Heat Transfer in Hydro-Magnetic Nano-Fluid Flow between Non-Parallel Plates Using DTM

Document Type : Research Paper


1 Mechanical Engineering Department, University of 20 aout 1955, El Hadaiek Road, B. O. 26, 21000 Skikda, Algeria.

2 Laboratory of Industrial Mechanics, Badji Mokhtar University of Annaba, B. O. 12, 23000 Sidi Amar Annaba, Algeria

3 Department of Civil Engineering, University of Birmingham, Edgbaston Birmingham B15 2TT, United Kingdom


This study presents a computational investigation on heat and flow behaviors between non parallel plates with the influence of a transverse magnetic field when the medium is filled with solid nanoparticles. The nonlinear governing equations are treated analytically via Differential Transform Method (DTM). Thereafter, obtained DTM results are validate with the help of numerical fourth order Runge-Kutta (RK4) solution. The main aim of this research work is to analyze the influence of varying physical parameters, in particular Reynolds number, nanofluid volume fraction, and Hartmann number. It was found that the presence of solid nanoparticles in a water base liquid has a notable effect on the heat transfer improvement within convergent-divergent channels. The comparison of DTM results with numerical RK4 solution also shows the validity of the analytical DTM technique. In fact, results demonstrate that the DTM data match perfectly with numerical ones and those available in literature.


