Buoyant plume above a horizontal line heat source

Abstract

The first problem dealt with in this paper is the solution of the equations concerning the steady laminar plume above a horizontal line heat source. While there are some controversies raised against what is proposed on this problem by Gebhart et al. [1], new numerical solutions which are more accurate are presented for Pr = 0.01, 0.03, 0.1, 0.3, 0.7, 1, 3, 5, 10, 30 and 100. Furthermore, the profiles of vertical velocity component and temperature are graphed so that there may be convenience of interpolation for an arbitrary Prandtl number. The relation between theory and experiment is taken up for consideration, by reviewing ail-inclusively the results of experiments made on the plumes in air, water and spindle oil as well as those hitherto reported on air and liquid silicone. While the natural motion of plume left undisturbed is extremely slow, it is considerably resembled to the fluttering of a flag. The photographs offered here represent typical motion of the plume in spindle oil. Generally speaking, experimental results are different from theories, but, so far as the temperature distribution in the plume is concerned, the similarity variable corresponding to the theory is applicable to it. The maximum temperatures in the plumes in air were about 15–20 per cent lower than the theoretical predictions in the whole range of Grashof number. Those in water and spindle oil were in good agreement with the theoretical predictions in the range of about Gr < 10 6.