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By introducing an additional sought-for function (ASF) and additional boundary conditions (ABC) using the integral heat balance method, an analytical solution to the problem of heat transfer in a fluid moving in a cylindrical pipe under the parabolic law of viscosity dependence on temperature was found. A function characterizing a change in temperature along the longitudinal coordinate in the center of the pipe was taken as an additional one. Its use is based on the infinite velocity of heat distribution described by a parabolic equation solution. According to it, the temperature of the liquid in the center of the pipe changes immediately after the ASF of the boundary condition is applied to its surface. The application of the ASF makes it possible to reduce a partial differential equation to an ordinary equation. ABCs are defined so that their fulfillment is equal to solving an equation at boundary points. It is shown that solving the equation at the boundary also leads to its solving inside the area with the accuracy depending on the number of additional boundary conditions used in obtaining the solution. The study of the results obtained showed a significant difference in the velocity profiles caused by fluid heating and cooling. So, when heated, the velocity profile approaches the profile of a core flow which is characterized by an almost constant velocity across the channel, and when cooled, it is elongated longitudinally. The studies performed showed a significant difference in the temperature distribution obtained with and without taking into account the viscosity dependence on temperature.

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