Influence of Vibration on Free Convection Heat transfer from Sinusoidal Surface

The influence of forced vibration on the free convection heat transfer from a sinusoidal surface has been experimentally investigated in this paper. A copper plate of [350×150×10 mm] length, width and thickness respectively has been used as a test sample where, the upper surface of this plate is manufactured by a wire-cutting machine as a sinusoidal surface with 0.3 amplitude to wavelength ratio. This plate is heated by electric heater under constant heat flux conditions ranging as [250, 500, 750, 1000, 1250 and 1500 W/m] and subjected to vertical forced vibration with frequencies [5, 10, 15, 20 and 25 Hz] and [3, 4 and 5 mm] peak to peak vibration amplitude, the Rayleigh number (Ra) ranging from [1.5×10 to 4.0×10], the vibrational Reynolds number (Rev) ranging as [2×10, 4×10, 6×10, 8×10 and 10×10] and the Prandtl number ranging from [0.707 to 0.710] at the ambient laboratory conditions approximately (25C) and pressure of (1 bar). This study is performed for three different positions of sinusoidal surface: horizontal, vertical and facing downward positions. This study concluded that the influence of vibration generally enhances the heat transfer rate and the vibrational mean Nesselt number (Nuvmean ); however the amount of this enhancement depending on the vibrational Reynolds number, Rayleigh number and the position of the heated surface as shown in the following empirical equations: For the horizontal position Nuvmean = 41.547 ∗ Ra 0.091 ∗ Rev 0.017 (1.1) For the vertical position Nuvmean = 22.66 ∗ Ra 0.119 ∗ Rev 0.018 (1.2) For the facing downward position Nuvmean = 0.98 ∗ Ra 0.269 ∗ Rev 0.037 (1.3) General Terms Numean : the mean Nusselt number, Rev : vibrational Reynolds number, Nuvmean : vibrational mean Nesselt number, Ra: Rayleigh number, q: heat flux (W m ), Qgen : Heat generation as a result of the passage of an electric current (Watt), V: the voltage (Volt), I: the current (Amp), Qconv : thermal energy transmitted by convection (Watt), Qrad .: thermal energy transmitted by radiation (Watt), Qcond : Thermal energy transmitted by conduction (Watt), Lc : Characteristic length (m), f: Vibration frequency (Hz), av: vibrational amplitude (m), v: Kinematic viscosity of air (m s ), β: Thermal expansion coefficient (1 K ), g: acceleration of the gravity = 9.81 (m s ), L: the length of test sample (m), T∞ : The fluid temperature (°C), Tsav : average surface temperature (°C), Nuvx: vibrational local Nesselt number, Pr: Prantl number, vx: vibrational local heat transfer coefficient (W m. °C ), K: thermal conductivity of fluid (W m. °C ), x and y: Cartesian coordinates.