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Mixed Convection Fluid Flow Over a Vertical Cone Saturated Porous Media with Double Dispersion and Injection/Suction Effects

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Abstract

This study reflects the combined impact of double dispersion and injection/suction on mixed convection flow over a vertical cone in an incompressible viscous fluid-saturated porous medium. The governing equations of the model are non-dimensionalized throughout the appropriate transformations and received non-similarity equations are solved numerically via bivariate Chebyshev spectral collocation quasi-linearization method. Computations are reported here graphically to analyze the impact of governing parameters at the different stream-wise locations on the velocity, temperatures, and concentration profiles, like Prandtl number, Schmidt number, buoyancy parameter, injection and suction parameter, thermal dispersion, and Solutal dispersion parameters. Skin friction, heat, and mass transfer rates are also reported in graphical and tabular form. To establish the efficiency of the adopted numerical technique, we have made a comparison with the earlier published results and found them to be of great consent. The residual analysis study also illustrated, which proves the convergence of the present results.

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References

  1. Jackson, J.D., Cotton, M.A., Axcell, B.P.: Studies of mixed convection in vertical tubes. Int. J. Heat Fluid Flow 10, 02–15 (1989)

    Google Scholar 

  2. Oztop, H.F., Dagtekin, I.: Mixed convection in two-sided lid-driven differentially heated square cavity. Int. J. Heat Mass Transf. 47, 1761–1769 (2004)

    MATH  Google Scholar 

  3. Chiu, K.C., Rosenberger, F.: Mixed convection between horizontal plates entrance effects. Int. J. Heat Mass Transf. 30, 1645–1654 (1987)

    Google Scholar 

  4. Chen, C.H.: Laminar mixed convection adjacent to vertical, continuously stretching sheets. Heat Mass Transf. 33, 471–476 (1998)

    Google Scholar 

  5. Merkin, J.H.: Mixed convection from a horizontal circular cylinder. Int. J. Heat Mass Transf. 20, 73–77 (1977)

    Google Scholar 

  6. Ramachandran, N., Chen, T.S., Armaly, B.F.: Mixed convection in stagnation flows adjacent to vertical surfaces. J. Heat Transf. 110(2), 373–377 (1988)

    Google Scholar 

  7. Awbi, H.B., Hatton, A.: Mixed convection from heated room surfaces. Energy Build. 32, 153–166 (2000)

    Google Scholar 

  8. Himasekhar, K., Sarma, P.K., Janardhan, K.: Laminar mixed convection from a vertical rotating cone. Int. Commun. Heat Mass Transf. 16, 99–106 (1989)

    Google Scholar 

  9. Wang, C.Y.: Boundary layer on a rotating cone, disc, axisymmetric surfaces with concentrated heat sources. Acta Mech. 81, 245–251 (1990)

    Google Scholar 

  10. Anilkumar, D., Roy, S.: Unsteady mixed convection flow on a rotating cone in a rotating fluid. Appl. Math. Comput. 155, 545–561 (2004)

    MathSciNet  MATH  Google Scholar 

  11. Yih, K.A.: Mixed convection about a cone in a porous medium: the entire region. Int. Commun. Heat Mass Transf. 26, 1041–1050 (1999)

    Google Scholar 

  12. Kumari, M., Pop, I., Nath, G.: Mixed convection along a vertical cone. Int. Commun. Heat Mass Transf. 16, 247–255 (1989)

    Google Scholar 

  13. Ravindran, R., Roy, S., Momoniat, E.: Effects of injection (suction) on a steady mixed convection boundary layer flow over a vertical cone. Int. J. Numer. Methods Heat Fluid Flow 19, 432–444 (2009)

    Google Scholar 

  14. Patil, P.M., Pop, I.: Effects of surface mass transfer on unsteady mixed convection flow over a vertical cone with chemical reaction. Heat Mass Transf. 47, 1453–1464 (2011)

