CONVECTION OF A VISCOUS INCOMPRESSIBLE COOLANT IN A HORIZONTAL CYLINDRICAL PIPE HEATED FROM BELOW. AN ANALYTICAL SOLUTION

To intensify heat transfer processes in nuclear power, it is proposed to use natural convection in horizontal heat exchange tubes. In the article, the problem of convection of a viscous, incompressible fluid in a horizontal cylinder heated from below is analyzed analytically. The proposed analytical method is based upon the use of basic functions that satisfy the initial equation but do not satisfy the boundary conditions. The problem with boundary conditions with a sufficient degree of accuracy is solved by dividing the area of the square described around the cylinder into a large number of smaller element cells. This separation has made it possible to obtain analytical expressions of critical Rayleigh numbers for different positions of current lines in a horizontal cylinder with a viscous, incompressible fluid.