Main Subjects

[1] G.B., Jeffery, The two dimensional steady motion of a viscous fluid, Philosophical Magazine, 29, 1915, 455-465.
[2] G., Hamel, Spiralförmige Bewegungen zäher Flüssigkeiten, Jahresbericht der Deutschen Mathematiker-Vereinigung, 25 1917, 34-60.
[3] L., Rosenhead, The steady two-dimensional radial flow of viscous fluid between two inclined plane walls, Proceedings of the Royal Society of London, A175, 1940, 436-467.
[4] M., Turkyilmazoglu, Extending the traditional Jeffery-Hamel flow to stretchable convergent/divergent channels, Computers and Fluids, 100, 2014, 196-203.
[5] M., Kezzar, M.R., Sari, Application of generalized decomposition method for solving nonlinear equation of Jeffery-Hamel Flow, Computational Mathematics and Modeling, 26, 2015, 284-297.
[6] N., Freidoonimehr, M.M., Rashidi, Dual Solutions for MHD Jeffery–Hamel Nano-Fluid Flow in Non-parallel Walls Using Predictor Homotopy Analysis Method, Journal of Applied Fluid Mechanics, 8, 2015, 911-919.
[7] W., Zechariah Carlson, On the Linear Stability Problem for Jeffery-Hamel Flows, Ph.D. dissertation, The University of Texas at Austin, 147 p., 2015.
[8] A., Shafiq, T.N., Sindhu, Statistical study of hydromagnetic boundary layer flow of Williamson fluid regarding a radiative surface, Results in Physics, 7, 2017, 3059-3067.
[9] T., Muhammad, T., Hayat, A., Alsaedi, A., Qayyum, Hydromagnetic unsteady squeezing flow of Jeffrey fluid between two parallel plates, Chinese Journal of Physics, 55, 2017, 1511-1522.
[10] P.V., Satya Narayana, B., Venkateswarlu, B., Devika, Chemical reaction and heat source effects on MHD oscillatory flow in an irregular channel, Ain Shams Engineering Journal, 7, 2016, 1079-1088.
[11] A., Salman, F., Chishtie, M., Asad, Analytical technique for magnetohydrodynamic (MHD) fluid flow of a periodically accelerated plate with slippage, European Journal of Mechanics - B/Fluids, 65,  2017, 192-198.
[12] S.U.S., Choi, J.A., Eastman, Enhancing thermal conductivity of fluids with nanoparticles, ASME International Mechanical Engineering Congress & Exposition, San Francisco, CA, November 12-17, 1995.
[13] S.A., Noreen, S., Nadeem, N.F.M., Noor, Free Convective MHD Peristaltic Flow of a Jeffrey Nanofluid with Convective Surface Boundary Condition: A Biomedicine-Nano Model, Current Nanoscience, 10, 2014, 432-440.
[14] M., Turkyilmazoglu, A note on the Correspondence between Certain Nanofluid Flows and Standard Fluid Flows, Journal of Heat Transfer, 137, 2015, 02450: 1-3.
[15] M., Turkyilmazoglu, Flow of nanofluid plane wall jet and heat transfer, European Journal of Mechanics - B/Fluids, 59, 2016, 18-24.
[16] R., Mohebbi, M.M., Rashidi, Numerical simulation of natural convection heat transfer of a nanofluid in an L-shaped enclosure with a heating obstacle, Journal of the Taiwan Institute of Chemical Engineers, 72, 2017, 72-84.
[17] M., Garoosi, M.M., Rashidi, Two phase flow simulation of conjugate natural convection of the nanofluid in a partitioned heat exchanger containing several conducting obstacles, International Journal of Mechanical Sciences, 130, 2017, 282-306.
[18] M.R., Sari, M., Kezzar, R., Adjabi, Heat transfer of copper-water nanofluid flow through converging-diverging channel, Journal of Central South University of Technology, 23, 2016, 484-496.
[19] M., Kezzar, M.R., Sari, Series Solution of Nanofluid Flow and Heat transfer Between Stretchable/Shrinkable Inclined Walls, International Journal of Computational Methods, 3, 2017, 2231–2255.
[20] M.M., Rashidi, M., Reza, S., Gupta, MHD stagnation point flow of micropolar nanofluid between parallel porous plates with uniform blowing, Powder Technology, 301, 2016, 876-885.
[21] N.A., Ramly, S., Sivasankaran, N.F.M., Noor, Zero and nonzero normal fluxes of thermal radiative boundary layer flow of nanofluid over a radially stretched surface, Scientia Iranica, 24, 2017, 2895-2903.
[22] M.I., Pryazhnikov, A.V., Minakov, V.Ya., Rudyak, D.V., Guzei, Thermal conductivity measurements of nanofluids, International Journal of Heat and Mass Transfer, 104, 2017, 1275–1282.
[23] G.J., Tertsinidou, C.M., Tsolakidou, M., Pantzali, M.J., Assael, New Measurements of the Apparent Thermal Conductivity of Nanofluids and Investigation of Their Heat Transfer Capabilities, Journal of Chemical & Engineering Data, 62, 2017, 491-507.
[24] M., Turkyilmazoglu, Convergent optimal variational iteration method and applications to heat and fluid flow problems, International Journal of Numerical Methods for Heat and Fluid Flow, 26, 2016, 790-804.
[25] M., Turkyilmazoglu, Parametrized Adomian decomposition method with optimum convergence, ACM Transactions on Modelling and Computer Simulation, 27(4), 2017, Article No. 21.
[26] K., Zhou, Differential transformation and its applications for electrical circuits, Huazhong Univ. Press, Wuhan, China, 1986.
[27] M.M., Rashidi, E., Erfani, New analytical method for solving Burgers’ and nonlinear heat transfer equations and comparison with HAM, Computer Physics Communications, 180, 2009, 1539-1544.
[28] M.M., Rashidi, M., Keimanesh, Using Differential Transform Method and Padé Approximant for Solving MHD Flow in a Laminar Liquid Film from a Horizontal Stretching Surface, Mathematical Problems in Engineering, 2010, Article ID 491319, 14 pages.
[29] M., Sheikholeslami, D.D., Ganji, Nanofluid flow and heat transfer between parallel plates considering brownian motion using DTM, Computer Methods in Applied Mechanics and Engineering, 283, 2015, 651-663.
[30] A.S., Dogonchi, M., Alizadeh, D.D., Ganji, Investigation of MHD Go-water nanofluid flow and heat transfer in a porous channel in the presence of thermal radiation effect, Advanced Powder Technology, 28, 2017, 1815-1825.
[31] S., Abbasbandy, E., Shivanian, Exact analytical solution of the MHD Jeffery-Hamel flow problem, Meccanica, 47, 2012, 1379-1389.
[32] M., Sheikholeslami, M., Gorji-Bandpy, D.D., Ganji, Investigation of nanofluid flow and heat transfer in presence of magnetic field using KKL model, Arabian Journal for Science and Engineering, 39(6), 2014, 5007-5016.