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Turbulent natural convestion boundary layers in an absorbing and emitting gas Shabany, Younes Sh. G.


Turbulent natural convection boundary layers along a vertical flat plate were numerically simulated for non-absorbing and absorbing gases. By varying the value of absorption coefficient of the gas, the effects of radiative heat transfer on the velocity and temperature profiles of the boundary layer were investigated. A broad range of absorption coefficients, including very high and very low values, were covered. Three different turbulence models were used to predict the mean characteristics of the turbulent natural convection boundary layer in a non-absorbing gas: the algebraic mixing length model proposed by Cebeci and Khattab; the low-Reynolds-number k-e models of Jones and Launder, and To and Humphrey. It was observed that the Jones and Launder model would predict a later transition if the grids in the flow direction were more refined. However, when the wall functions and extra source terms in the k and e equations were applied only before the point of maximum velocity, this deficiency was removed. The model in this case was called modified Jones and Launder model. A comparison between the calculated results and the experimental data of Tsuji and Nagana showed that the modified Jones and Launder model was able to predict fairly well the natural convection boundary layer. Turbulent natural convection boundary layers in an absorbing and emitting gas were then calculated using the modified Jones and Launder turbulence model. The calculations were done for two wall temperatures; Tw = 60°C and Tw = 200°C with T⍵ = 25°C for both cases. It was observed that as the absorption coefficient of the gas increased, velocities and temperatures in the inner region of boundary layer increased, but turbulent viscosities decreased. The convective heat transfer rate also decreased. However, this trend reversed at some value of absorption coefficient. It was shown that there was a relation between the range of influence of radiation, compared to the boundary layer thickness, and the type of behavior mentioned above. A comparison between the results for different wall temperatures revealed that, for the limiting cases of optically thin and optically thick gas, the normalized velocity profile ur, and normalized temperature profile tr, were independent of temperature difference between the wall and the medium at a specified Rayleigh number. The convective component of the Nusselt number became a function only of Rayleigh number. For the case of an optically intermediate gas a dependence on wall to gas temperature difference was noted.

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