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Research Papers: Natural and Mixed Convection

Effect of Thermal Conductivity and Thickness of the Walls on the Natural Convection in a Horizontal Viscoelastic Jeffreys Fluid Layer

[+] Author and Article Information
Ildebrando Pérez-Reyes

Facultad de Ciencias Químicas,
Universidad Autónoma de Chihuahua,
Nuevo Campus Universitario,
Circuito Universitario S/N,
Chihuahua, 31125, México
e-mail: ildebrando3@gmail.com

Luis Antonio Dávalos-Orozco

Departamento de Polímeros,
Instituto de Investigaciones en Materiales,
Universidad Nacional Autónoma de México,
Ciudad Universitaria,
Circuito Exterior S/N, Delegación Coyoacán,
México D. F. 04510, México
e-mail: ldavalos@unam.mx

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received December 17, 2017; final manuscript received July 24, 2018; published online August 28, 2018. Assoc. Editor: Zhixiong Guo.

J. Heat Transfer 140(12), 122501 (Aug 28, 2018) (9 pages) Paper No: HT-17-1754; doi: 10.1115/1.4041048 History: Received December 17, 2017; Revised July 24, 2018

It is a common practice to use ideal thermal boundary conditions to investigate natural convection. These correspond to very good conducting walls and to very bad conducting walls. In particular, this has been the case in natural convection of viscoelastic fluids. In this paper, these conditions are generalized by taking into account the finite thermal conductivities and thicknesses of the walls in the natural convection of a viscoelastic Jeffreys fluid heated from below. The goal is to present more realistic results related to experimental conditions. The critical Rayleigh number Rc, the frequency of oscillation ωc, and the wavenumber kc have been plotted varying the properties of the walls from the case of very good thermal conductivity to very poor thermal conductivity. In order to understand the convective phenomena, two parameters are fixed and the other one varied among the nondimensional relaxation time F, the relative retardation time E, and the Prandtl number Pr of the viscoelastic fluid. The role of the relative retardation time E on the thermal instability is discussed in detail.

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References

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Figures

Grahic Jump Location
Fig. 1

Here, Pr = 1 and F = 0.1. Curves for E = 0.05: (a) Rc, (b) kc, and (c) ωc against X, and curves for E = 0.1: (d) Rc, (e) kc, and (f) ωc against X. D = 0.1 and D = 100 are indicated by dashed and solid lines, respectively. For E = 0.05, the codimension-two points (squared symbols) are located at (X=15,Rc=1070.2453,kc=4.93,ωc=12.69) and (X=2.5,Rc=1072.4573,kc=4.91,ωc=12.69) for D = 0.1 and D = 100, respectively. For E = 0.1, the codimension-two points (squared symbols) are located at (X=6.5,Rc=1208.37,kc=4.63,ωc=10.7046) and (X=1.4,Rc=1218.412,kc=4.65,ωc=10.6711) for D = 0.1 and D = 100, respectively.

Grahic Jump Location
Fig. 2

Here, Pr = 1 and F = 100. Curves for E = 0.05: (a) Rc, (b) kc, and (c) ωc against X, and curves for E = 0.1: (d) Rc, (e) kc, and (f) ωc against X. D = 0.1 and D = 100 are indicated by dashed and solid lines, respectively.

Grahic Jump Location
Fig. 3

Here, Pr = 10 and F = 0.1. Curves for E = 0.05: (a) Rc, (b) kc, and (c) ωc against X, and curves for E = 0.1: (d) Rc, (e) kc, and (f) ωc against X. D = 0.1 and D = 100 are indicated by dashed and solid lines, respectively. For E = 0.1, the codimension-two points (squared symbols) are located at (X=90,Rc=869.3051,kc=4.79,ωc=29.6799) and (X=13,Rc=859.6092,kc=4.76,ωc=30.0254) for D = 0.1 and D = 100, respectively.

Grahic Jump Location
Fig. 4

Here, Pr = 100 and F = 0.1. Curves for E = 0.05: (a) Rc, (b) kc, and (c) ωc against X, and curves for E = 0.1: (d) Rc, (e) kc, and (f) ωc against X. D = 0.1 and D = 100 are indicated by dashed and solid lines, respectively. For E = 0.05, the codimension-two points (squared symbols) are located at (X=315,Rc=799.4064,kc=4.75,ωc=56.6341) and (X=33,Rc=794.3594,kc=4.73,ωc=56.9388) for D = 0.1 and D = 100, respectively. For E = 0.1, the codimension-two points (squared symbols) are located at (X=40,Rc=937.7560,kc=4.5,ωc=35.0395) and (X=7,Rc=926.9811,kc=4.48,ωc=35.6971) for D = 0.1 and D = 100, respectively.

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