Theoretical study of vibrating effect on heat transfer in laminar flow

Abstract

Green’s function method was adopted to study the problem of vibrating effect on heat transfer in laminar flow with constant flux and the influence of Prandtl number and the vibrating frequency on the heat transfer characteristics was investigated. The results show that the variation of the frequency leads to a different distribution of the unsteady velocity and temperature; with a lower frequency, the vibrating will weaken the heat transfer, but the heat transfer will be enhanced with a higher frequency. A lower Prandtl number leads to a strenuous variation of heat transfer.

Key words： vibrating; full developed; heat transfer

Acknowledgements

This work was supported by the National Basic Research Program of China (No. 2007CB206903).

Notation
a	thermal diffusivity/(m2·s-1)
i	imaginary factor
J_{\mathrm{0}}	Bessel function of the first kind of order 0
J_{\mathrm{1}}	Bessel function of the first kind of order 1
N_{\mathrm{0}}	Bessel function of the second kind of order 0
N_{\mathrm{1}}	Bessel function of the second kind of order 1
Nu	Nusselt number
p	pressure/Pa
Pr	Prandtl number
q	heat flux/(W·m-2)
r	radius coordinate/m
r_{\mathrm{0}}	tube radius/m
Re	Reynolds number
t	time/s
T	temperature/K
u	velocity component in axial direction/(m·s-1)
x	axial coordinate/m
Greek symbols
\beta	dimensionless amplitude of vibration parameter
\theta	temperature difference/K
\mu	viscosity/(kg·m-1·s-1)
\nu	kinematic viscosity/(m2·s-1)
\rho	density/(K·m-3)
\omega	angular velocity/(rad· s-1)
\ast	dimensionless quantity

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