Advertisement

Wärme - und Stoffübertragung

, Volume 14, Issue 3, pp 165–171 | Cite as

Turbulent boundary layer heat transfer for a constant property particle-laden gas flow

  • T. K. Bose
Article

Abstract

Solution of a turbulent boundary layer for a constant property, particle-laden gas flow is obtained by a differential method. A dimensionless analysis shows importance of an interaction parameter in increasing heat flux. Boundary layer analysis is done in usual manner by transforming partial differential equations and solution is started at the leading edge by Runge-Kutta method. Velocity and temperature profiles at downstream planes for gas and particles are calculated by an implicit finite-difference iterative procedure, and numerical results are compared with available experimental data.

Keywords

Heat Transfer Boundary Layer Heat Flux Turbulent Boundary Layer Differential Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Nomenclature

C

density-viscosity ratio, Eqs.(13b,c)

c

specific heat, J/kg°K

cpg

isobaric specific heat of gas, J/kg°K

cs

specific heat of solid particles, J/kg° K

c*

dimensionless specific heat=cs/cpg

cf

friction coefficient, Eq. (20a)

ds

average particle diameter, m

F1-F5

functions defined in Eqs. (13e-i)

f

dimensionless stream function

K

constant defined in Eq.(13a)

k

heat conductivity coefficient, W/m°K

M

loading ratio=ρse use/(ρge uge)

N1, N2

characteristic number

Pr

Prandtl number

Prt

turbulent Prandtl number

p

gas pressure, N/m2 or bar

q

heat flux on wall, W/m2

Re

Reynolds number

Sct

turbulent Schmidt number

St

Stanton number

T

static temperature, °K

stagnation temperature=T+(u2 /2c), °K

*

dimensionless temperature

TL

integral time scale, sec

u,v

velocity components in x,y-directions, m/sec

V

dimensionless · normal velocity=\( - \sqrt {2\xi } \psi _\xi \)

x,y

coordinate directions along and normal to surface, m

α14

constants

β

pressure gradient parameter, Eq.(13d)

δ

boundary layer thickness, m

ɛm

eddy viscosity coefficient, m2/sec

ɛh

eddy conductivity coefficient, m2 /sec

ɛpg

eddy density diffusion coefficient, m2/sec

Λg

spatial coordinate, m

μ

(gas) dynamic viscosity coefficient, kg/msec

ν

(gas) kinematic viscosity coefficient

ρ

density, kg/m3

\(\tilde \rho \)

density of material, kg/m3

ψ

stream function

ξ, η

transformed coordinates, Eqs.(11a,b)

τ

relaxation time

\(\tilde \tau \)

shear stress

Subscripts and Superscripts

e

property at edge of boundary layer

g

gas

s

solid particles

w

wall

x,y

partial derivative with respect to x,y coordinate, respectively

ξ, η

partial derivative with respect to ξ, η coordinate, respectively

()t

time-dependent variable

()

time-averaged variable

Grenzschichtwärmeübertragung für eine turbulente Gasströmung mit festen Partikeln und konstanten Stoffeigenschaften

Zusammenfassung

Eine Differentialmethode ermöglicht die Lösung einer turbulenten Grenzschichtströmung konstanter Eigenschaften mit Feststoffpartikeln. Die durchgeführte Dimensionsanalyse zeigt die Bedeutung eines Wechselwirkungsparameters für die Erhöhung der Wärmestromdichte. Die Grenzschichtbetrachtung wird in üblicher Weise durch eine Transformation der partiellen Differentialgleichungen durchgeführt, mit Lösungsbeginn an der Anlaufkante nach dem Runge-Kutta Verfahren. Geschwindigkeits- und Temperatur-Profile für die Gas- und Partikelströmung werden in stromab gelegenen Ebenen mittels eines impliziten finiten Differenzenverfahrens iterativ bestimmt. Die numerischen Ergebnisse werden mit verfügbaren Experimenten verglichen.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Soo, S.L.: Fluid Dynamics of Multiphase Systems. Waltham/Mass: Blaisdell Publ. Co. (1967)Google Scholar
  2. 2.
    Depew, C.A.; Kramer, T. J.: Heat transfer to flowing gas-solid mixtures, Advances in Heat Transfer, Vol. 9. New York: Academic Press (1973)Google Scholar
  3. 3.
    Wallis, G.B.: One-dimensional Two-phase Flow. New York: McGraw Hill (1969)Google Scholar
  4. 4.
    Brandon, C.A.; Grizzle, T.A.: A test of similarity variable for dilute fluid-solid heat transfer, Progress in Heat and Mass Transfer, Vol.6. New York: Pergamon Press (1972)Google Scholar
  5. 5.
    Spalding, D.B.: Review of the book Turbulent Shear Flows. Intern. J. Heat and Mass Transfer 23 (1980) 580Google Scholar
  6. 6.
    Cebeci, T.; Smith, A.M.O.: Turbulent Boundary Layers. New York: Academic Press (1975)Google Scholar
  7. 7.
    Bose, T.K.: Turbulent boundary layers with large free-stream to wall temperature ratio. Wärme- und Stoffübertragung 12 (1979) 211–220Google Scholar
  8. 8.
    Bose, T.K.: Comparison of rocket nozzle heat transfer calculation methods. J. Spacecraft and Rockets 15 (1978) 253–255Google Scholar
  9. 9.
    Lees, L.: Laminar heat transfer over blunt-nosed bodies at hypersonic speeds. Jet Propulsion 26 (1956) 259–269Google Scholar
  10. 10.
    Blottner, F.N.: Finite difference methods of solution of the boundary layer equation. AIAA J. 8 (1970) 193–205Google Scholar
  11. 11.
    Melville, W.K.; Bray, K.N.C.: A model of the two-phase turbulent jet. Intern. J. Heat and Mass Transfer 22 (1979) 647–657Google Scholar
  12. 12.
    Hinze, J.O.: Turbulence. New York: McGraw Hill (1975)Google Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • T. K. Bose
    • 1
  1. 1.Indian Institute of TechnologyMadrasIndia

Personalised recommendations