Analytical study of flow field and heat transfer of a non-Newtonian fluid in an axisymmetric channel with a permeable wall

Sheikhzadeh, Ghanbarali; Mollamahdi, Mahdi; Abbaszadeh, Mahmoud

doi:10.22061/jcarme.2017.2003.1174

Document Type : Research Paper

Authors

¹ University of kashan

² university of kashan

https://doi.org/10.22061/jcarme.2017.2003.1174

Abstract

In this study, the momentum and energy equations of laminar flow of a non-Newtonian fluid are solved in an axisymmetric porous channel using the least square and Galerkin methods. The bottom plate is heated by an external hot gas, and a coolant fluid is injected into the channel from the upper plate. The arising nonlinear coupled partial differential equations are reduced to a set of coupled nonlinear ordinary differential equations using stream function.These equations can be solved using the different numerical method. The numerical solution is conducted using fourth order Rung-Kutta method. With comparing the results obtained from the analytical and numerical methods, a good adaptation can be seen between them. It can also be observed that the results of the Galerkin method have further conformity with the numerical results and the Galerkin method is simpler than the least square method and requires fewer computations. The effects of Reynolds number, Prandtl number and power law index of non-Newtonian fluid is examined on flow field and heat transfer. The results show that Nusselt number increases by increasing Reynolds number, Prandtl number, and power law index.

Graphical Abstract

Keywords

20.1001.1.22287922.2018.7.2.3.3

Main Subjects

Computational Fluid Dynamics (CFD)

References

[1] SW. Yuan, and AB. Finkelstein, “Laminar pipe flow with injection and suction through a porous wall”, Transaction of the ASME, Vol. 78, No. 1, pp. 719-724, (1956).

[2] JL. White, and AB. Metzner, “Constitutive equations for viscoelastic fluids with application to rapid external flows”, AIChE Journal, Vol. 11, No. 2, pp. 324-330, (1965).

[3] RM. Terill, “Laminar flow in a uniformly porous channel with large injection”, Aeronautics Q, Vol. 16, No. 1, pp. 322-332, (1965).

[4] L. L. Debruge, and L. S. Han, “Heat transfer in a Channel with Porous Wall for Turbine Cooling”, Journal of Heat Transfer, Vol. 94, No. 4, pp. 385-390, (1972).

[5] C. Kurtcebe, and M. Z. Erim, “Heat transfer of a non-Newtonian viscoinelastic fluid in an axisymmetric channel with a porous wall for turbine cooling application”, International Communication in Heat and Mass Transfer, Vol. 29, No. 7, pp. 971-982 (2002).

[6] M. Esmaeilpour, G. Domairry, N. Sadoughi, and A.G. Davodi, Homotopy Analysis Method for the heat transfer of a non-Newtonian fluid flow in an axisymmetric channel with a porous wall”, Commun Nonlinear Sci Numer Simulat, Vol. 15, No. 9, pp. 2424-2430, (2010).

[7] M. Hosseini, Z. Sheikholeslami, and D.D. Ganji, “Non-Newtonian fluid flow in an axisymmetric channel with porous wall”, Journal of Propulsion and power Research, Vol. 2, No. 4, pp. 254-262, (2013).

[8] H. R. Ashorynejad, K. Javaherdeh, M. Sheikholeslami, and D.D. Ganji, “Investigation of the heat transfer of a non-Newtonian fluid flow in an axisymmetric channel with porous wall using Parameterized Perturbation Method (PPM) ”, Journal of The Franklin Institute, Vol. 351, No. 2, pp. 701-712, (2014).

[9] M. Hatami, and D. D. Ganji, “Heat transfer and flow analysis for SA-TiO2 non-Newtonian nanofluid passing through the porous media between two coaxial cylinders”, Journal of Molecular Liquids, Vol. 188, pp. 155-161, (2013).

[10] M. Hatami, and D. D. Ganji, “Thermal performance of circular convective–radiative porous fins with different section shapes and materials”, Energy Conversion and Management, Vol. 76, pp. 185-193, (2013).

[11] M. Hatami, and D. D. Ganji, “Thermal and flow analysis of microchannel heat sink (MCHS) cooled by Cu–water nanofluid using porous media approach and least square method”, Energy Conversion and Management, Vol. 78, pp. 347-358, (2014).

