Velocity and temperature profiles for laminar flow in a tube of radius ro=10 mm have the form u(r)=0.1[1−(rro⁄)2] T(r)=344.8+75.0(rro⁄)2−18.8(rro⁄)4 With units of m/s and K, respectively. Determine the corresponding value of the mean (or bulk) temperature, Tm, at this axial position.

Awall of 0.5m thickness is to be constructed from a material which has average thermal conductivity of 1.4 w/mk. the wall is to be insulated with a material having an average thermal conductivity of 0.35 w/mk so that heat loss per square meter shall not exceed 1450 w. assume inner wall surface temperature of 1200°c and outer surface temperature of the insulation to be 15°c. calculate the thickness of insulation required.