Research Article
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Year 2019, Volume 48, Issue 2, 372 - 383, 01.04.2019
https://doi.org/10.15672/hujms.545240

Abstract

References

  • R. Cai and C. Gou, Algebraically explicit analytical solutions for unsteady non- Newtonian swirling flow in an annular pipe, Sci. China Ser. G, 49 (4), 396-400, 2006.
  • R.P. Chhabra and J.F. Richardson, Non-Newtonian Flow: Fundamentals and Engineering Applications, Elsevier, 1999.
  • C. Fetecau and C. Fetecau, Unsteady flows of Oldroyd-B fluids in a channel of rectangular cross-section, Int. J. Nonlinear Mech. 40, 1214-1219, 2005.
  • C. Fetecau, M. Imran, C. Fetecau and I. Burdujan, Helical flow of an Oldroyd-B fluid due to a circular cylinder subject to time-dependent shear stresses, Z. Angew. Math. Phys. 61, 959-969, 2010.
  • C. Fetecau, A. Mahmood, C. Fetecau and D. Vieru, Some exact solutions for the helical flow of a generalized Oldroyd-B fluid in a circular cylinder, Comput. Math. Appl. 56 (12), 3096-3108, 2008.
  • A.K. Ghosh and P. Sana, On hydromagnetic rotating flow of an Oldroyd-B fluid near an oscillating plate, Z. Angew. Math. Phys. 60, 1135-1155, 2009.
  • T. Hayat, A.M. Siddiqui and S. Asghar, Some simple flows of an Oldroyd-B fluid, Int. J. Eng. Sci. 39, 135-147, 2001.
  • M. Jamil and C. Fetecau, Some exact solutions for rotating flows of a generalized Burgers fluid in cylindrical domains, J. Nonnewton. Fluid Mech. 165 (23), 1700-1712, 2010.
  • M. Jamil, N.A. Khan and A.A. Zafar, Translational flows of an Oldroyd-B fluid with fractional derivatives, Comput. Math. Appl. 62 (3), 1540-1553, 2011.
  • M. Kamran, M. Imran and M. Athar, Exact solutions for the unsteady rotational flow of an Oldroyd-B fluid with fractional derivatives induced by a circular cylinder, Meccanica 48 (5), 1215-1226, 2013.
  • M. Kamran, M. Imran, M. Athar and M.A. Imran, On the unsteady rotational flow of fractional Oldroyd-B fluid in cylindrical domains, Meccanica 47 (3), 573-584, 2012.
  • S.M. Kang, W. Nazeer, M. Athar, M.D. Hisham and Y.C. Kwun, Velocity and shear stress for an Oldroyd-B fluid within two cylinders, Bound. Value Probl. 40, doi: 10.1186/s13661-016-0541-7, 2016.
  • C.F. Lorenzo and T.T. Hartley, Generalized Functios for the Fractional Calculus, NASA/TP-1999-20942/REV 1, 1999.
  • A. Mahmood, S. Ullah and G. Bolat, Some exact solutions for the rotational flow of a generalized second-grade fluid between two circular cylinders, Arch. Mech. 60 (5), 385-401, 2008.
  • A. Mahmood, S. Ullah and Q. Rubab, Exact solutions for a rotational flow of generalized second grade fluids through a circular cylinder, Bul. Acad. Ştiinţe Repub. Mold. Mat. 58 (3), 9-17, 2008.
  • V. Mathur and K. Khandelwal, Exact solution for the flow of Oldroyd-B fluid between coaxial cylinders, Int. J. Eng. Res. Technol. 3 (1), 949-954, 2014.
  • M. Mustafa, T. Hayat and A. Alsaedi, Rotating flow of Oldroyd-B fluid over stretchable surface with Cattaneo-Christov heat flux: Analytic solutions, Int. J. Numer. Methods Heat Fluid Flow 27 (10), 2207-2222, 2017.
  • M.D. Raisinghania, Advanced Differential Equations, S. Chand & Company, New Delhi, 1991.
  • K.R. Rajagopal and R.K. Bhatnagar, Exact solutions for some simple flows of an Oldroyd-B fluid, Acta Mech. 113, 233-239, 1995.
  • R.S. Rivlin and J.L. Ericksen, Stress-deformation relations for isotropic materials, Arch. Ration. Mech. Anal. 4, 323-425, 1955.
  • P.N. Srivastava, Non-steady helical flow of a visco-elastic liquid, Arch. Mech. 18, 145-150, 1966.
  • M. Tanveer, S. Ullah, Najeeb A. Khan, Nadeem A. Khan and N. Rehman, MHD flow of generalized Oldroyd-B fluid over an infinite oscillating plate with slip condition using Fox H-function, J. Comput. Theor. Nanosci. 14 (3), 1362-1370, 2017.
  • D. Tong and Y. Liu, Exact solutions for the unsteady rotational flow of a non- Newtonian fluid in an annular pipe, Int. J. Eng. Sci. 43, 281-289, 2005.
  • S. Ullah, A. Ullah and M. Iqbal, Withdrawal and drainage of thin film flow of a generalized Oldroyd-B fluid on non-isothermal cylindrical surfaces, AIP Adv. 5 (12), 127242-1 - 1227242-13, 2015.
  • D. Yao, A non-Newtonian fluid model with finite strech and rotational recovery, J. Nonnewton. Fluid Mech. 230, 12-18, 2016

