Circular tube nonisothermal flow

For nonisothermal flows of gases through a circular tube, the heat exchange rate can be estimated using the formula [267]... 

More detailed information about heat transfer in turbulent nonisothermal flows through a circular tube or plane channel, as well as various relations for Nusselt numbers, can be found in the books [185,254,267,406], which contain extensive literature surveys. 

Equation for the temperature distribution. In the region of hydrodynamic and thermal stabilization, nonisothermal rectilinear steady-state flow of a power-law fluid in a circular tube of radius a at constant temperature on the tube surface is described by Eqs. (6.4.1), (6.5.7), and (6.6.1). We assume that the no-slip condition is satisfied on the tube wall, and the boundary conditions for temperature are given in (6.5.8). 

Obviously, for a nonisothermal flow in a circular tube of a power-law fluid with exponential dependence of the consistence factor on temperature and arbitrary index n, the critical value of the volume rate of flow is twice that in the isothermal case. 

A similar problem on a nonisothermal rectilinear flow of a viscoplastic Shvedov-Bingham fluid in a circular tube for the case in which the yield stress and the plastic viscosity are inversely proportional to temperature was studied in [298],... 

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