Research Article

Heat transfer investigation of Non- Newtonian Fluid between two vertically infinite fl at plates by numerical and analytical solutions

Pourmehran O*, Rahimi-Gorji M, Tavana M, Gorji-Bandpy M and Ganji DD

Published: 05/18/2017 | Volume 1 - Issue 1 | Pages: 001-011


In natural convection, the fluid motion occurs by natural means such as buoyancy. Heat transfer by natural convection happens in many physical problems and engineering applications such as geothermal systems, heat exchangers, petroleum reservoirs and nuclear waste repositories. These problems and phenomena are modeled by ordinary or partial differential equations. In most cases, experimental solutions cannot be applied to these problems, so these equations should be solved using special techniques. In this paper, natural convection of a non-Newtonian fluid flow between two vertical flat plates is investigated analytically and numerically. Collocation Method (CM) and fourth-order Runge -Kutta numerical method (NUM) are used to solve the present problem. These methods are powerful and convenient algorithms in finding the solutions for the equations. While these are capable of reducing the size of calculations. In order to compare with exact solution, velocity and temperature profiles are shown graphically. The obtained results are valid with significant accuracy.

Read Full Article HTML DOI: 10.29328/journal.hbse.1001001 Cite this Article


  1. McCabe WL, Smith JC, Harriott P. Unit operations of chemical engineering. McGraw-Hill New York. 1993. Ref.:
  2. Bruce RW, Na TY. Natural convection flow of Powell-Eyring fluids between two vertical flat plates. ASME. 1967. Ref.:
  3. Shenoy AV, Mashelkar RA. Thermal convection in non-Newtonian fluids. Advances in heat transfer. 1982; 15: 143-225. Ref.:
  4. Dunn JE, Rajagopal KR. Fluids of differential type: critical review and thermodynamic analysis. International Journal of Engineering Science. 1995; 33: 689-729. Ref.:
  5. Nayfeh AH. Perturbation methods. 2008. Ref.:
  6. Ganji SS, Ganji DD, Karimpour S. He’s energy balance and He’s variational methods for nonlinear oscillations in engineering. International Journal of Modern Physics B. 2009; 23: 461-471. Ref.:
  7. Rahimi-Gorji M, Pourmehran O, Gorji-Bandpy M, Ganji D. Unsteady squeezing nanofluid simulation and investigation of its effect on important heat transfer parameters in presence of magnetic field. Journal of the Taiwan Institute of Chemical Engineers. 2016; 67: 467-475. Ref.:
  8. Pourmehran O, Gorji TB, Gorji-Bandpy M. Magnetic drug targeting through a realistic model of human tracheobronchial airways using computational fluid and particle dynamics. Biomechanics and modeling in mechanobiology. 2016; 15: 1355-1374. Ref.:
  9. Pourmehran O, Rahimi-Gorji M, Ganji D. Heat transfer and flow analysis of nanofluid flow induced by a stretching sheet in the presence of an external magnetic field. Journal of the Taiwan Institute of Chemical Engineers. 2016; 65: 162-171. Ref.:
  10. Rahimi-Gorji M, Pourmehran O, Gorji-Bandpy M, Gorji T. CFD simulation of airflow behavior and particle transport and deposition in different breathing conditions through the realistic model of human airways. Journal of Molecular Liquids. 2015; 209: 121-133. Ref.:
  11. Pourmehran O, Rahimi-Gorji M, Gorji-Bandpy M, Gorji TB. Simulation of magnetic drug targeting through tracheobronchial airways in the presence of an external non-uniform magnetic field using Lagrangian magnetic particle tracking. Journal of Magnetism and Magnetic Materials. 2015; 393: 380-393. Ref.:
  12. Rahimi-Gorji M, Pourmehran O, Gorji-Bandpy M, Ganji DD. An analytical investigation on unsteady motion of vertically falling spherical particles in non-Newtonian fluid by Collocation Method. Ain Shams Engineering Journal. 2015; 6: 531-540. Ref.:  
  13. Pourmehran O, Rahimi-Gorji M, Hatami M, Sahebi SAR, Domairry G. Numerical optimization of microchannel heat sink (MCHS) performance cooled by KKL based nanofluids in saturated porous medium. Journal of the Taiwan Institute of Chemical Engineers. 2015; 55: 49-68. Ref.:
  14. Pourmehran O, Rahimi-Gorji M, Gorji-Bandpy M, Ganji D. Analytical investigation of squeezing unsteady nanofluid flow between parallel plates by LSM and CM. Alexandria Engineering Journal. 2015; 54: 17-26. Ref.:
  15. Rahimi-Gorji M, Pourmehran O, Hatami M, Ganji D. Statistical optimization of microchannel heat sink (MCHS) geometry cooled by different nanofluids using RSM analysis. The European Physical Journal Plus. 2015; 130: 22. Ref.:
  16. Hammes M, Boghosian M, Cassel K, Watson S, Funaki B, et al. Increased Inlet Blood Flow Velocity Predicts Low Wall Shear Stress in the Cephalic Arch of Patients with Brachiocephalic Fistula Access. PloS one. 2016; 11. Ref.:
  17. Javid Mahmoudzadeh Akherat SM, Cassel K, Boghosian M, Dhar P, Hammes M. Are Non-Newtonian Effects Important in Hemodynamic Simulations of Patients With Autogenous Fistula? Journal of Biomechanical Engineering. 2017; 139. Ref.:
  18. Fakour M, Ganji DD, Khalili A, Bakhshi A. HEAT TRANSFER IN NANOFLUID MHD FLOW IN A CHANNEL WITH PERMEABLE WALLS. Heat Transfer Research. 2017; 48. Ref.:
  19. Fakour M, Vahabzadeh A, Ganji DD. Study of heat transfer and flow of nanofluid in permeable channel in the presence of magnetic field. Propulsion and Power Research. 2015; 4: 50-62. Ref.:
  20. Fakour M, Ganji DD, Abbasi M. Scrutiny of underdeveloped nanofluid MHD flow and heat conduction in a channel with porous walls. Case Studies in Thermal Engineering. 2014; 4: 202-214. Ref.:
  21. Fakour M, Vahabzadeh A, Ganji DD, Hatami M. Analytical study of micropolar fluid flow and heat transfer in a channel with permeable walls. Journal of Molecular Liquids. 2015; 204: 198-204. Ref.:
  22. Rahbari A, Fakour M, Hamzehnezhad A, Vakilabadi MA, Ganji DD. Heat transfer and fluid flow of blood with nanoparticles through porous vessels in a magnetic field: A quasi-one dimensional analytical approach. Mathematical Biosciences. 2017; 283: 38-47. Ref.:
  23. Etbaeitabari A, Barakat M, Imani AA, Domairry G, Jalili P. An analytical heat transfer assessment and modeling in a natural convection between two infinite vertical parallel flat plates. Journal of Molecular Liquids. 2013; 188: 252-257. Ref.:
  24. Ozisik MN. Heat conduction. John Wiley & Sons. 1993. Ref.:
  25. Stern RH, Rasmussen H. Left ventricular ejection: model solution by collocation, an approximate analytical method. Computers in biology and medicine. 1996; 26: 255-261. Ref.:
  26. Vaferi B, Salimi V, Baniani DD, Jahanmiri A, Khedri S. Prediction of transient pressure response in the petroleum reservoirs using orthogonal collocation. Journal of Petroleum Science and Engineering, (2012) 98:156-163.Ref.: