Abstract
The use of velocity and temperature distributions in moving fluids is of theoretical and practical significance. Designing efficient heat exchange equipment, development of modes of thermal and thermomechanical processing of products, determination of heat losses in pipeline systems is related to the need to determine the velocity and temperature fields in the flows of fluids and gases. This article presents the development results of an approximate analytical method for mathematical modeling of heat transfer process in laminar flows. The main provisions of the method are demonstrated using the example of solving the heat exchange problem in a plane parallel channel. The combined use of the thermal balance integral method and location method allowed obtaining a simple in form analytical solution of the problem under study. Note that accuracy of the solutions obtained depends on the number of approximations performed, i.e. on the number of N (points of a spatial variable), in which the initial differential equation is satisfied exactly. So, already at \( N = 2 \), a ratio error is not more than 10% in the range of changes along the longitudinal coordinate \( 0.1 \le\upeta < \infty \) and at \( N = 10 \) decreases to 1%. Analytical form of the resulting solutions allows one to analyze isotherm fields inside the channel, to calculate the dimensionless values of the average mass temperature, the Nusselt number, etc.
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Acknowledgment
The reported study was funded by RFBR, project number 20-38-70021 and the Council on grants of the President of the Russian Federation as part of the research, project number MK-2614.2019.8.
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Eremin, A., Gubareva, K. (2021). Approximate Analytical Method for Solving the Heat Transfer Problem in a Flat Channel. In: Murgul, V., Pukhkal, V. (eds) International Scientific Conference Energy Management of Municipal Facilities and Sustainable Energy Technologies EMMFT 2019. EMMFT 2019. Advances in Intelligent Systems and Computing, vol 1259. Springer, Cham. https://doi.org/10.1007/978-3-030-57453-6_30
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