Heat Transfer in Laminar Pipe Flow

For a cylindrical channel with all of the heat transfer resistance assumed to be on the reaction fluid side (U 3.5 k/d at low Reynolds numbers [15]), this equation becomes  

Assuming the temperature dependence of the reaction rate follows the Arrhenius form, the ratio of the maximum rates at the maximum radial mean (bulk) temperature and the wall temperature must satisfy the following constraint defined earlier  

Combining the last two expressions and eliminating T, the criterion for isothermal performance gives the following constraint on the channel diameter  

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T. F. Lin, K. H. Hawks, and W. Leidenfrost, Analysis of Viscous Dissipation Effect on Thermal Entrance Heat Transfer in Laminar Pipe Flows with Convective Boundary Conditions, Wiirme-und Stoffubertragung, (17) 97-105,1983. 

In Chapter 1, we considered the problem of heat transfer in laminar pipe flow. If it is permissible to ignore axial conduction, the transport equation we derived there was given by Eq. 1.31 with the term kd T/dz 0... 

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