    Google Scholar 

  15. Moallemi, M.K., Jang, K.S.: Prandtl number effects on laminar mixed convection heat transfer in a lid-driven cavity. Int. J. Heat Mass Transf. 35, 1881–1892 (1992)

    MATH  Google Scholar 

  16. Makinde, O.D.: MHD mixed convection from a vertical plate embedded in a porous medium with a convective boundary condition. Int. J. Therm. Sci. 49, 1813–1820 (2010)

    Google Scholar 

  17. Mamun Molla, M., Hossain, M.: Anwar: Radiation effect on mixed convection laminar flow along a vertical wavy surface. Int. J. Therm. Sci. 46, 926–935 (2007)

    Google Scholar 

  18. Hossain, M.A., Munir, M.S., Pop, I.: Natural convection flow of a viscous fluid with viscosity inversely proportional to linear function of temperature from a vertical wavy cone. Int. J. Therm. Sci. 40, 366–377 (2001)

    Google Scholar 

  19. Srinivasacharya, D., Pranitha, J., RamReddy, Ch.: Magnetic and double dispersion effects on free convection in a non-Darcy porous medium saturated with power-law fluid. Int. J. Comput. Methods Eng. Sci. Mech. 13, 210–218 (2012)

    MathSciNet  Google Scholar 

  20. Pranitha, J., Suman, G.V., Srinivasacharya, D.: Effects of double dispersion on mixed convection in a power-law fluid saturated porous medium with variable properties using Lie scaling group transformations. Proc. Eng. 127, 362–369 (2015)

    Google Scholar 

  21. Pranitha, J., Suman, G.V., Srinivasacharya, D.: Influence of variable properties and double dispersion on mixed convection in a power-law fluid-saturated non-Darcy porous medium. Spec. Top. Rev. Porous Media Int. J. 8(3), 177–195 (2017)

    Google Scholar 

  22. Murthy, P.V.S.N., Mukherjee, S., Srinivasacharya, D., Krishna, P.: Combined radiation and mixed convection from a vertical wall with suction/injection in a non-Darcy porous medium. Acta Mech. 168(3–4), 145–156 (2004)

    MATH  Google Scholar 

  23. Murthy, J.V.R., Bahali, N.K., Srinivasacharya, D.: Unsteady flow of micropolar fluid through a circular pipe under a transverse magnetic field with suction/injection. Seluk J. Appl. Math. 11(2), 13–25 (2010)

    MathSciNet  MATH  Google Scholar 

  24. Ishak, A., Nazar, R., Arifin, N.M., Pop, I.: Dual solutions in mixed convection flow near a stagnation point on a vertical porous plate. Int. J. Therm. Sci. 47, 417–422 (2008)

    Google Scholar 

  25. Ismael, M.A., Pop, I., Chamkha, A.J.: Mixed convection in a lid-driven square cavity with partial slip. Int. J. Therm. Sci. 82, 47–61 (2014)

    Google Scholar 

  26. Meena, O.P., Janapatla, P., Chamkha, A.J.: Influence of the Soret and Dufour on mixed convection flow over a vertical cone with injection/suction effects. J. Porous Med. 24, 73–88 (2021)

    Google Scholar 

  27. Meena, O.P.: Mixed convection flow over a vertical cone with double dispersion and chemical reaction effects. Heat Transf. Res. (2020). https://doi.org/10.1002/htj.22086

    Article  Google Scholar 

  28. Chamkha, A.J., Al-Mudhaf, A.: Unsteady heat and mass transfer from a rotating vertical cone with a magnetic field and heat generation or absorption effects. Int. J. Therm. Sci. 44, 267–276 (2005)

    Google Scholar 

  29. Takhar, H.S., Chamkha, A.J., Nath, G.: Flow and heat transfer on a stretching surface in a rotating fluid with a magnetic field. Int. J. Therm. Sci. 42, 23–31 (2003)

