Entropy Analysis for Unsteady MHD Boundary Layer Flow and Heat Transfer of Casson Fluid over a Stretching Sheet

Mohamed Ahmed MANSOUR; Abd Elnaser Sobhy Mohamed MAHDY; Sameh Elsayed AHMED; Shadia Saber MOHAMED

Authors

Mohamed Ahmed MANSOUR Mathematics Department, Faculty of Sciences, Assiut University, Assiut
Abd Elnaser Sobhy Mohamed MAHDY Mathematics Department, Faculty of Sciences, South Valley University, Qena
Sameh Elsayed AHMED Mathematics Department, Faculty of Sciences, South Valley University, Qena
Shadia Saber MOHAMED Mathematics Department, Faculty of Sciences, South Valley University, Qena

Keywords:

Entropy, MHD, Casson fluid, stretching sheet, viscous dissipation

Abstract

This paper investigates the entropy generation analysis of the unsteady two-dimensional magnetohydrodynamic (MHD) flow of electrically conducting non-Newtonian Casson fluid and heat transfer towards a stretching sheet in the presence of uniform transverse magnetic field with viscous dissipation and Joule heating effects. Using similarity solutions, the governing partial differential equations are transformed into ordinary differential equations and then solved numerically by MATLAB function bvp4c. The results of the present study indicate that the flow and temperature fields are significantly influenced by unsteadiness parameter Casson parameter , magnetic parameter Prandtl number and Eckert number It is found that the fluid velocity initially decreases with increase in the unsteadiness parameter and that temperature decreases significantly due to the unsteadiness parameter. Also, the effect of increasing values of the Casson parameter is to suppress the velocity field and the temperature distributions. The influences of the same parameters, as well as the Reynolds number and the Brinkman number on the entropy generation, are also discussed.

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

References

LJ Crane. Flow past a stretching plate. Z. Angew. Math. Phys. 1970; 21, 645-7.

B Sakiadis. Boundary layer behavior on continuous solid surfaces: I. Boundary layer equations for two dimensional and axisymmetric flow. AIChE J. 1961; 7, 26-8.

B Sakiadis. Boundary layer behavior on continuous solid surfaces: II. The boundary layer on a continuous flat surface. AIChE J. 1961; 7, 221-5.

L Howarth. On the Calculation of Steady Flow in the Boundary Layer near the Surface of a Cylinder in a Stream. H.M.S.O. Publisher, London, 1934.

P Gupta and A Gupta. Heat and mass transfer on a stretching sheet with suction or blowing. Can. J. Chem. Eng. 1977; 55, 744-6.

C Wang. The three‐dimensional flow due to a stretching flat surface. Phys. Fluids 1984; 27, 1915-7.

S Mishra and S Jena. Numerical solution of boundary layer MHD flow with viscous dissipation. The Sci. World J. 2014; 2014, 756498.

ME Ali and E Magyari. Unsteady fluid and heat flow induced by a submerged stretching surface while its steady motion is slowed down gradually. Int. J. Heat Mass Trans. 2007; 50, 188-95.

IH Andersson, JB Aarseth and BS Dandapat. Heat transfer in a liquid film on an unsteady stretching surface. Int. J. Heat Mass Trans. 2000; 43, 69-74.

BS Dandapat, B Santra and K Vajravelu. The effects of variable fluid properties and thermocapillarity on the flow of a thin film on an unsteady stretching sheet. Int. J. Heat Mass Trans. 2007; 50, 991-6.

E Elbashbeshy and M Bazid. Heat transfer over an unsteady stretching surface. Heat Mass Trans. 2004; 41, 1-4.

S Sharidan, T Mahmood and I Pop. Similarity solutions for the unsteady boundary layer flow and heat transfer due to a stretching sheet. Int. J. Appl. Mech. Eng. 2006; 11, 647-54.

A Ishak, R Nazar and I Pop. Heat transfer over an unsteady stretching permeable surface with prescribed wall temperature. Nonlinear Anal. Real World Appl. 2009; 10, 2909-13.

S Mukhopadhyay. Effect of thermal radiation on unsteady mixed convection flow and heat transfer over a porous stretching surface in porous medium. Int. J. Heat Mass Trans. 2009; 52, 3261-5.

S Mukhopadhyay. Effects of slip on unsteady mixed convective flow and heat transfer past a porous stretching surface. Nucl. Eng. Des. 2011; 241, 2660-5.

