Estimation of Surface Temperature and Heat Flux Using Inverse Solution for One-Dimensional Heat Conduction

Abstract

An analytical method has been developed for the inverse heat conduction problem using the Laplace transform technique when the temperatures are known at two positions within a finite body. On the basis of these known temperatures, a closed form to the inverse solution can be obtained to predict surface conditions. The method first approximates the measured temperatures with a half polynomial power series of time as well as a time lag, which takes for a monitor to sense the temperature change at the point. The expressions for the surface temperature and the surface heat flux are explicitly obtained in the form of the power series of time. The surface temperature and heat flux calculated for some representative problems show agreement with the known values. The method can be applied to the case where an initial temperature distribution exists.

Characteristics of boiling curve in transition region between nucleate boiling and film boiling

“…For one-dimensional conditions, if the temperatures at two points inside the heated block are measured, surface heat flux and temperature can be estimated from the recent solution by Monde et al [8,9], in which surface temperature and heat flux are obtained with The approximation function for measured temperature (Eq. (1)) is expressed in a half polynomial series with time.…”

“…Temperatures at two points, which are positioned at about 2 mm and 5 mm from the boiling surface, are measured with a 1 mm ground sheathed thermocouple. The two measured temperatures are used in the estimation of surface temperature and heat flux by a one-dimensional inverse heat conduction solution [8,9]. In this paper, the purpose of using gold as a test material is to minimize the fowling effect.…”

“…A method to estimate surface temperature and heat flux, i.e., a solution to a one-dimensional inverse heat conductivity problem, has been developed with great success by Monde et al [8,9] recently. In this paper, the method is used for the estimation of surface temperature and heat flux to obtain boiling curves, especially the transition boiling curve.…”

Measurement of Boundary Conditions - Surface Heat Flux and Surface Temperature

“…A considerable number of research studies (Burggraf, 1964;Sparrow et al, 1964;Imber, 1974;Shoji, 1978;Monde, 2003aMonde, , 2003bWoodfield, 2006aWoodfield, , 2006b) have adopted analytical approaches for solving the IHCPs. Although limited to fairly simple geometry, explicit analytical solutions to IHCP have been derived and are very fast computational.…”

Multisensor methods to estimate thermal diffusivity

“…In several papers, Monde et al [8], [9], [10], [11] develop analytical methods based on the Laplace transform to obtain a closed form solution for transient temperatures throughout a body using temperature measurements from two locations, estimate thermal diffusivity and conductivity. Woodfield improved these techniques to handle less smooth temperature changes.…”