limiting nusselt numbers for laminar forced convection in asymmetrically heated annuli with viscous dissipation

analytical expressions for the nusselt number at the inner and outer pipes, kept at unequal temperatures, for laminar forced convection through annuli including viscous dissipation have been obtained in the conduction limit. this article examines the dependence of the limiting nusselt numbers on the brinkman number and the degree of asymmetry in inner and outer pipe temperatures. further, the limiting temperature profile obtained when viscous dissipation is included serves the purpose of providing the downstream boundary condition needed in solving the elliptic form of conservation of thermal energy equation that arises when axial conduction is included.