Heat transfer by laminar forced convection to a Bingham plastic in the entrance region of a circular tube is investigated. Uniform velocity and temperature profiles are assumed at the inlet of the constant wall temperature tube. All Theological properties are taken to be constants in the analysis. The governing conservation equations are solved using a finite difference technique for a range of the parameters of the problem—dimensionless plug radius ā and Prandtl number Pr. The results show that the mean Nusselt numbers—beyond an initial entrance length—are higher for Bingham plastics than for Newtonian fluids. This increase in Num becomes more significant with increasing dimensionless plug radius, while the entrance length increases with decreasing Prandtl number.