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Thermal performance of a vertical fin in a non-Newtonian ambient medium

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Abstract

The problem of free convection from a fin situated in a quiescent non-Newtonian medium exhibiting power law relation between the rate of angular deformation and the shear stress is theoretically investigated. The equation of thermal diffusion in the fin is coupled to the constitutive equations of the medium set to motion due to the buoyant forces. The analysis is accomplished by treating equations in integral form. The results obtained indicate profound influence of the fin parameter and the flow behaviour index of the power law on the local and average heat transfer coefficients. The results further reveal that for a wide range of fin parameters, the local heat transfer coefficients are exhibiting non-monotonically varying characteristics along the length of the fin. The results are manipulated by the method of regression to compute the average heat transfer coefficient as a function of the modified Rayleigh number, fin parameter and the flow behaviour index.

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Abbreviations

A :

cross sectional area of the fin, m2

E :

efficiency of the fin defined in equation (29)

f :

function variable defined in equation (16)

g :

acceleration due to gravity, m/s2

h :

local heat transfer coefficient, W/m2−K

h m :

average heat transfer coefficients, W/m2−K

\(\bar h_{{\text{iso}}}\) :

average heat transfer coefficient for isothermal plate when T W=T W,L for 0<x<L, W/m2−K

k :

thermal conductivity, W/m−K

L :

length of the fin, m

M :

fin parameter defined in equation (15)

n :

flow behaviour index

Nu:

local Nusselt number, hL/k

Nu m :

average Nusselt number, h m L/k

Pr m :

modified Prandtl number defined in equation (18)

P :

perimeter of the fin, m

Q fin :

heat dissipation at the base of the fin, i.e., at x=L

Q iso :

heat removal at the lateral surface of the fin under isothermal conditions

Ra*:

modified Rayleigh number defined in equation (14)

T :

temperature

T + :

dimensionless temperature (T w−T ∞)/(T w,L−T ∞)

u x :

characteristic velocity appearing in equation (9)

u, v :

x and y components of velocity respectively

x, y, z :

position coordinates

x + :

position of the base of the infinitely long fin as shown in Fig. 1b

x + R :

x R /L (Fig. 1b)

α :

thermal diffusivity, m2/s

β :

coefficient of thermal expansion, K−1

δ :

thickness of the boundary layer, m

μ :

consistency index for power-law fluid, N · sn/m2

ϱ :

density of the fluid, kg/m3

ν :

μ/ϱ, N · sn · m/kg

φ :

dimensionless velocity function defined in equation (17)

η :

dimensionless space variable, (x/L)

θ w :

(T w−T ∞), K

∞:

medium

iso:

isothermal plate

L:

fluid

w:

wall

w, L:

base of the fin

References

  1. G.D. Raithby and K.G.T. Hollands, A general method of obtaining approximate solutions to laminar and turbulent free convection problems. In: James P. Hartnett and Thomas F. Irvine, Jr. (eds.) Advances in Heat Transfer. Academic Press, Vol. 11 (1975) pp. 265–315.

  2. A.J. Ede, Advances in free convection. In: J.P. Hartnett and T.F. Irvine, Jr. (eds.) Advances in Heat Transfer. Academic Press, Vol. 4 (1967) pp. 1–64.

  3. Y. Jaluria, Natural Convection Heat and Mass Transfer. Pergamon Press, New York (1980).

    Google Scholar 

  4. Y.I. Cho and James P. Hartnett, Non-Newtonian fluids in circular pipe flow. In: J.P. Hartnett and T.F. Irvine, Jr. (eds.) Advances in Heat Transfer. Academic Press, Vol. 15 (1982) pp. 59–134.

  5. A.V. Shenoy and R.A. Mashelkar, Thermal convection in Non-Newtonian fluids. In: J.P. Hartnett and T.F. Irvine, Jr. (eds.) Advances in Heat Transfer. Academic Press, Vol. 15 (1982) pp. 142–223.

  6. C. Tien, Laminar natural convection heat transfer from vertical plate to power-law fluid. Appl. Sci. Res. Sect. A 17 (1967) 233–248.

    Google Scholar 

  7. A. Acrivos, A theoretical analysis of Laminar natural convection heat transfer to non-Newtonian fluids. AIChEJ. 6 (1966) 584.

    Google Scholar 

  8. E.M. Sparrow and S. Acharya, A natural convection fin with a solution-determined non-monotonically varying heat transfer coefficient. J. Heat Transfer 103 (1981) 218–225.

    Google Scholar 

  9. I.G. Reilly, C. Tien and M. Adelman, Experimental study of natural convective heat transfer from a vertical plate in a non-Newtonian fluid. Can. J. Chem. Engg. 43 (1965) 157.

    Google Scholar 

  10. S. Kakac, Y. Yener and E. Atesoglu, The effects of the temperature-dependent fluid properties on natural convection — summary and review. In: S. Kakac, W. Aung and R. Viskanta (eds.) Natural Convection — Fundamentals and Applications. Hemisphere Publishing Corporation (1985) pp. 729–773.

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Author notes

  1. V. Dharma Rao

    Present address: Department of Chemical Engineering, Andhra University, Waltair

Authors and Affiliations

  1. Department of Mechanical Engineering, College of Engineering, Andhra University, 530 003, Visakhapatnam, India

    P. K. Sarma, T. Subrahmanyam & V. Dharma Rao

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  1. P. K. Sarma
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  2. T. Subrahmanyam
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  3. V. Dharma Rao
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Sarma, P.K., Subrahmanyam, T. & Rao, V.D. Thermal performance of a vertical fin in a non-Newtonian ambient medium. Appl. Sci. Res. 45, 319–337 (1988). https://doi.org/10.1007/BF00457065

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  • DOI: https://doi.org/10.1007/BF00457065

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