MR dampers, Smart Mater. Struct. 2013; 22:045001.
- Nadeem S. Akram S. Peristaltic transport of a hyperbolic tangent fluid model in an asymmetric channel, Z. Naturforsch.2009; 64a: p.559567.
- Nadeem S. Akram S. Effects of partial slip on the peristaltic transport of a hyperbolic tangent fluid model in an asymmetric channel. Int. J. Numer. Methods Fluids.2010; 63:p. 374-394.
- Nadeem S. Rehman A. Lee C. Lee J. Boundary layer flow ofsecond grade fluid in a cylinder with heat transfer, Math. Prob.Eng.2012; 212:dx.doi.org/10.1155/2012/640289.
- Gorla RSR. Axisymmetric thermal boundary layer of amicropolar fluid on a cylinder, Int. J. Eng. Sci. 1985; 23: p.401-407.
- Gorla RGR. Ameri A. Boundary layer flow of a micropolarfluid on a continuous moving cylinder. Acta Mech. 1985; 57:p.203-214.
- Rehman A. Nadeem S. Malik MY. Stagnation flow of couplestress nanofluid over an exponentially stretching sheet through a porous medium. J. Power Technol. 2013; 93 (2): p.122-132.
- Nadeem S. Rehman A. Vajravelu K. Lee J. Lee C. Axisymmetric stagnation flow of a micropolar nanofluid in amoving cylinder, Math. Prob. Eng.2012;18: dx.doi.org/10.1155/2012/378259.
- Ishak A.Nazar R. Pop I. Uniform suction/blowing effect onflow and heat transfer due to a stretching cylinder, Appl. Math.Mod. 2008; 32:p.2059-2066.
- Wang CY. Natural convection on a vertical stretching cylinder. Commun. Nonlinear Sci. Numer. Simulat. 2012; 17: p. 1098-1103.
- Naseer M. Yousaf Malik M. Nadeem S.Rehman A. The boundary layer flow of hyperbolic tangent fluid over a vertical exponentially stretching cylinder. Alexandria Engineering Journal. 2014;53: p.747-750.

- The Flow of Hyperbolic Tangent Fluid Over Exponentially Stretching Cylinder with Heat Source or Sink

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1 Department of BS and H (Mathematics), Sree Vidyanikethan Engineering College (Autonomous), A. Rangampet, Tirupati-517102, (A.P), IN

2 Dept. of Mathematics, GITAM University, Bangalore Campus, Bangalore, Karnataka (St.), IN

3 Sri Padmavathi Mahila Degree and PG College, Tirupati, (A.P), IN

4 Dept. of H. and S., Annamacharya Institute of Science and Technology (Autonomous), Rajampet-516126, Y.S.R. Kadapa (Dt), A.P.(St.), IN

#### Authors

**Affiliations**

1 Department of BS and H (Mathematics), Sree Vidyanikethan Engineering College (Autonomous), A. Rangampet, Tirupati-517102, (A.P), IN

2 Dept. of Mathematics, GITAM University, Bangalore Campus, Bangalore, Karnataka (St.), IN

3 Sri Padmavathi Mahila Degree and PG College, Tirupati, (A.P), IN

4 Dept. of H. and S., Annamacharya Institute of Science and Technology (Autonomous), Rajampet-516126, Y.S.R. Kadapa (Dt), A.P.(St.), IN

#### Source

Research Journal of Science and Technology, Vol 9, No 4 (2017), Pagination: 576-582#### Abstract

The present problem is the steady boundary layer flow and heat transfer of a hyperbolic tangent fluid flowing over a vertical exponentially stretching cylinder in its axial direction with heat source or sink. After applying usual boundary layer with a suitable similarity transformation to the given partial differential equations and the boundary conditions, a system of coupled nonlinear ordinary differential equations is obtained. This system of ordinary differential equations subject to the boundary conditions is solved with the help of Runge-Kutta method along shooting technique. The effects of the involved parameters such as Reynolds number, Prandtl number, Weissennberg number, power law index parameter and the natural convention parameter are presented through the graphs. The associated physical properties on the flow and heat transfer characteristics that are the skin friction coefficient and Nusselt number are presented for various parameters.#### Keywords

Hyperbolic, Cylinder, Heat Source or Sink, Reynolds Number, Weissennberg Number.#### References