Study of velocity and shear stress for unsteady flow of incompressible Oldroyd-B fluid between two concentric rotating circular cylinders

Year 2019, Volume 48, Issue 2, 372 - 383, 01.04.2019
https://doi.org/10.15672/hujms.545240

Abstract

This investigation deals with the study of unsteady flow of incompressible Oldroyd-B fluid between two rotating circular cylinders, both cylinders are rotating around their common axis $(r=0)$. The governing differential equations are formulated with appropriate boundary conditions and then solved by means of Laplace and Hankel transforms to obtain velocity and shear stress for unsteady flow of Oldroyd-B fluid between two infinite concentric rotating circular cylinders. The obtained solutions can easily be reduced to equivalent solutions for Maxwell and classical Newtonian fluids. Finally, the influence of different physical parameters on the fluid velocity and shear stress is graphically underlined and discussed.

References

  • R. Cai and C. Gou, Algebraically explicit analytical solutions for unsteady non- Newtonian swirling flow in an annular pipe, Sci. China Ser. G, 49 (4), 396-400, 2006.
  • R.P. Chhabra and J.F. Richardson, Non-Newtonian Flow: Fundamentals and Engineering Applications, Elsevier, 1999.
  • C. Fetecau and C. Fetecau, Unsteady flows of Oldroyd-B fluids in a channel of rectangular cross-section, Int. J. Nonlinear Mech. 40, 1214-1219, 2005.
  • C. Fetecau, M. Imran, C. Fetecau and I. Burdujan, Helical flow of an Oldroyd-B fluid due to a circular cylinder subject to time-dependent shear stresses, Z. Angew. Math. Phys. 61, 959-969, 2010.
  • C. Fetecau, A. Mahmood, C. Fetecau and D. Vieru, Some exact solutions for the helical flow of a generalized Oldroyd-B fluid in a circular cylinder, Comput. Math. Appl. 56 (12), 3096-3108, 2008.
  • A.K. Ghosh and P. Sana, On hydromagnetic rotating flow of an Oldroyd-B fluid near an oscillating plate, Z. Angew. Math. Phys. 60, 1135-1155, 2009.
  • T. Hayat, A.M. Siddiqui and S. Asghar, Some simple flows of an Oldroyd-B fluid, Int. J. Eng. Sci. 39, 135-147, 2001.
  • M. Jamil and C. Fetecau, Some exact solutions for rotating flows of a generalized Burgers fluid in cylindrical domains, J. Nonnewton. Fluid Mech. 165 (23), 1700-1712, 2010.
  • M. Jamil, N.A. Khan and A.A. Zafar, Translational flows of an Oldroyd-B fluid with fractional derivatives, Comput. Math. Appl. 62 (3), 1540-1553, 2011.
  • M. Kamran, M. Imran and M. Athar, Exact solutions for the unsteady rotational flow of an Oldroyd-B fluid with fractional derivatives induced by a circular cylinder, Meccanica 48 (5), 1215-1226, 2013.
  • M. Kamran, M. Imran, M. Athar and M.A. Imran, On the unsteady rotational flow of fractional Oldroyd-B fluid in cylindrical domains, Meccanica 47 (3), 573-584, 2012.
  • S.M. Kang, W. Nazeer, M. Athar, M.D. Hisham and Y.C. Kwun, Velocity and shear stress for an Oldroyd-B fluid within two cylinders, Bound. Value Probl. 40, doi: 10.1186/s13661-016-0541-7, 2016.
  • C.F. Lorenzo and T.T. Hartley, Generalized Functios for the Fractional Calculus, NASA/TP-1999-20942/REV 1, 1999.
  • A. Mahmood, S. Ullah and G. Bolat, Some exact solutions for the rotational flow of a generalized second-grade fluid between two circular cylinders, Arch. Mech. 60 (5), 385-401, 2008.
  • A. Mahmood, S. Ullah and Q. Rubab, Exact solutions for a rotational flow of generalized second grade fluids through a circular cylinder, Bul. Acad. Ştiinţe Repub. Mold. Mat. 58 (3), 9-17, 2008.
  • V. Mathur and K. Khandelwal, Exact solution for the flow of Oldroyd-B fluid between coaxial cylinders, Int. J. Eng. Res. Technol. 3 (1), 949-954, 2014.
  • M. Mustafa, T. Hayat and A. Alsaedi, Rotating flow of Oldroyd-B fluid over stretchable surface with Cattaneo-Christov heat flux: Analytic solutions, Int. J. Numer. Methods Heat Fluid Flow 27 (10), 2207-2222, 2017.
  • M.D. Raisinghania, Advanced Differential Equations, S. Chand & Company, New Delhi, 1991.
  • K.R. Rajagopal and R.K. Bhatnagar, Exact solutions for some simple flows of an Oldroyd-B fluid, Acta Mech. 113, 233-239, 1995.
  • R.S. Rivlin and J.L. Ericksen, Stress-deformation relations for isotropic materials, Arch. Ration. Mech. Anal. 4, 323-425, 1955.
  • P.N. Srivastava, Non-steady helical flow of a visco-elastic liquid, Arch. Mech. 18, 145-150, 1966.
  • M. Tanveer, S. Ullah, Najeeb A. Khan, Nadeem A. Khan and N. Rehman, MHD flow of generalized Oldroyd-B fluid over an infinite oscillating plate with slip condition using Fox H-function, J. Comput. Theor. Nanosci. 14 (3), 1362-1370, 2017.
  • D. Tong and Y. Liu, Exact solutions for the unsteady rotational flow of a non- Newtonian fluid in an annular pipe, Int. J. Eng. Sci. 43, 281-289, 2005.
  • S. Ullah, A. Ullah and M. Iqbal, Withdrawal and drainage of thin film flow of a generalized Oldroyd-B fluid on non-isothermal cylindrical surfaces, AIP Adv. 5 (12), 127242-1 - 1227242-13, 2015.
  • D. Yao, A non-Newtonian fluid model with finite strech and rotational recovery, J. Nonnewton. Fluid Mech. 230, 12-18, 2016

