Prandtl Number Effects on Natural Convection in an Enclosed Vertical Layer

1971 ◽  
Vol 93 (2) ◽  
pp. 253-254 ◽  
Author(s):  
R. K. MacGregor ◽  
A. F. Emery
Keyword(s):  
Natural Convection ◽  
Prandtl Number ◽  
Vertical Layer

Unsteady Natural Convection Heat Transfer Past a Vertical Flat Plate Embedded in a Porous Medium Saturated With Fractional Oldroyd-B Fluid

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Jinhu Zhao ◽  
Liancun Zheng ◽  
Xinxin Zhang ◽  
Fawang Liu ◽  
Xuehui Chen
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Porous Medium ◽  
Natural Convection ◽  
Prandtl Number ◽  
Fractional Derivative ◽  
Convection Heat Transfer ◽  
Natural Convection Heat Transfer ◽  
Convection Heat ◽  
Elastic Effect

This paper investigates natural convection heat transfer of generalized Oldroyd-B fluid in a porous medium with modified fractional Darcy's law. Nonlinear coupled boundary layer governing equations are formulated with time–space fractional derivatives in the momentum equation. Numerical solutions are obtained by the newly developed finite difference method combined with L1-algorithm. The effects of involved parameters on velocity and temperature fields are presented graphically and analyzed in detail. Results indicate that, different from the classical result that Prandtl number only affects the heat transfer, it has remarkable influence on both the velocity and temperature boundary layers, the average Nusselt number rises dramatically in low Prandtl number, but increases slowly with the augment of Prandtl number. The maximum value of velocity profile and the thickness of momentum boundary layer increases with the augment of porosity and Darcy number. Moreover, the relaxation fractional derivative parameter accelerates the convection flow and weakens the elastic effect significantly, while the retardation fractional derivative parameter slows down the motion and strengthens the elastic effect.

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

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Ryoichi Chiba
Keyword(s):  
Natural Convection ◽  
Prandtl Number ◽  
Random Process ◽  
Wall Temperature ◽  
Correlation Time ◽  
Channel Wall ◽  
Velocity Fields ◽  
Transient Temperature ◽  
Horizontal Distance ◽  
Mean Square

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.

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