- CraneL. Flow past a stretching plate, Z. Angew. Math .Phy, 1970; 21:p.645-647.
- CortellR. Flow and Heat transfer of fluid through a pours medium over a stretching sheet with internal heat generation/absorption suction/blowing, Fluid Dyn. Res. 2005; 37:p.231-245.
- Ahmad K. HanoufZ. IshakA. Mixed convection Jeffrey fluid flow over an exponentially stretching sheet with magnetohydrodynamic effect, AIP Advances. 2016; 6: 035024.
- IbrahimW. MakindeO. D. Magnetohydrodynamic stagnation point flow and heat transfer of Casson nanofluid past a stretching sheet with slip and convective boundary condition. Journal of Aerospace Engineering, 2016; 29(2): 04015037.
- EegunjobiAS. MakindeO.D. Second law analysis for MHD permeable channel flow with variable electrical conductivity and asymmetric Navier slips. Open Physics. 2015; 13: p.100-110.
- KhanI. M. MalikY. SalahuddinT. Khan.M. Khalil Ur Rehman, Homogenous-heterogeneous reactions in MHD flow of Powell-Eyring fluid over a stretching sheet with Newtonian heating. Neural Comput and Applic. DOI 10.1007/s00521-017-2943-6.
- WangTY. Mixed convection heat transfer from a vertical plate to non-Newtonian fluids, Int. J. Heat Fluid Flow. 1995; 16: p.56-61.
- WangCY. Natural convection on a vertical stretching cylinder.Commun. Nonlinear Sci. Numer. Simulat. 2012; 17:p.1098-1103.
- NadeemS. AkramS. Peristaltic transport of a hyperbolic tangent fluid model in an asymmetric channel, Z. Naturforsch. 2009; 64a: p.559–567.
- NadeemS. AkramS. Effects of partial slip on the peristaltic transport of a hyperbolic tangent fluid model in an asymmetric channel, Int. J. Numer. Methods Fluids.2010; 63: p.374–394.
- NadeemS.RehmanA. LeeC. LeeJ. Boundary layer flow of second grade fluid in a cylinder with heat transfer, Math. Prob. Eng. 2012; 212:dx.doi.org/10.1155/2012/640289.
- SalahuddinT. MalikM.Y, Hussain A. Muhammad Awais. KhanI. KhanM. Analysis of tangent hyperbolic nanofluid impinging on a stretching cylinder near the stagnation point, Results in Physics.2017; 7: p.426–434.
- Pavithra GM. Gireesha BJ. Effect of internal heat generation/absorption on dusty fluid flow over an exponentially stretching sheet with viscous dissipation. J Math. 2013:dx.doi.org/10.1155/2013/583615.
- GorlaRSR. Axisymmetric thermal boundary layer of a micropolar fluid on a cylinder, Int. J. Eng. Sci. 1985; 23:p.401-407.
- Gorla RGR. AmeriA. Boundary layer flow of a micropolar fluid on a continuous moving cylinder, Acta Mech. 1985; 57:p.203-214.
- IshakA.NazarR. PopI. Uniform suction/blowing effect on flow and heat transfer due to a stretching cylinder, Appl. Math. Mod. 2008; 32: p.2059-2066.
- Naseer M. MalikY. NadeemS. RehmanA. The boundary layer flow of hyperbolic tangent fluid over a vertical exponentially stretching cylinder, Alexandria Engineering Journal.2014; 53:p.747-750.

- The Flow of Magnetohydrodynamic Flow Over Cylinder with Heat Source or Sink

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1 Department of BS&H (Mathematics), Sree Vidyanikethan Engineering College (Autonomous), A. Rangampet, Tirupati-517102, (A.P), IN

2 Dept. of Mathematics, S.V. University, Tirupati (A.P), IN

3 Dept. Of Mathematics, GITAM University, Bangalore (K.A), IN

4 Dept. of Mechanical Engineering, NIT Warangal, Warangal (Telangana), IN

#### Authors

**Affiliations**

1 Department of BS&H (Mathematics), Sree Vidyanikethan Engineering College (Autonomous), A. Rangampet, Tirupati-517102, (A.P), IN

2 Dept. of Mathematics, S.V. University, Tirupati (A.P), IN

3 Dept. Of Mathematics, GITAM University, Bangalore (K.A), IN

4 Dept. of Mechanical Engineering, NIT Warangal, Warangal (Telangana), IN

#### Source

Research Journal of Science and Technology, Vol 9, No 4 (2017), Pagination: 583-588#### Abstract

A theoretical analysis performed for investigating steady boundary layer flow of magnetohydrodynamic flow over cylinder with heat source/sink. Proposed mathematical model has a tendency to characterize the effect of magnetohydrodynamic flow over cylinder heat source/sink. The non-linear ordinary differential equations are solved using the Runge-Kutta method. The characteristics of velocity and temperature boundary layers for different physical parameters such as heat source parameter*Q*

_{H}, Reynolds number Re, the Prandtl number Pr , the magnetic field parameter

*M*and power law index parameter

*n*. Moreover, the local friction factor coefficients, Nusselt number are also estimated and discussed for aforesaid physical parameters. It is observed that heat transfer rate increases with in power law index parameter and magnetic field parameter while decrease in power law index parameter and Reynolds number.

#### Keywords

Stretching Cylinder, Magnetohydrodynamic, Prandtl Number, Power Law Index Parameter.#### References

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- Convective Condition and Exponentially Decaying Heat Source on Mhd Carreau Dusty Fluid Over a Stretching Sheet Filled With Darcy Porous.

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1 Dept. of Mathematics, GITAM University, Bangalore-562163(Karnataka), IN

2 Dept. of Mathematics UBDT College of Engineering, Davangere 577004 (Karnataka), IN

3 Dept. of Mathematics, GITAM University, Bangalore-577004 (Karnataka), IN

#### Authors

**Affiliations**

1 Dept. of Mathematics, GITAM University, Bangalore-562163(Karnataka), IN

2 Dept. of Mathematics UBDT College of Engineering, Davangere 577004 (Karnataka), IN

3 Dept. of Mathematics, GITAM University, Bangalore-577004 (Karnataka), IN

#### Source

Research Journal of Science and Technology, Vol 9, No 4 (2017), Pagination: 505-510#### Abstract

This study presents the effect of magnetic field on the flow and heat transfer of an incompressible Carreau fluid over stretching sheet with uniform suspended dust particle. The relevant governing equations are first simplified under usual boundary layer assumptions and then transformed into ordinary differential equations (ODEs) by similarity transformations. The transformed ordinary nonlinear differential equations are solved numerically by R-K with Shooting Technique. The effects of certain parameters on the dimensionless velocity, temperature profile are presented graphically and also calculated the thermo physical properties of the flow friction factor, Local Nusselt and Sherwood number. The important outcome of this study is magnetic parameter enhances the temperature profile of fluid phase but decreases the velocity of both fluid and dust phase.#### Keywords

Exponentially Decaying Heat Source, Darcy Porous Layers, Convective Conditions, Dusty Fluid, Carreau Fluid, Stretching Sheet.#### References

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