Graetz problem for the casson fluid model with prescribed heat flux in a circular duct
Tóm tắt
Từ khóa
Tài liệu tham khảo
N. Ali, Z. Asghar, O.A. Bég, M. Sajid, Bacterial gliding fluid dynamics on a layer of non-Newtonian slime: perturbation and numerical study. J. Theor. Biol. 397, 22–32 (2016)
Z. Asghar, N. Ali, M. Sajid, Interaction of gliding motion of bacteria with rheological properties of the slime. Math. Biosci. 290, 31–40 (2017)
Z. Asghar, N. Ali, O.A. Bég, T. Javed, Rheological effects of micropolar slime on the gliding motility of bacteria with slip boundary condition. Results Phys. 9, 682–691 (2018)
Z. Asghar, N. Ali, A mathematical model of the locomotion of bacteria near an inclined solid substrate: effects of different waveforms and rheological properties of couple-stress slime. Can. J. Phys. 97(5), 537–547 (2019)
S. Shaw, G. Mahanta, P. Sibanda, Non-linear thermal convection in a Casson fluid flow over a horizontal plate with convective boundary condition. Alex. Eng. J. 55(2), 1295–1304 (2016)
L. Graetz, Uber die Warmeleitungsfahigheit von Flus- singkeiten, part 1. Ann. Phys. Chem. 18, 79–94 (1883). (part 2, 25, 337–357 (1885))
R.K. Shah, A.L. London, Laminar Flow Forced Convection in Ducts (Academic Press, New York, 1978)
R.K. Shah, M.S. Bhatti, Laminar convective heat transfer in ducts, in Handbook of Single-Phase Convective Heat Transfer, 2nd edn., ed. by S. Kakac, R.K. Shah, W. Aung (Wiley, New York, 1987). (Chapter 3)
B.C. Lyche, R.B. Bird, The Graetz-Nusselt problem for a power-law non-Newtonian fluid. Chem. Eng. Sci. 6(1), 35–41 (1956)
H.L. Toor, Heat generation and conduction in the flow of a viscous compressible liquid. Trans. Soc. Rheol. 1(1), 177–190 (1957)
A.R. Mansour, An analytical solution of laminar heat transfer to power-law non-Newtonian fluids in circular ducts Graetz-Nusselt problem. Int. Commun. Heat Mass Transf. 16(2), 199–204 (1989)
R. Siegel, E.M. Sparrow, T.M. Hallman, Steady laminar heat transfer in a circular tube with prescribed wall heat flux. Appl. Sci. Res. Sect. A 7, 386–392 (1958)
R.S. Parikh, R. Mahalingam, Laminar tube flow heat transfer in non-Newtonian fluids under arbitrary wall heat flux. Int. Commun. Heat Mass Transf. 15(1), 1–16 (1988)
A.F. Flores, J.C. Gottifredi, G.V. Morales, O.D. Quiroga, Heat transfer to power-law fluids flowing in pipes and flat ducts with viscous heat generation. Chem. Eng. Sci. 46(5–6), 1385–1392 (1991)
A.A. McKillop, Heat transfer for laminar flow of non-Newtonian fluids in entrance region of a tube. Int. J. Heat Mass Transf. 7(8), 853–862 (1964)
A.R. Chandrupatla, V.M.K. Sastri, Laminar forced convection heat transfer of a non-Newtonian fluid in a square duct. Int. J. Heat Mass Transf. 20(12), 1315–1324 (1977)
J.P. Hartnett, M. Kostic, Heat transfer to a viscoelastic fluid in laminar flow through a rectangular channel. Int. J. Heat Mass Transf. 28(6), 1147–1155 (1985)
N.P. Thien, R.I. Tanner, A new constitutive equation derived from network theory. J. Nonnewton. Fluid Mech. 2(4), 353–365 (1977)
P.M. Coelho, F.T. Pinho, P.J. Oliveira, Fully developed forced convection of the Phan-Thien–Tanner fluid in ducts with a constant wall temperature. Int. J. Heat Mass Transf. 45(7), 1413–1423 (2002)
M.F. Letelier, D.A. Siginer, Friction effects in pipe flow of phan-thien-tanner fluids, in ASME international mechanical engineering congress and exposition, vol. 19180, (American Society of Mechanical Engineers, New York City, 2000), pp.113–115
M.F. Letelier, D.A. Siginer, On the fully developed tube flow of a class of non-linear viscoelastic fluids. Int. J. Non-Linear Mech. 40(4), 485–493 (2005)
P.J. Oliveira, F.T. Pinho, Analytical solution for fully developed channel and pipe flow of Phan-Thien–Tanner fluids. J. Fluid Mech. 387, 271–280 (1999)
P.M. Coelho, F.T. Pinho, P.J. Oliveira, Thermal entry flow for a viscoelastic fluid: the Graetz problem for the PTT model. Int. J. Heat Mass Transf. 46(20), 3865–3880 (2003)
P.J. Oliveira, P.M. Coelho, F.T. Pinho, The Graetz problem with viscous dissipation for FENE-P fluids. J. Nonnewton. Fluid Mech. 121(1), 69–72 (2004)
N. Casson, Flow equation for pigment-oil suspensions of the printing ink-type. Rheol. Disper. Syst., 84–104 (1959)
