Skip to main content
SpringerLink
Log in

Effects of viscous dissipation on heat transfer in an oscillating flow past a flat plate

  • Published:
Applied Scientific Research Aims and scope Submit manuscript

Abstract

Theoretical investigation has been carried out of laminar thermal boundary layer response to harmonic oscillations in velocity associated with a progressive wave imposed on a steady free stream velocity and convected in the free stream direction. Series solutions are derived both to velocity and temperature field and the resulting equations are solved numerically. The functions affecting the temperature field are shown graphically for different values of Prandtl number. It is observed that there is more reduction in the rate of heat transfer for P r<1 and a rise in the rate of heat transfer for P r>1 due to the presence of oscillatory free-stream.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

u, v :

velocity components in the x and y direction

x, y :

Cartesian coordinate axes

t :

time

U, U 0 :

instantaneous value of and mean free stream velocity

ρ :

density of fluid

ν :

kinematic viscosity

T, T w, T∞ :

temperature of the fluid, wall and free stream fluid

c p :

specific heat at constant pressure

α :

thermal diffusivity

λ :

amplitude of free stream velocity

ω :

frequency

θ p :

non-dimensional temperature (T−T ∞/T w−T ∞)

P r :

Prandtl number (μc p/K)

E c :

Eckert number (U 20 /c p(T w−T ∞))

β :

a parameter (\((\sqrt {\omega x/U_0 } )\))

δ 0 :

boundary layer thickness of the oscillation of a harmonic oscillation of frequency θ(\((\sqrt {2v/\omega } )\))

δ :

ordinary boundary layer thickness (\((\sqrt {vx/\bar U} )\))

Ū :

time-averaged, time-independent external velocity

A, B, C, D, E, K, L, M, N, P :

functions used in expansion for u and θ

Nu :

Nusselt number (hx/k)

Δθ :

T w−% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8V4rqqrFfpeea0Jc9yq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepGe9fr-xfr-x% frpeWZqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaacIcadaGcaa% qaaiaadAhacaWG4bGaai4laiqadwfagaqeaaWcbeaakiaacMcaaaa!3CA6!\[(\sqrt {vx/\bar U} )\]

k :

thermal conductivity

References

  1. Lighthill, M. J., Proc. Roy. Soc. A224 (1954) 1.

    Google Scholar 

  2. Lin, C. C., Proc. 9th Int. Congress Appl. Mech. 4 (1957) 155.

    Google Scholar 

  3. Hill, P. G. and A. H. Stenning, Trans. ASME, J. Basic Eng., 82D (1960) 593.

    Google Scholar 

  4. Kestin, J., P. F. Maeder, and H. E. Wang, Appl. Sci. Res. A10 (1961) 1.

    Google Scholar 

  5. Patel, M. H., Proc. Roy. Soc. A327 (1975) 99.

    Google Scholar 

  6. Schlichting, H., Boundary layer theory, McGraw Hill, 1960, p. 234 and 331.

Download references

Author information

Authors and Affiliations

  1. Simon Eng. Laboratories, Manchester Univ., Manchester, UK

    H. S. Takhar

  2. Dept. of Math., Indian Inst. of Techn., Bombay - 76, India

    V. M. Soundalgekar

Authors
  1. H. S. Takhar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. M. Soundalgekar
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Takhar, H.S., Soundalgekar, V.M. Effects of viscous dissipation on heat transfer in an oscillating flow past a flat plate. Appl. Sci. Res. 33, 101–111 (1977). https://doi.org/10.1007/BF00383195

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00383195

Keywords

Search

Navigation