On the Computation of Heat-Transfer Coefficients from Imperfect Temperature Measurements

An approximate theoretical model is developed to estimate the effects of errors in temperature measurement on the computation of heat-transfer coefficients, h, from the numerical solution of Fourier's equation. The model predicts that, depending on the Biot number and the algorithm used, a small random error on temperature will produce an amplified random error on the calculated instantaneous value of h and a bias in the average value, <h>. ‘Experimental results’, simulated using Monte Carlo methods, are in reasonable agreement with the model, and it is shown that improved estimates of the heat-transfer coefficient can be obtained by using smoothing curves to minimize the effects of noise on measured temperatures.

If the temperature measurements have a small positive bias, the theoretical model and ‘experimental results’ show that there can be a large negative bias in the calculated value of h. It is also shown that ‘missing thermocouples’ can be partially compensated for by using interpolation polynomials, but there are dangers that these will cause systematic rather than random errors.