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Research Papers: Natural and Mixed Convection

Numerical Study of Natural Convection in a Ferrofluid-Filled Corrugated Cavity With Internal Heat Generation

[+] Author and Article Information
Fatih Selimefendigil

Associate Professor
Department of Mechanical Engineering,
Celal Bayar University,
Manisa 45140, Turkey
e-mail: fatih.selimefendigil@cbu.edu.tr

Hakan F. Öztop

Professor
Department of Mechanical Engineering,
Technology Faculty,
Firat University,
Elaziğ 23119, Turkey
e-mail: hfoztop1@gmail.com

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received December 2, 2014; final manuscript received June 30, 2016; published online August 2, 2016. Assoc. Editor: Dr. Portonovo S. Ayyaswamy.

J. Heat Transfer 138(12), 122501 (Aug 02, 2016) (14 pages) Paper No: HT-14-1777; doi: 10.1115/1.4034063 History: Received December 02, 2014; Revised June 30, 2016

In this paper, numerical simulations for the natural convection in a ferrofluid-filled corrugated cavity with internal heat generation under the influence of a magnetic dipole source were performed. The cavity is heated from below and cooled from above while vertical side walls are assumed to be adiabatic. A magnetic dipole source was located under the bottom heated wall. The governing equations were solved by Galerkin weighted residual finite-element formulation. The influence of external Rayleigh number (between 104 and 5 × 105), internal Rayleigh number (between 104 and 5 × 106), magnetic dipole strength (between 0 and 4), horizontal (between 0.2 and 0.8) and vertical (between −5 and −2) locations of the magnetic dipole source on fluid flow, and heat transfer are numerically investigated. It was observed that depending on heating mechanism (the external or internal heating), the presence of corrugation of the bottom wall either enhances or deteriorates the absolute value of the averaged heat transfer. The strength and locations of the magnetic dipole source affect the distribution of the flow and thermal patterns within the cavity for both flat and corrugated wall cavity. The net effect of the complicated interaction of the internal heating, external heating, and ferroconvection of magnetic source results in heat transfer enhancement with increasing values of magnetic dipole strength. Wall corrugation causes more enhancement of averaged heat transfer and this is more pronounced for low values of vertical location of magnetic source.

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Figures

Grahic Jump Location
Fig. 2

Code validation against the existing numerical results of Ref. [31]. (a) Velocity profiles at the middle of the enclosure and (b) local Nusselt number distributions along heated wall at Rayleigh number of 105.

Grahic Jump Location
Fig. 1

Geometry and the boundary conditions for the cavity with internal heat generation under the influence of a magnetic dipole source

Grahic Jump Location
Fig. 3

Effects of varying external Rayleigh numbers on the streamlines (a)–(f) and isotherms (g)–(l) for flat and corrugated cavity (RaI=106, γ=4, A=0.5, and B=−2): (a) flat, RaE = 104, (b) flat, RaE = 105, (c) flat, RaE = 5 × 105, (d) corrugated, RaE = 104, (e) corrugated, RaE = 105, (f) corrugated, RaE = 5 × 105, (g) flat, RaE = 104, (h) flat, RaE = 105, and (i) flat, RaE = 5 × 105

Grahic Jump Location
Fig. 4

Variation of local and averaged Nusselt number for various external Rayleigh numbers along the heated wall for flat and corrugated cavity (RaI=106, γ=4, A=0.5, and B=−2): (a) local Nusselt number, flat, (b) local Nusselt number, corrugated, and (c) averaged Nusselt number

Grahic Jump Location
Fig. 5

Effects of varying internal Rayleigh numbers on the streamlines (a)–(f) and isotherms (g)–(l) for flat and corrugated cavity (RaE=105, γ=2, A=0.5, and B=−2):(a) flat, RaI = 104, (b) flat, RaI = 105, (c) flat, RaI = 106, (d) corrugated, RaI = 104, (e) corrugated, RaI = 105, (f) corrugated, RaI = 106, (g) flat, RaI = 104, (h) flat, RaI = 105, and (i) flat, RaI = 106

Grahic Jump Location
Fig. 6

Local and averaged Nusselt number along the heated wall for various internal Rayleigh numbers (RaE=105, γ=2, A=0.5, and B=−2):(a) local Nusselt number, flat, (b) local Nusselt number, corrugated, and (c) averaged Nusselt number

Grahic Jump Location
Fig. 7

Effect of varying magnetic dipole strength on the streamlines (a)–(f) and isotherms (g)–(l) (RaE=5×104, RaI=105, γ=2, A=0.5, and B=−2): (a) flat, γ = 0, (b) flat, γ = 2, (c) flat, γ = 4, (d) corrugated, γ = 0, (e) corrugated, γ = 2, (f) corrugated, γ = 4, (g) flat, γ = 0, (h) flat, γ = 2, and (i) flat, γ = 4

Grahic Jump Location
Fig. 8

Variation of local and averaged Nusselt number for various values of magnetic dipole strength along the heated wall for flat and corrugated cavity (RaE=5×104, RaI=105, γ=2,A=0.5, and B=−2):(a) local Nusselt number, flat, (b) local Nusselt number, corrugated, and (c) averaged Nusselt number

Grahic Jump Location
Fig. 9

Streamlines (a)–(f) and isotherms (g)–(l) for various horizontal positions of the magnetic dipole source for flat and corrugated cavity (RaE=5×104, RaI=105, γ=2.5, andB=−2):(a) flat, A = 0.2, (b) flat, A = 0.5, (c) flat, A = 0.8, (d) corrugated, A = 0.2, (e) corrugated, A = 0.5, (f) corrugated, A = 0.8, (g) flat, A = 0.2, (h) flat, A = 0.5, and (i) flat, A = 0.8

Grahic Jump Location
Fig. 10

Local and averaged Nusselt number distributions along the heated wall for various horizontal positions of the magnetic dipole source for flat and corrugated cavity (RaE=5×104, RaI=105, γ=2.5, and B=−2):(a) local Nusselt number, flat, (b) local Nusselt number, corrugated, and (c) averaged Nusselt number

Grahic Jump Location
Fig. 11

Streamlines (a)–(f) and isotherms (g)–(l) for various vertical locations of the magnetic dipole source for flat and corrugated cavity (RaE=5×104, RaI=105, γ=2.5, and A=0.5): (a)flat, B=−2, (b) flat, B=−3, (c) flat, B=−5, (d) corrugated, B=−2, (e) corrugated, B=−3, (f) corrugated, B=−5, (g) flat, B=−2, (h) flat, B=−3, and (i) flat, B=−5

Grahic Jump Location
Fig. 12

Local and averaged Nusselt number distributions along the heated wall for various vertical locations of the magnetic dipole source for flat and corrugated cavity (RaE=5×104,RaI=105, γ=2.5, and B=−2): (a) local Nusselt number, flat, (b) local Nusselt number, corrugated, and (c) averaged Nusselt number

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