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

Abstract

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

REFERENCES

  1. McCabe WL, Smith JC, Harriott P. Unit operations of chemical engineering. McGraw-Hill New York. 1993. Ref.: https://goo.gl/ZPbfG3
  2. Bruce RW, Na TY. Natural convection flow of Powell-Eyring fluids between two vertical flat plates. ASME. 1967. Ref.: https://goo.gl/kZIHjc
  3. Shenoy AV, Mashelkar RA. Thermal convection in non-Newtonian fluids. Advances in heat transfer. 1982; 15: 143-225. Ref.: https://goo.gl/5CM5CD
  4. Dunn JE, Rajagopal KR. Fluids of differential type: critical review and thermodynamic analysis. International Journal of Engineering Science. 1995; 33: 689-729. Ref.: https://goo.gl/yOaMb0
  5. Nayfeh AH. Perturbation methods. 2008. Ref.: https://goo.gl/gq0nGe
  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.: https://goo.gl/SVMwsa
  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.: https://goo.gl/lO2LpS
  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.: https://goo.gl/0et8vE
  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.: https://goo.gl/Wqeh6m
  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.: https://goo.gl/7pVooK
  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.: https://goo.gl/KSc8EI
  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.: https://goo.gl/ZCzxl4  
  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.: https://goo.gl/uZd5CO
  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.: https://goo.gl/YK3gCu
  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.: https://goo.gl/f5oKpj
  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.: https://goo.gl/i3sGCg
  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.: https://goo.gl/y9Svvn
  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.: https://goo.gl/pg9hvr
  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.: https://goo.gl/GXH0rG
  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.: https://goo.gl/14dEOB
  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.: https://goo.gl/k4kefw
  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.: https://goo.gl/81Hd29
  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.: https://goo.gl/ws2q0Z
  24. Ozisik MN. Heat conduction. John Wiley & Sons. 1993. Ref.: https://goo.gl/PNxseq
  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.: https://goo.gl/t5prSP
  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.: https://goo.gl/E7kEwS