Theoretical analysis of the viscosity correction factor for heat transfer in pipe flow

In most heat transfer applications, knowledge of the viscosity variation is important. Thus viscosity correction factors have been researched and proposed for almost a century. One of the most successful relations was reported by Sieder-Tate in 1936, which has been widely used in engineering analysis and design. In this study, we have improved on the Sieder-Tate relation, following a classical theoretical analysis of the thermal boundary layer. An exact solution to the viscosity correction factor was obtained which shows that the Sieder-Tate correction factor over-predicts the heat transfer coefficient in the case of cold wall (cooling) and does not hold properly for hot wall (heating). We have found that a relation of μ∞μw0.254 (in case of cooling) and μ∞μw0.087 in the case of heating is better than the Sieder-Tate factor of μ∞μw0.14 (uniformly applied to both the heating and cooling cases). Here μ∞ and μw are the bulk and wall viscosity coefficients respectively. The theoretical analysis also shows that the above correction factors are limited to small values of lnμwμ∞ (for cold wall) and lnμ∞μw (for hot wall). However a general solution has been obtained and the correlation developed by Petukhov (1970) closely matches the exact solution for the case of cold wall cooling of a fluid.