Details

Primary Language English
Subjects Mathematics
Journal Section Mathematics
Authors

Saif ULLAH (Primary Author)
0000-0003-0250-3931


Muhammad TANVEER This is me
0000-0001-6004-7888


Sana BAJWA This is me
0000-0003-0965-4863

Publication Date April 1, 2019
Published in Issue Year 2019, Volume 48, Issue 2

Cite

Bibtex @research article { hujms546371, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2019}, pages = {372 - 383}, doi = {10.15672/hujms.545240}, title = {Study of velocity and shear stress for unsteady flow of incompressible Oldroyd-B fluid between two concentric rotating circular cylinders}, key = {cite}, author = {Ullah, Saif and Tanveer, Muhammad and Bajwa, Sana} }
APA Ullah, S. , Tanveer, M. & Bajwa, S. (2019). Study of velocity and shear stress for unsteady flow of incompressible Oldroyd-B fluid between two concentric rotating circular cylinders . Hacettepe Journal of Mathematics and Statistics , 48 (2) , 372-383 . DOI: 10.15672/hujms.545240
MLA Ullah, S. , Tanveer, M. , Bajwa, S. "Study of velocity and shear stress for unsteady flow of incompressible Oldroyd-B fluid between two concentric rotating circular cylinders" . Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 372-383 <https://dergipark.org.tr/en/pub/hujms/article/546371>
Chicago Ullah, S. , Tanveer, M. , Bajwa, S. "Study of velocity and shear stress for unsteady flow of incompressible Oldroyd-B fluid between two concentric rotating circular cylinders". Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 372-383
RIS TY - JOUR T1 - Study of velocity and shear stress for unsteady flow of incompressible Oldroyd-B fluid between two concentric rotating circular cylinders AU - Saif Ullah , Muhammad Tanveer , Sana Bajwa Y1 - 2019 PY - 2019 N1 - doi: 10.15672/hujms.545240 DO - 10.15672/hujms.545240 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 372 EP - 383 VL - 48 IS - 2 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.545240 UR - https://doi.org/10.15672/hujms.545240 Y2 - 2017 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics Study of velocity and shear stress for unsteady flow of incompressible Oldroyd-B fluid between two concentric rotating circular cylinders %A Saif Ullah , Muhammad Tanveer , Sana Bajwa %T Study of velocity and shear stress for unsteady flow of incompressible Oldroyd-B fluid between two concentric rotating circular cylinders %D 2019 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 48 %N 2 %R doi: 10.15672/hujms.545240 %U 10.15672/hujms.545240
ISNAD Ullah, Saif , Tanveer, Muhammad , Bajwa, Sana . "Study of velocity and shear stress for unsteady flow of incompressible Oldroyd-B fluid between two concentric rotating circular cylinders". Hacettepe Journal of Mathematics and Statistics 48 / 2 (April 2019): 372-383 . https://doi.org/10.15672/hujms.545240
AMA Ullah S. , Tanveer M. , Bajwa S. Study of velocity and shear stress for unsteady flow of incompressible Oldroyd-B fluid between two concentric rotating circular cylinders. Hacettepe Journal of Mathematics and Statistics. 2019; 48(2): 372-383.
Vancouver Ullah S. , Tanveer M. , Bajwa S. Study of velocity and shear stress for unsteady flow of incompressible Oldroyd-B fluid between two concentric rotating circular cylinders. Hacettepe Journal of Mathematics and Statistics. 2019; 48(2): 372-383.
IEEE S. Ullah , M. Tanveer and S. Bajwa , "Study of velocity and shear stress for unsteady flow of incompressible Oldroyd-B fluid between two concentric rotating circular cylinders", Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 2, pp. 372-383, Apr. 2019, doi:10.15672/hujms.545240