    Google Scholar 

  30. Meena, O.P.: Mixed convection nanofluid flow over a vertical wedge saturated in porous medium with influence of thermal dispersion using Lie group scaling. Comput. Therm. Sci. Int. J. 12, 91–105 (2020)

    Google Scholar 

  31. Meena, O.P.: Mixed convection nanofluid flow over a vertical wedge saturated in porous medium with influence of double dispersion using Lie group scaling. Spec. Top. Rev. Porous Med. Int. J. 11(3), 297–311 (2020)

    Google Scholar 

  32. Meena, O.P., Pranitha, J.: Power-law nanofluid on mixed convection with influence of double dispersion saturated non-Darcy porous media. AIP Conf. Proc. 2246, 020019 (2020)

    Google Scholar 

  33. Pranitha, J., Meena, O.P.: Influence of double dispersion on natural convection flow over a vertical cone saturated porous media with Soret and Dufour effects. Int. J. Eng. Sci. (IJES) 02, 09–15 (2020)

    Google Scholar 

  34. Ishak, A., Nazar, R.: Mixed convection boundary layers in the stagnation-point flow toward a stretching vertical sheet. Meccanica 41, 509–518 (2006)

    MATH  Google Scholar 

  35. Chew, G.F.: Double Dispersion Relations and Unitarity as the Basis for a Dynamical Theory of Strong Interactions. Lawrence Berkeley National Laboratory, Berkeley (1960)

    MATH  Google Scholar 

  36. Rajagopal, A.K., Cohen, M.H.: Double dispersion relations in quantum statistical mechanics-II. Proc. Indian Acad. Sci. 71, 149–166 (1970)

    Google Scholar 

  37. Fried, J.J., Combarnous, M.: Dispersion in porous media. Adv. Hydrosc. 1, 169–282 (1976)

    Google Scholar 

  38. Georgiadis, J.G., Catton, I.: Dispersion in cellular convection in porous layers. Int. J. Heat Mass Transf. 31, 1081–1091 (1988)

    MATH  Google Scholar 

  39. Murthy, P.V.S.N.: Effect of double dispersion on mixed convection heat and mass transfer in non-Darcy porous medium. J. Heat Transf. 122(3), 476–484 (2000)

    Google Scholar 

  40. El-Amin, M.F.: Double dispersion effects on natural convection heat and mass transfer in non-Darcy porous medium. Appl. Math. Comput. 156, 1–17 (2004)

    MathSciNet  MATH  Google Scholar 

  41. Kairi, R.R., Narayana, P.A.L., Murthy, P.V.S.N.: The effect of double dispersion on natural convection heat and mass transfer in a non-Newtonian fluid saturated non-Darcy porous medium. Transp. Porous Med. 76, 377–390 (2009)

    MathSciNet  Google Scholar 

  42. Kairi, R.R., Murthy, P.V.S.N.: Effect of double dispersion on mixed convection heat and mass transfer in a non-Newtonian fluid-saturated non-Darcy porous medium. J. Porous Med. 13(8), 749–757 (2010)

    Google Scholar 

  43. Mohamad, A.A., Bennacer, R., El-Ganaoui, M.: Double dispersion, natural convection in an open-end cavity simulation via Lattice Boltzmann Method. Int. J. Therm. Sci. 49, 1944–1953 (2010)

    Google Scholar 

  44. Afify, A.A., Elgazery, N.S.: Effect of double dispersion on non-Darcy mixed convective flow over vertical surface embedded in porous medium. Appl. Math. Mech. 34, 1247–1262 (2013)

    MathSciNet  Google Scholar 

  45. Awad, F.G., Sibanda, P., Murthy, P.V.S.N.: A note on double dispersion effects in a nanofluid flow in a non-Darcy porous medium. J. Heat Transf. 137(10), 104501 (2015)

