Banana effect is much similar to bowing in cryogenic piping for LNG loading/unloading line.
The temperature profile may not be clearly defined between coking and quenching.
As so it may well be estimated as linear temperature variation from maximim to minimum.
The reference is “Bowing of Cryogenic Pipelines”, W.G.FLIEDER, Transactions od ASME, Sep, 1961.
See http://sites.google.com/site/fareastpiper/reference in more information
Far East Piper