Article abstract

Advancement in Scientific and Engineering Research

Research Article | Published May 2019 | Volume 4, Issue 1, pp. 1-16.

doi: https://doi.org/10.33495/aser_v4i1.19.101

 

Heat transfer and fluid dynamics on inclined smooth and rough surfaces by the application of the similarity and integral methods

 


 

 

Élcio Nogueira1*

Marcus V. F. Soares2

Luiz Cláudio Pimentel3

 

Email Author

 

1. Faculty of Technology of the State University of Rio de Janeiro - FAT/UERJ, Brazil.
2. Engineering Company - Engevale, Brazil.

3. Institute of Geosciences of the Federal University of Rio de Janeiro - IGEO/UFRJ, Brazil.





……....…...………..........................…………....………............…............……...........……........................................................………...……..…....……....…

Citation: Nogueira E, Soares MVF, Pimentel LC (2019). Heat transfer and fluid dynamics on inclined smooth and rough surfaces by the application of the similarity and integral methods. Adv. Sci. Eng. Res.. 4(1): 1-16.

……....…...………..........................…………....………............…............……...........……........................................................………...……..…....……....…

 Abstract 


The main objective of the analysis is to review and discuss the principles of the similarity method applied to the boundary layer on inclined surfaces, in laminar regime, and that can be extended to a turbulent regime. The emphasis applies to theoretical aspects related to the concept of similarity, but theoretical results were obtained in order to compare with empirical expressions and experimental results. Results are obtained for the hydrodynamic and thermal fields, such as coefficient of friction and Stanton number, as a function of the pressure gradient parameter and the Prandtl number. The fourth order Runge-Kutta method is applied, starting from the expansion in power series as the first approximation for the mathematical solution of hydrodynamic and thermal problems, in laminar regime. The Integral Method is applied to obtain an approximate solution for the flow in turbulent regime, by similarity variables method. Numerical and graphical results are presented in sufficient numbers to emphasize the consistency of the model developed in the determination of parameters related to thermal and hydrodynamic boundary layers on smooth and rough surfaces.

Keywords  Similarity method   fourth order Runge Kutta Method   hydrodynamic boundary layer   thermal boundary layer   

 

 

Copyright © 2019 Author(s) retain the copyright of this article.

This article is published under the terms of the Creative Commons Attribution License 4.0

 

 

  References 

 

Abbasi M, Nava GH, Petroudi IM (2014). “Analytic Solution of Hydrodynamic and Thermal Boundary Layer over a Flat Plate in a Uniform Stream of a Fluid with Convective Surface Boundary Condition”. Indian J. Sci. Res.1 (2):241-247.

Bhattacharyya K, Uddin MS, Layek GC (2016). “Exact Solution for Thermal Boundary Layer in Casson Fluid Flow over a Permeable Shrinking Sheet with Variable Wall Temperature and Thermal Radiation”. Alexandria Eng. J. 55:1703-1712.

Blasius H (1908). "Boundary layers in liquids with low friction”. Z. Math, und Phys. 56:1. (In German).

Bognar G, Hriczó K (2011). “Similarity Solutions a Thermal Boundary Layer Models of a non-Newtonian Fluid with a Convective Surface Boundary Condition”. Acta Polytechnica Hungarica 8:6.

Castilho L (1997). “Similarity Analyses of Turbulent Boundary Layer”. A Dissertation Submitted in a Partial Requirement for the Degree of Doctor of Philosophy, State University of Buffalo.

Evans HL (1968). “Laminar Boundary-Layer-Theory”. Addison-wesley Publishing company.

Grapher 5.01.15.0 (2004). Golden Software, Inc. Falkner VM, Skan SW (1930). “Some approximate solutions of the boundary layer equations”. British Aero. Res. Council, Reports and Memoranda. p. 1314.

Falkner VM, Skan SW (1931). LXXXV Solutions of the boundary-layer equations. Phil. Mag. 12(7):865-896.

Hager WH (2003). “Blasius: A Life in Research and Education”. Experiments in Fluids, 34:566-571.

Kays WM, Crawford ME (1983). “Convective Heat and Mass Transfer”. Tata McGraw-Hill Publishing Co. Ltd, New Delhi.