    Google Scholar 

  46. El-Hakiem, M.A., Abdullah, A.A.: Effect of radiation and double dispersion on mixed convection heat and mass transfer in non-Darcy porous medium. J. Eng. Appl. Sci. 3(1), 1 (2016)

    Google Scholar 

  47. Srinivasacharya, D., RamReddy, C., Naveen, P.: Effects of nonlinear Boussinesq approximation and double dispersion on a micropolar fluid flow under convective thermal condition. Heat Trans Asian Res. 1–21 (2018)

  48. Motsa, S.S., Magagula, V.M., Sibanda, P.: A bivariate Chebyshev spectral collocation quasilinearization method for nonlinear evolution parabolic equations. Sci. World J. (2014). https://doi.org/10.1155/2014/581987

    Article  Google Scholar 

  49. Pop, I., Ingham, D.B.: Convective Heat Transfer: Mathematical and Computational Modelling of Viscous Fluids and Porous Media. Pergamon, Oxford (2001)

    Google Scholar 

  50. Bejan, A.: Convection Heat Transfer. Wiley, New York (2004)

    MATH  Google Scholar 

  51. Canuto, C., Hussaini, M.Y., Quarteroni, A., Zang, T.A.: Spectral Methods in Fluid Dynamics. Springer, Berlin (1988)

    MATH  Google Scholar 

  52. Magagula, V.M., Motsa, S.S., Sibanda, P.: A new bivariate spectral collocation method with quadratic convergence for systems of nonlinear coupled differential equations. Appl. Comput. Math. 18(2), 113–122 (2019)

    MathSciNet  MATH  Google Scholar 

  53. Bellman, R., Kalaba, R.: Quasilinearisation and Non-linear Boundary-Value Problems. Elsevier, New York (1965)

    Google Scholar 

  54. Magagula, V.M., Motsa, S.S.: Precious Sibanda, On the Bivariate Spectral Quasilinearization Method for Nonlinear Boundary Layer Partial Differential Equations. Applications of Heat, Mass and Fluid Boundary Layers, pp. 177–190. Woodhead Publishing, Sawston (2020)

    Google Scholar 

  55. Meena, O.P.: Spectral quasi-linearization method for a porous channel problem with micropolar flow. J. Compos. Theory 12, 40–45 (2019)

    Google Scholar 

  56. He, J.-H.: Variational iteration method: a kind of non-linear analytical technique—some examples. Int. J. Non-Linear Mech. 34(4), 699–708 (1999)

    MATH  Google Scholar 

  57. He, J.-H.: Homotopy perturbation method: a new nonlinear analytical technique. Appl. Math. Comput. 135(1), 73–79 (2003)

    MathSciNet  MATH  Google Scholar 

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Funding

Mr. Om Prakash Meena is thankful to CSIR-UGC for the financial assistance as a Junior Research Fellow (F. No. 16-6 (DEC. 2018)/2019 (NET/CSIR), UGC-Ref. No.: 1111/ (CSIR-UGC NET DEC. 2018)).

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  1. Department of Mathematics, National Institute of Technology Warangal, Warangal, 506004, India

    Om Prakash Meena, Pranitha Janapatla & D. Srinivasacharya

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  1. Om Prakash Meena
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  3. D. Srinivasacharya
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Contributions

All the authors have worked jointly without any conflict of interest and formulated the model jointly. OPM and PJ worked on the numerical simulations of the model which was cross verified by DP. OPM and Dr. Pranitha have written the manuscript, and it took a well shaped after DP suggestions. Finally, all the author’s have read it and approved.

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Correspondence to Om Prakash Meena.

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Meena, O.P., Janapatla, P. & Srinivasacharya, D. Mixed Convection Fluid Flow Over a Vertical Cone Saturated Porous Media with Double Dispersion and Injection/Suction Effects. Int. J. Appl. Comput. Math 7, 59 (2021). https://doi.org/10.1007/s40819-021-00990-y

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