# Heat removal from oscillating flow in a vertical annular channel

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## Abstract

In this study, heat removal from a surface, which is located into the reciprocating flow in a vertical annular liquid column, is investigated experimentally. The experiments are carried out for four different oscillation frequencies and three heat fluxes while the amplitude remains constant for all cases. Instantaneous and time-averaged surface and bulk temperature variations are presented. The cycle-averaged values are considered in the calculation of heat transfer using the experimental measurements. Heat removal from the cold surface due to the oscillating liquid column is determined in terms of Nusselt number. Based on the experimental data, an empirical equation is obtained for the cycle averaged Nusselt number as a function of kinetic Reynolds number.

## Keywords

Heat Transfer Nusselt Number Heat Removal Heat Transfer Enhancement Average Nusselt Number## List of symbols

*A*cross-sectional area of liquid column (m

^{2})*A*_{o}dimensionless oscillation amplitude (

*A*_{o}=*x*_{m}/*D*)*A*_{p}cross-sectional area of piston (m

^{2})*c*_{p}specific heat of fluid (kJ/kg-K)

*D*hydraulic diameter of test duct (m) (

*D*= 2(*r*_{2}−*r*_{1}) )*h*convective heat transfer coefficient (W/m

^{2}-K)*H*_{1}cycle-averaged enthalpies Eq. 6 (J)

*k*thermal conductivity (W/m-K)

*L*total distance from probe1 to exit (m)

*L*_{c}cooler length (m)

- ℓ
_{o} distance from probes to cooler (m)

*Pr*Prandtl Number (

*Pr*=*v*/α)*Q*_{k}total heat loss to environment over a cycle (J)

*Q*_{c}total heat transferred from water over a cycle (J)

*q*_{e}total wall heat flux given from heater (W)

*q*_{c}^{″}heat flux from control volume to cooler (W/m

^{2})*q*_{d}^{″}heat flux from glass tube to environment (W/m

^{2})*Ra*Rayleigh number (

*Ra*=*Gr**Pr*)*R*flywheel radius (m)

*Re*_{ω}kinetic Reynolds number \({{\left({\operatorname{Re} _{\omega} = {\omega D^{2}} \mathord{\left/ {\vphantom {{\omega D^{2}} \nu}} \right. \kern-\nulldelimiterspace} \nu} \right)}}\)

*r*radial coordinate

*r*_{1}inner radius of annulus (m)

*r*_{2}outer radius of annulus (m)

*x*_{m}oscillation amplitude (m)

*t*time (s)

- Δ
*t* relative time (s) (this time is used for time periodic state)

*T*temperature

*T*_{b}bulk temperature (°C)

*T*_{1}probe temperatures (°C)

*T*_{2}exit temperatures from control volume (°C)

*T*_{wc}space-cycle averaged wall temperatures (°C)

*u*mean velocity (m/s)

*u*_{m}maximum velocity (m/s)

*y*vertical coordinate

- Δ
*y* distance from initiative of cooler (m)

## Greek symbols

- α
thermal diffusivity (m

^{2}/s)- δ
momentum boundary layer thickness (m)

- ρ
fluid density (kg/m

^{3})- ω
angular frequency (rad/s)

*v*kinematic viscosity (m

^{2}/s)

## Subscripts

- l
liquid

- a
air

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