A Chamkha, AM Ali and MA Mansour. Similarity solution for unsteady heat and mass transfer from a stretching surface embedded in a porous medium with suction/injection and chemical reaction effects. Chem. Eng. Commun. 2010; 197, 846-58.

T Hayat and M Awais. Simultaneous effects of heat and mass transfer on time‐dependent flow over a stretching surface. Int. J. Numer. Meth. Fluids 2011; 67, 1341-57.

S Mukhopadhyay and RSR Gorla. Unsteady MHD boundary layer flow of an upper convected Maxwell fluid past a stretching sheet with first order constructive/destructive chemical reaction. J. Nav. Archit. Mar. Eng. 2012; 9, 123-33.

T Hayat, M Awais, A Safdar and AA Hendi. Unsteady three dimensional flow of couple stress fluid over a stretching surface with chemical reaction. Nonlinear Anal. Model. Control. 2012; 17, 47-59.

T Hayat, SA Shehzad and A Alsaedi. Soret and Dufour effects on magnetohydrodynamic (MHD) flow of Casson fluid. J. Appl. Math. Mech. 2012; 33, 1301-12.

M Mustafa, T Hayat, I Pop and A Aziz. Unsteady boundary layer flow of a Casson fluid due to an impulsively started moving flat plate. Heat Tran. Asian Res. 2011; 40, 563-76.

S Mukhopadhyay, P Ranjan De, K Bhattacharyya and GC Layek. Casson fluid flow over an unsteady stretching surface. Ain Shams Eng. J. 2013; 4, 933-8.

K Bhattacharyya, T Hayat and A Alsaedi. Analytic solution for magnetohydrodynamic boundary layer flow of Casson fluid over a stretching/shrinking sheet with wall mass transfer. Chin. Phys. B. 2013; 22, 024702.

K Bhattacharyya, T Hayat and A Alsaedi. Exact solution for boundary layer flow of Casson fluid over a permeable stretching/shrinking sheet. ZAMM Z. Angew. Math. Mech. 2014; 94, 522-8.

M Qasim and S Noreen. Heat transfer in the boundary layer flow of a Casson fluid over a permeable shrinking sheet with viscous dissipation. Eur. Phys. J. Plus. 2014; 129, 1-8.

A Bejan. Second-law analysis in heat transfer and thermal design. Adv. Heat Trans. 1982; 15, 1-58.

A Bejan. Entropy generation minimization: The new thermodynamics of finite‐size devices and finite‐time processes. J. Appl. Phys. 1996; 79, 1191-218.

O Mahian, S Mahmud and S Z Heris. Analysis of entropy generation between co-rotating cylinders using nanofluids. Energy 2012; 44, 438-46.

HF Oztop and K Al-Salem. A review on entropy generation in natural and mixed convection heat transfer for energy systems. Renew. Sust. Energ. Rev. 2012; 16, 911-20.

S Aïboud and S Saouli. Second law analysis of viscoelastic fluid over a stretching sheet subject to a transverse magnetic field with heat and mass transfer. Entropy 2010; 12, 1867-84.

S Aïboud and S Saouli. Entropy analysis for viscoelastic magnetohydrodynamic flow over a stretching surface. Int. J. Nonlinear Mech. 2010; 45, 482-9.

M Govindaraju, NV Ganesh, B Ganga and AK Abdul Hakeem. Entropy generation analysis of magneto hydrodynamic flow of a nanofluid over a stretching sheet. J. Egyptian Math. Soc. 2015; 23, 429-34.

LC Woods. The Thermodynamics of Fluid Systems. Clarendon Press Oxford, 1975.

MHAbolbashari, N Freidoonimehr, F Nazari and MM Rashidi. Entropy analysis for an unsteady MHD flow past a stretching permeable surface in nano-fluid. Powder Technol. 2014; 267, 256-67.

MM Rashidi, AB Parsa, L Shamekhi and E Momoniat. Entropy generation analysis of the revised Cheng-Minkowycz problem for natural convective boundary layer flow of nanofluid in a porous medium. Therm. Sci. 2015; 19, S169-78.

MM Rashidi, S Mahmud, N Freidoonimehr and B Rostami. Analysis of entropy generation in an MHD flow over a rotating porous disk with variable physical properties. Int. J. Exergy 2015; 16, 481-503.

MH Abolbashari, N Freidoonimehr, F Nazari and MM Rashidi. Analytical Modeling of Entropy Generation for Casson Nano-fluid Flow Induced by a Stretching Surface. Adv. Powder Technol. 2015; 26, 542-52.