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Flow and heat transfer due to impulsive motion of a cone in a viscous fluid

Impuls-und Wärmeübertragung an einem plötzlich in Bewegung versetzten Konus in einem zähen Fluid

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Abstract

Numerical solution has been obtained for the development of the flow over a cone which is impulsively set into motion. Initially the flow is described by the solution of Rayleigh and then it tends to the ultimate steady state solution of Falkner-Skan equation. But due to the leading edge effect the semi-similar equation describing the transient flow changes its character after certain time and the solution depends also on the ultimate steady state solution of the Falkner-Skan equation. A second-order upwind difference scheme has been used for discretisation. The temperature distribution and heat transfer has also been obtained for constant wall temperature as well as for constant heat flux at the wall. With the increase ofm, Falkner-Skan parameter, the magnitude of skin friction and wall heat transfer increases. It has been found that form≥−0.275 flow separation does not occur.

Zusammenfassung

Es wird eine numerische Lösung für die sich entwickelnden Strömungs-und Temperaturfelder an einem plötzlich in Bewegung versetzten Konus angegeben. Anfänglich läßt sich die Strömung durch die Lösung von Rayleigh beschreiben, im stationären Endzustand durch die Lösung der Falkner-Skan Gleichung. Wegen des Eintrittseffekts an der Konusstirn ändert die den nichtstationären Strömungszustand beschreibende halb-ähnliche Gleichung nach einer bestimmten Zeit ihren Charakter und die Lösung hängt zusätzlich von der stationären Endlösung der Falkner-Skan Gleichung ab. Für die Diskretisierung wird ein rückseitiges Differenzschema zweiter Ordnung verwendet. Die Berechnung des Temperaturfeldes und des Wärmeübergangs erfolgt sowohl für konstante Wandtemperatur, wie für konstanten Wärmefluß. Mit zunehmenden Falkner-Skan Parameterm steigen auch Wandreibung und Wärmeübertragung. Fürm≥−0,275 tritt keine Ablösung auf.

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Abbreviations

C p :

specific heat at a constant pressure

f :

velocity function

F :

non-dimensional velocity function

k :

thermal conductivity

m :

Falkner-Skan parameter

Pr :

Prandtl number

t :

time

t * :

=(m+3)×t/3

T :

temperature

u :

velocity inx direction

U :

free stream velocity

v :

velocity iny direction

V :

stands for eitherF or θ

x :

coordinate parallel to the wall

y :

coordinate normal to the wall

α i ,i=1, 2, 3, 4, 5, 6:

are variable co-efficients

η:

semi-similar variable

θ:

non-dimensional temperature function

μ:

co-efficient of viscosity

v :

kinematic viscosity

ζ:

semi-similar variable

τ:

non-dimensional time

ψ:

stream function

e :

at infinity

i, j :

at grid point (i, j)

w :

at the wall

η:

derivative with respect to η

ξ:

derivative with respect to ξ

′:

derivative with respect to η

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology, 721302, Kharagpur, India

    S. Bhattacharyya, A. Pal & N. Datta

Authors
  1. S. Bhattacharyya
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  2. A. Pal
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  3. N. Datta
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Bhattacharyya, S., Pal, A. & Datta, N. Flow and heat transfer due to impulsive motion of a cone in a viscous fluid. Heat and Mass Transfer 30, 303–307 (1995). https://doi.org/10.1007/BF01463920

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  • DOI: https://doi.org/10.1007/BF01463920

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