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Stability of natural convective motion induced by internal heat sources in a slot with a moving sidewall

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Summary

The stability of plane parallel convective motion in an inclined slot induced by uniformly distributed heat sources is studied. One of the side walls of the slot is assumed to move on either direction. The spectral collocation method is employed to solve the problem. Depending on the Prandtl number, angle of inclination and direction and speed of the sidewall movement, the stability boundary gets affected. In general the flow is stabilized for −60°≤α≤60°, α being the angle of inclination. Multiple jumps occur in the critical wavenumber when α reaches 45° and the sidewall is moving up.

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Abbreviations

c p :

specific heat capacity

g :

acceleration due to gravity

Gr:

Grashof number

h :

half slot width

k :

wave number

n :

number of collocation points

\(\hat n\) :

vertical unit vector

p :

pressure

Pr:

Prandtl number

Q :

volume density of internal heat sources

Re:

Reynolds number

t :

nondimensional time

T :

nondimensional temperature

u 0 :

dimensional velocity of moving side wall

\(\bar \upsilon\) :

nondimensional velocity vector

x :

coordinate axis normal to the slot

z :

coordinate axis parallel to the slot

\(\hat k\) :

unit vector in thez direction

α:

angle of inclination of the slot

β:

coefficient of thermal expansion

ν:

kinematic viscosity

∇:

Laplacian operator

ϱ:

density

ϰ:

thermal diffusivity

Ψ:

dimensionless stream function

λ:

complex eigenvalue

*:

dimensional quantity

(i):

ith derivative

0:

basic state

References

  1. Lennie, T. B., McKenzie, D. P., Moore, D. R. Weiss, N. O.: The breakdown of steady convection. J. Fluid Mech.188, 47–85 (1988).

    Google Scholar 

  2. Gershuni, G. Z., Zhukhovitskii, E. M., Iakimov, A. A.: On stability of plane-parallel convective motion due to internal heat sources. Int. J. Heat Mass Transfer17, 717–726 (1974).

    Google Scholar 

  3. Gershuni, G. Z., Zhukhovitskii, E. M., Iakimov, A. A.: Two kinds of instability of stationary convective motion induced by internal heat sources. PMM37, 544–548 (1973).

    Google Scholar 

  4. Mohammad, A. A., Viskanta, R.: Stability of lid-driven shallow cavity heated from below. Int. J. Heat Mass Transfer32, 2155–2166 (1989).

    Google Scholar 

  5. Chen, J. C., Hsieh, C. K.: Linear stability of natural convection in a tall vertical slot with a moving sidewall. Int. J. Heat Mass Transfer36, 1471–1476 (1993).

    Google Scholar 

  6. Chen, Y. C., Chung, J. N.: The linear stability of mixed convection in a vertical channel flow. J. Fluid Mech.325, 29–51 (1996).

    Google Scholar 

  7. Chen, Y. C., Chung, J. N.: Stability of mixed convection in a differentially heated vertical channel. J. Heat Transfer120, 127–132 (1998).

    Google Scholar 

  8. Yao, L. S., Rogers, B. B.: Mixed convection in an annulus of large aspect ratio. J. Heat Transfer111, 683–689 (1989).

    Google Scholar 

  9. Kolyshkin, A. A., Vaillancourt, R.: On the stability of nonisothermal circular Couette flow. Phys. Fluids A5, 3136–3146 (1993).

    Google Scholar 

  10. Canuto, C., Hussaini, M. Y., Quarteroni, A., Zang, T. A.: Spectral methods in fluid dynamics. Berlin: Springer 1988.

    Google Scholar 

  11. Moler, C. B., Stewart, G. W.: An algorithm for generalized matrix eigenvalue problems. SIAM J. Numer. Anal.10, 241–256 (1973).

    Google Scholar 

  12. Golub, G. H., Loan, V.: Matrix computations. Oxford: North Oxford Academic Publ. 1986.

    Google Scholar 

  13. Gershuni, G. Z.: On the stability of plane convective motion of a liquid. Zh. Tech. Fiz.23, 1838–1844 (1953).

    Google Scholar 

  14. Hart, J. E.: Stability of the flow in a differentially heated inclined box. J. Fluid Mech.47, 547–576 (1971)

    Google Scholar 

  15. Gill, A. F., Davey, A.: Instabilities of a buoyancy-driven system. J. Fluid Mech.75, 775–793 (1969).

    Google Scholar 

  16. Ozisik, M. N.: Thermal stability of a vertical fluid layer with volumetric energy sources. Washington: Hemisphere, 1985.

    Google Scholar 

  17. Sparrow, E. M., Goldstein, R. J., Jonsson, V. K.: Thermal instability in a horizontal fluid layer: effect of boundary conditions and nonlinear temperature profile. J. Fluid Mech.18, 513–528 (1964).

    Google Scholar 

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  1. S. Saravanan & P. Kandaswamy

    Present address: Department of Mathematics, Bharathiar University, 641 046, Coimbatore, India

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    1. S. Saravanan
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    2. P. Kandaswamy
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    Saravanan, S., Kandaswamy, P. Stability of natural convective motion induced by internal heat sources in a slot with a moving sidewall. Acta Mechanica 152, 203–215 (2001). https://doi.org/10.1007/BF01176955

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    • DOI: https://doi.org/10.1007/BF01176955

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