An Inverse Method for Estimating Outer-wall Heat Flux of Fluid Flowing in a Circular Pipe

C.-K. Chen, L.-W. Wu, and Y.-T. Yang (Taiwan)


Simulation, Modeling, Heat Transfer, Inverse Method, Turbulent Pipe Flow


This study addresses the conjugate heat transfer problem of thermally developing, hydrodynamically developed turbulent flow in a circular pipe. An inverse method is used to estimate the unknown heat flux on the external surface of the circular pipe based on temperature measurements taken at several different locations within the fluid. The present approach rearranges the matrix forms of the governing differential equations, and then combines the reverse matrix method and the linear least-squares-error method to determine the unknown boundary conditions of the pipe flow. The dimensionless temperature data obtained from the direct problem are used to simulate the temperature measurement, and the influence of errors in these measurements upon the precision of the estimated results is also considered. The proposed method provides several advantages over the traditional methods, namely it yields a solution within a single computational iteration, no prior information is required about the functional form of the outer-wall heat flux, no initial guesses of the unknown parameter values are required, and the inverse problem can be solved in a linear domain. This study also considers the influence of the locations and numbers of sensors used upon the accuracy of the estimated results.

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