Estimation of Inlet Conditions of Fluid Flow in a Thick Pipe Using Inverse Technique

A conjugate heat transfer problem of steady laminar flow in a circular pipe with a thick wall is considered for estimating inlet conditions of fluid flow in a thick pipe. An inverse method is used to estimate the unknown velocity and temperature of the fluid at the inlet of the pipe based on temperature data obtained on the outer surface along the pipe's length by subjecting the pipe's outer surface to uniform heat flux. Simulations are run for two-dimensional steady laminar flow in COMSOL for different data sets of inlet velocity and inlet temperature to obtain the temperature data along the length of the pipe. Then the curve is fitted using this data by using nonlinear regression analysis with the Bayesian framework. This fitted curve acts as a forward model for estimating the flow conditions at the inlet. The simulated and surrogated temperatures are compared using a Bayesian framework for the guess sample of parameters. To sample the parameter space of inlet conditions (vi, Ti) of fluid flow, Metropolis–Hastings algorithm has been used. Point estimates of v and T and their associated standard deviation (SD) are estimated.