[12] M. Mollmahdi, M. Abbaszadeh, and G. A. Sheikhzadeh, “Flow field and heat transfer in a channel with a permeable wall filled with Al2O3-Cu/water micropolar hybrid nanofluid, effects of chemical reaction and magnetic field”, Journal of Heat and Mass Transfer Research, Vol. 3, No. 2, pp. 101-114, (2016).

[13] A. Vahabzadeh, M. Fakour, D. D. Ganji, and H. Bakhshi, “Analytical investigation of the one dimensional heat transfer in logarithmic various surfaces”, Alexandria Engineering Journal, Vol. 55, No. 1, pp. 113-117, (2016).

[14] M. Fakour, D. D. Ganji, A. Khalili, and A. Bakhshi, “Heat Transfer in Nanofluid MHD Flow in a Channel With Permeable Walls”, Heat Transfer Research, Vol. 48, No. 3, pp. 221-228, (2017).

[15] A. Rahbari, M. Fakour, A. Hamzehnezhad, M. Akbari Vakilabadi, and D. D. Ganji, “Heat transfer and fluid flow of blood with nanoparticles through porous vessels in a magnetic field: A quasi-one dimensional analytical approach”, Heat and Mass Transfer, Vol. 283, pp. 38-47, (2017).

[16] R. H. Stern, and H. Rasmussen, “Left ventricular ejection: model solution by collocation and approximate analytical method”, Computers in Biology and Medicine, Vol. 26, No. 3, (1996).

[17] B. Vaferi, V. Salimi, D. D. Baniani, A. Jahanmiri, S. Khedri, “Prediction of transient pressure response in the petroleum reservoisers using orthogonal collocation”, Journal of Petroleum Science and Engineering, Vol. 98-99, No. 1, pp. 156-163, (2012).

[18] F. A. Hendi, A. M. Albugami, “Numerical solution for Fredholm-Volterra integral equation of the second kind by using collocation and Galerkin methods”, Journal of King Saud University, Vol. 22, No. 1, pp. 37-40, (2010).

[19] A. Aziz, and M. N. Bouaziz, “ A least square method for a longitudinal fin with tempreture dependent internal heat generation and thermal conductivity”, Energy Conversion and Management, Vol. 52, No. 8-9, pp. 2876-2882, (2011).

[20] M. Hatami, M. Sheikholeslami, and D. D. Ganji, “Laminar flow and heat transfer of nanofluid between contracting and rotating disks by least square method”, Powder Techonology, Vol. 253, No. 1, pp. 769-779, (2014).

[21] M. Hatami, J. Hatami, and D. D. Ganji, “Computer simulation of MHD blood conveying gold nanoparticles as a third grade non-Newtonian nanofluid in a hollow porous vessel”, Computer Methods and Programs in Biomedicine, Vol. 113, No. 2, pp. 632-641, (2014).

[22] M. Hatami, S. Mosayebidorcheh, and D. Jing, Two-phase nanofluid condensation and heat transfer modeling using least square method (LSM) for industrial applications”, Heat and Mass Transfer, Vol. 53, No. 6, pp. 2061-2072, (2017).

[23] S. Mosayebidorcheh, M. A. Tahavori, T. Mosayebidorcheh, and D. D. Ganji, “Analysis of nano-bioconvection flow containing both nanoparticles and gyrotactic microorganisms in a horizontal channel using modified least square method (MLSM) ”, Journal of Molecular Liquids, Vol. 227, pp. 356-365, (2017).

[24] R. S. Rivlin, “Plane strain of a net formed by inextensible cords, Journal Rational. Mech., Vol. 4, No. 2, pp. 323-425, (1995).

[25] R. C. Sherma, “Thermosolutal Convection in a Rivlin-Ericksen Rotating Fluid in Porous Medium in Hydromagnetics”, Indian Journal of Pure and Applied Mathematics, Vol. 34, No. 1, pp. 143-156, (2001).

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Journal of Computational & Applied Research in Mechanical Engineering (JCARME)

Analytical study of flow field and heat transfer of a non-Newtonian fluid in an axisymmetric channel with a permeable wall

References

References

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Volume 7, Issue 2 - Serial Number 14
March 2018
Pages 161-173

Analytical study of flow field and heat transfer of a non-Newtonian fluid in an axisymmetric channel with a permeable wall

References

References

Send comment about this article

Volume 7, Issue 2 - Serial Number 14March 2018Pages 161-173

Volume 7, Issue 2 - Serial Number 14
March 2018
Pages 161-173