S. Mukhopadhyay, P.R. De, K. Bhattacharyya, G.C. Layek, Casson fluid flow over an unsteady stretching surface. Ain Shams Eng. J. 4(4), 933–938 (2013)
R.P. Chhabra, J.F. Richardson, Non-Newtonian fluid behaviour. Non-newtonian Flow Appl. Rheol. 1–55 (2008)
B. Das, R.L. Batra, Secondary flow of a Casson fluid in a slightly curved tube. Int. J. Non-Linear Mech. 28(5), 567–577 (1993)
D.S. Sankar, U. Lee, Two-fluid non-linear model for flow in catheterized blood vessels. Int. J. Non-Linear Mech. 43(7), 622–631 (2008)
D.S. Sankar, A two-fluid model for pulsatile flow in catheterized blood vessels. Int. J. Non-Linear Mech. 44(4), 337–351 (2009)
S. Mukhopadhyay, I.C. Mondal, A.J. Chamkha, Casson fluid flow and heat transfer past a symmetric wedge. Heat Transf. Asian Res. 42(8), 665–675 (2013)
M.Y. Malik, M. Naseer, S. Nadeem, A. Rehman, The boundary layer flow of Casson nanofluid over a vertical exponentially stretching cylinder. Appl. Nanosci. 4, 869–873 (2014)
M.H. Abolbashari, N. Freidoonimehr, F. Nazari, M.M. Rashidi, Analytical modeling of entropy generation for Casson nano-fluid flow induced by a stretching surface. Adv. Powder Technol. 26(2), 542–552 (2015)
M.W.S. Khan, N. Ali, Thermal entry flow problem for Giesekus fluid inside an axis-symmetric tube through isothermal wall condition: a comparative numerical study between exact and approximate solution. Z. Naturforschung A 76(11), 973–984 (2021)
Z. Asghar, M.W. Saeed Khan, M.A. Gondal, A. Ghaffari, Channel flow of non-Newtonian fluid due to peristalsis under external electric and magnetic field. Proc. Inst. Mech. Eng. Part E J. Process Mech. Eng. 26, 09544089221097693 (2022)
M.W.S. Khan, N. Ali, Z. Asghar, Critical investigation of thermally developing nanofluid flow within in slippery tube and channel: an extended Graetz-Nusselt problem with longitudinal conduction and power-law nanofluid. Sci. Iran. 29(6), 3582–3590 (2022)
M.W. Saeed Khan, N. Ali, Z. Asghar, Mathematical modelling of classical Graetz-Nusselt problem for axisymmetric tube and flat channel using the Carreau fluid model: a numerical benchmark study. Z. Naturforschung A 76(7), 589–603 (2021)
N. Ali, M.W.S. Khan, A note on classical Graetz problem based on Cattaneo-Christov heat flux model. Eur. Phys. J. Plus 137(4), 1–7 (2022)
M.W.S. Khan, N. Ali, Z. Asghar, Thermal and rheological effects in a classical Graetz problem using a nonlinear Robertson-Stiff fluid model. Heat Transf. 50(3), 2321–2338 (2021)
N. Ali, M.W.S. Khan, M. Sajid, The Graetz-Nusselt problem for the curved channel using spectral collocation method. Phys. Scr. 96(5), 055204 (2021)
M.W. Saeed Khan, N. Ali, O.A. Bég, Thermal entrance problem for blood flow inside an axisymmetric tube: the classical Graetz problem extended for Quemada’s bio-rheological fluid with axial conduction. Proc. Inst. Mech. Eng. [H] 236(6), 848–859 (2022)
M.W.S. Khan, N. Ali, Theoretical analysis of thermal entrance problem for blood flow: an extension of classical Graetz problem for Casson fluid model using generalized orthogonality relations. Int. Commun. Heat Mass Transf. 109, 104314 (2019)
P. Nagarani, A. Lewis, Peristaltic flow of a Casson fluid in an annulus. Korea-Austral. Rheol. J. 24(1), 1–9 (2012)
A.V. Mernone, J.N. Mazumdar, S.K. Lucas, A mathematical study of peristaltic transport of a Casson fluid. Math. Comput. Model. 35(7–8), 895–912 (2002)
R. Ponalagusamy, Blood flow through an artery with mild stenosis: a two-layered model, different shapes of stenoses and slip velocity at the wall. J. Appl. Sci. 7(7), 1071–1077 (2007)
T. Min, J.Y. Yoo, Laminar convective heat transfer of a Bingham plastic in a circular pipe with uniform wall heat flux: the Graetz problem extended. J. Heat Transf. 121, 556–563 (1999)
M.S. Arif, K. Abodayeh, Y. Nawaz, The modified finite element method for heat and mass transfer of unsteady reacting flow with mixed convection. Front. Phys. 10, 802 (2022)
H. Khan, J. Alzabut, A. Shah, Z.Y. He, S. Etemad, S. Rezapour, A. Zada, On fractal-fractional waterborne disease model: a study on theoretical and numerical aspects of solutions via simulations. Fractals 31, 23400558 (2023)