Russian Journal of Applied Chemistry, 2008, Vol. 81, No. 3, pp. 533−541. © Pleiades Publishing, Ltd., 2008.
Original Russian Text © N.A. Gazizulin, 2008, published in Khimicheskaya Promyshlennost’, 2008, Vol. 85, No. 1, pp. 30−38.
MODELING AND CALCULATION
OF TECHNOLOGICAL PROCESSES
Heat Exchange in Apparatus with a Blade Agitator
N. A. Gazizulin
Kazan State Technological University, Kazan, Russia
Received June 2, 2007
Abstract—Three-dimensional model of a convective heat exchange in the apparatus with two blade agitators
equipped with an outside heating device was formulated using the equations of laminar motion of viscous ﬂ uid
and of energy. The Arrhenius−Frenkel−Eyring equation was used to account for the temperature dependence on
the ﬂ uid viscosity. A numerical computations of the ﬁ elds of velocity, pressure, and temperature were performed
with algorithm Simple. The results were presented as isotherms in the meridional, and in the horizontal sections
Study of heat exchange in apparatus with an agitator
is of interest both for ﬁ nding theoretical dependencies
describing the change of a temperature ﬁ eld over the
volume of the apparatus and in connection with wide
range of the technological application of heat exchanger.
In the present work attempts on numerical computation of
convective heat exchange in the apparatus with the two
blade agitators under the condition of laminar motion of
viscous ﬂ uid were done.
STATEMENT OF A PROBLEM
In regard to the ﬁ xed frame of reference the equations
of continuity dynamics in terms of stress, energy, and
continuity will read (in vector form) 
For viscous ﬂ uid taking into account general Newton’s
law Р = -рЕ + 2μD and according to rules of the actions
with operator ∇  equation (1) is reduced to:
Assuming constant viscosity the last item in right
side of the equation (4) is eliminated, and equation (4)
simpliﬁ es to Nav
ier−Stokes equation. The numerical
computation by the equation (4) is connected with the
feature of the viscosity change over the ﬂ uid volume.
The fluid viscosity variation versus temperature is
taken into account. To describe temperature dependence
on the coefﬁ cient of the ﬂ uid dynamic viscosity the
Arrhenius−Frenkel−Eyring equation is used .
Introducing the cylindrical system of coordinates r,
ϕ, z the projects of the velocity vector within the system
are u, v, w, respectively. The ﬂ uid free surface is regarded
as the surface of rotation. The basis in a space connected
with a current point on the free surface and consisting of
a vector of a normal is
and of tangents to this surface of vectors is also
Boundary conditions for the velocity on solid walls
are reduced to the conditions of zero convective ﬂ ow
v T a T ,
v T a T
;; , ;; .