Kays WM, Moffat RJ, Thiebhr HW (1969). “Heat Transfer to the Highly Accelerated Turbulent Boundary Layer with and without Mass Addition”. Report Nº HMT-6.

Microsoft Fortran Power Station Version 4.0 (1995). Microsoft Corporation.

Sobamowo MG, Yinusa AA, Oluwo AA, Alozie SI (2018). “Finite element analysis of flow and heat transfer of dissipative Casson-Carreau nanofluid over a stretching sheet embedded in a porous medium”. Aeronautics and Aerospace Open Access J. Res. Article 2:5.

Nazeer M, Ali N, Tariq J (2017) “Numerical simulation of MHD flow of micropolar fluid inside a porous inclined cavity with uniform an non-uniform heated bottom-wall”. Can. J. Phys. 96(6):576-593.

Myers TG (2010). “An Approximate Solution Method for Boundary Layer Flow of a Power Law Fluid over a Flat Plate”. Int. J. Het and Mass Transfer, 53:2337-2346.

Khan NA, Khan S, Ara A (2017) “Flow of micro polar fluid over an off centered rotating disk with modified Darcy's law”. Propulsion Power Res. 6(4):285-295.

Ali N, Nazeer M, Tariq J, Mudassar R (2019). “Finite element analysis of bi-viscosity fluid enclosed in a triangular cavity under thermal and magnetic effects”. The Eur. Phys. J. 134:2.

Nogueira É, Soares MVF (2018). “Flat plate boundary layer: revisiting the Similarity Method”. Cadernos UniFOA, Volta Redonda, 37:15-31.

Oderinu RA (2014). “Shooting Method via Taylor Series for Solving Two Point Boundary Value Problem on an Infinite Interval”. Gen. Math. Notes 24(1):74-83.

Pimenta MM, Moffat RJ, Kays WM (1975). “The Turbulent Boundary Layer: An experimental Study of the Transport of Momentum and Heat Transfer with Effects of Roughness”. Report Nº HMT-21.

Puttkammer PP (2013). “Boundary Layer over a Flat Plate”. BSc Report, University of Twente, Enschede.

Rabari MF, Hamzehnezhad A, Akbari VM, Ganji DD (2017) “Heat transfer and fluid flow of blood with nanoparticles through porous vessels in a magnetic field: A quasi-one-dimensional analytical approach”. Math. Biosci. 283:38-47.

Rahman MM (2011). “Locally Similar Solutions for a Hydromagnetic and Thermal Slip Flow Boundary Layers over a Flat Plate with Variable Fluid Properties and Convective Surface Boundary Condition”. Meccanica, 46:1127-1143. doi: 10.1007/s11012-010-9372-2.

Aziz RC, Hashim I, Abbasbandy S (2018). “Flow and Heat Transfer in a Nanofluid Thin Film over an Unsteady Stretching Sheet”. Sains Malaysiana 47(7):1599-1605.

Schultz-Grunow F (1941): NA TM-986, Washington. Schlichting H (1968). McGraw-Hill Book Company, New York.

Sheikhzadeh MM, Abbaszadeh M (2018). “Analytical study of flow field and heat transfer of a non-Newtonian fluid in an axisymmetric channel with a permeable wall”. J. Comput. Appl. Res. Mech. Eng. 7(2):161-173.

Simpson RL (1989). “Turbulent Boundary-Layer Separation”. Ann. Rev. Fluid Mech, 21:205-340. Silva FAP (1990). "Boundary Layer Theory: Notes of Classes”. Mechanical Engineering Program. (In Portuguese).

Spalding DB, Pun WM (1962). “A Review of Methods for Predicting Heat-Transfer Coefficients for Laminar Uniform-Property Boundary Layers Flows”. Int. J. Heat Mass Transf. 5:239-249.

Pergamon Press. Stemmer C (2010). “Boundary Layer Theory: Falkner-Scan Solution (Flat-Plate Boundary Layer with Pressure Gradients)”. Lehrstuhf für Aerodynamik, Tecnische Universität Münchem, Boundary Layer Theory, GIST.

Stull RB (1988). “An Introduction on Boundary Layer Meteorology”. Atmospheric Sciences Library, Kluwer Academic Publishers, London.

Tannehill JC, Anderson DA, Plecher RH (1997). “Computational Fluid Mechanics and Heat Transfer”. Second Edition, Taylor & Francis.