ON A METHOD FOR CALCULATING HEAT TRANSFER IN A MOVING FLUID TAKING INTO ACCOUNT ENERGY DISSIPATION
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ON A METHOD FOR CALCULATING HEAT TRANSFER IN A MOVING FLUID TAKING INTO ACCOUNT ENERGY DISSIPATION I. V. Kudinov, A. V. Eremin, R. M. Klebleev∗ , and V. K. Tkachev
UDC 536.2 (075)
Abstract: An approximate analytical solution to a heat transfer problem for a moving fluid in a cylindrical channel is obtained using an additional new function and additional boundary conditions in the heat balance integral method and taking into account energy dissipation under a first-order boundary condition that varies along the longitudinal coordinate. The use of an additional new function that determines the temperature change along the longitudinal variable in the center of the channel makes it possible to reduce the solution of the partial differential equation to the integration of an ordinary differential equation. Additional boundary conditions are found in such a way that their satisfaction for the new solution is equivalent to the satisfaction of the differential equation at boundary points. Keywords: heat transfer in a moving fluid, variable boundary conditions, energy dissipation, additional new function, additional boundary conditions, heat balance integral method. DOI: 10.1134/S0021894420040094
Obtaining exact analytical solutions to heat transfer problems for fluids moving in circular channels taking into account energy dissipation at variable wall temperature along the longitudinal coordinate is not possible due to the nonlinearity of these problems. A point of practical interest is to obtain their approximate analytical solutions with accuracy sufficient for engineering applications. Heat conduction theory uses methods based on the determination of the temperature perturbation front (depth of the heated layer) [1–6]. These methods include the heat balance integral method, in which the heat conduction process is divided into two time stages (for moving fluids, along the longitudinal variable), the first of which is characterized by a gradual advance of the temperature perturbation front from the body surface to its center, and the second by a temperature change over the entire range of the spatial variable (for moving fluids, the transverse coordinate). The solutions obtained using the integral method are not exact enough. Previously [7–10], additional boundary conditions have been used to obtain a more exact solution. It has been shown that as the number of approximations n increases, the travel time of the temperature perturbation front from the body surface to the center decreases. In the limit as n → ∞, the velocity of the perturbation front also tends to an infinite value, which indicates that heat propagates with infinite velocity. This implies that with an increase in the number of approximations, the time of the first stage of the process decreases and the time of the second stage increases. Therefore, solutions obtained for the first stage can be used only for small and ultra-small values of times (for moving fluids, the longitudinal spatial variable). In view of the above, we consider a solution method which makes it possibl
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