Consider laminar flow in a circular tubewith a fully developed velocity profile.Let the heat be added at a constant rate along the tube from  x+ =0  to  x+ =0.10 . Thereafter ,let the tube surface be adiabatic.Calculate and plot the tube surface temperature as a function of  x+.

Consider a concentric circular-tube annulus ,with outer diameter 2.5cm and inner diameter 1.25cm,in which the air is flowing under fully developed ,constant heat -rate conditions. Heat is supplied to the inner tube ,and the outer tube is externally insulated . The radiation emissivity of both tube surfaces is 0.8 .The mixed mean temperature of air at a particular point in question is 260 degrees centigrade. The inner- tube surface temperature at this point is 300 degC. What is total heat flux from the inner tube surface at this point? What is the outer tube surface temperature at this point ? What percentage of the heat supplied to the inner tube is transfered directly to the air, and what percentage indirectly from the outer surface ?

The reynolds number is sufficiently low that the flow is laminar . Assume that the air is transparent to the thermal radiation.