Stochastic Analysis of Natural Convection in Vertical Channels with Random Wall Temperature

Abstract

This study attempts to derive the statistics of temperature and velocity fields of laminar natural convection in a heated vertical channel with random wall temperature. The wall temperature is expressed as a random function with respect to time, or a random process. First, analytical solutions of the transient temperature and flow velocity fields for an arbitrary temporal variation in the channel wall temperature are obtained by the integral transform and convolution theorem. Second, the autocorrelations of the temperature and velocity are formed from the solutions, assuming a stationarity in time. The mean square values of temperature and velocity are computed under the condition that the fluctuation in the channel wall temperature can be considered as white noise or a stationary Markov process. Numerical results demonstrate that a decrease in the Prandtl number or an increase in the correlation time of the random process increases the level of mean square velocity but does not change its spatial distribution tendency, which is a bell-shaped profile with a peak at a certain horizontal distance from the channel wall. The peak position is not substantially affected by the Prandtl number or the correlation time.

On entropy generation due to transient MHD radiative free convection with induced magnetic field in a porous medium channel

“…Barik et al 31 examined mass transfer in free convection with chemical reaction inside a vertical channel. Chiba 32 adopted a statistical approach to explore laminar convection with random channel wall temperature. Sarper et al 33 discussed discrete heating effects on natural convection inside a parallel walls channel.…”