ME 663 Advanced Heat Transfer

Assignment No.02: Due on 29/10/2014

Question 1: Consider a thermally fully developed steady-state laminar flow of a constant-

property fluid through a circular pipe with a constant heat flux condition imposed on the pipe

wall. Neglect axial conduction, viscous dissipationterm; and assume that the velocity profile

may be approximated by a uniform velocity across the entire flow area. Determine the

temperature profile and Nusselt number.

Question 2: Consider a fully developed steady-state laminar flow of a constant-property fluid

through a circular pipe with a constant heat flux condition imposed on the pipe wall. Neglect

axial conduction, but include the effect of viscous dissipation. Determine the temperature

profile and Nusselt number.

Question 3: Determine the velocity profile, the temperature profile and Nusselt number for

the steady, incompressible, laminar, fully developed flow and heat transfer in a parallel plate

channel with itsbottom wall kept at constant heat flux, q1 and top plate at constant heat flux at

q2 Also calculate the Nusselt number when (a) symmetric heating i.e. q1=q2 and (b) top wall

is insulated i.e. q2=0. Neglect viscous dissipation term.

Question 4: In a journal bearing, the lubricating oil fills the clearance between the shaft and

its housing. The radius of the insulated shaft is ri and it angular velocity is . The housing

radius is ro and its temperature is Tw. Assume steady state, laminar flow and constant

properties. All components, except tangential component of the velocity can be ignored for

simplicity. The pressure is assumed to be constant everywhere and temperature is varying in

radial direction only. Derive the expression for tangential velocity, v and determine the

maximum temperature rise in oil and heat dissipated per unit length at housing.

Question 5: Engine oilis flowing at 0.05 kg/s through a circular pipe of radius 0.5 cm. The

oil enters at 35 oC and heated up to 45 oC by atmospheric pressure steam condensing on the

wall of the pipe. Calculate length of the tube required. Assume steady, incompressible,

laminar, fully developed flow with constant properties. The properties of oil at 40 oC are

=876 kg/m3,cp=1964 J/kg-k,k=0.144 W/m-K,=0.210, Pr=2870.