Heat exchangers design under variable overall heat transfer coefficient: Improved analytical and numerical approaches

In typical heat exchanger design methods it is generally assumed that the overall heat transfer coefficient is constant and uniform; however, the heat transfer coefficients on the hot and cold sides of the heat exchanger may vary with flow Reynolds number, surface geometries, fluid thermophysical properties, and other factors. In this article we present simple analytical and numerical methods for calculating heat transfer area for data sets introduced earlier in the literature. For the analytical methods presented in the article, the variation in the overall heat transfer coefficient with the local hot and cold fluid temperature difference is expressed as a power-law model and as a general polynomial model. The procedure for calculating the heat transfer area with the power-law model is explained with respect to a simple closed-form solution, while the polynomial model can also provide an analytical solution that seems to be quite accurate for the data sets examined. It is also shown that a Chebyshev numerical integration scheme that requires four points compared to the Simpson method of three points is quite accurate (within 1% of the exact value).