Numerical Computation of Heat and Mass Diffusion

Abstract

Channel flows depicting that of a river in which effluents are released at half the river depth and in the middle of the stream width is numerically modelled using the K-E model. The flow modelled was such that the main free stream velocity is 5 mls with secondary flows (V and W) of 0.5 mls and temperature of 30 °c and zero species concentration. The jet of fluid which is released co-axially in the main stream has a velocity of 10 mis, temperature of 100 °c and a concentration of 5 units per volume of species at the point of release. The velocity, temperature and mass transfer profiles showed a good symmetry along the channel width with a sharp peak value signifying the effect of release which reduces gradually on moving downstream. The momentum, heat and mass transport were found to decay to an asymptotic value on moving down stream away from the point of release. The depthwise momentum, heat, and mass transport decayed in the region around the point of release in a good agreement with the theoretic;:alsolution of axi-symmetric plumes. Downstream away from the point of release, it was noticed that the driving force which is the high momentum, temperature, and mass gradients resulting from the jet of fluid ejected at the point of release reduces gradually. This resulted in a mixed-up region of flow in which both the depthwise momentum, heat, and mass-concentration decayed to asymp,totic value just 1 above the free stream values. The decay mode was found to adopt a decreasing trend in the region around the point of release to change to an increasing one at some distance downstream. The same behaviour is found near the channel walls and descending downstream but with smaller magnitude compared to the central region since the effect of release also decreases on moving towards the channel walls together with the effect of the wall itself on turbulence. The iso-velocity are found to confirm the fact that the flow in the channel is sYmmetrical about the centre plane. The resulting down stream velocity was found to stabilize to a value of order 1.2Uo' Uo being the free stream velocity. In the case of the isotherms, again they were found to be symmetrical about the centre plane with a maximum range of 1.3To' To being the free stream temperature. Nearly a similar result to that of temperature was found for the mass transport.·