Slug flow is an idealized tube flow condition for which the velocity is assumed to be uniform over the entire tube cross section. For the case of laminar slug flow with a uniform surface heat flux, determine the form of the fully developed temperature distribution T(r) and the Nusselt number NuD.

Air is to be cooled in the evaporator section of a refrigerator by passing it over a bank of 0.8-cm-outer-diameter and 0.4-m-long tubes inside which the refrigerant is evaporating at -20°c. air approaches the tube bank in the normal direction at 0°c and 1 atm with a mean velocity of 4 m/s. the tubes are arranged in-line with longitudinal and transverse pitches of sl- st 1.5 cm. there are 30 rows in the flow direction with 15 tubes in each row. determine (a) the refrigeration capacity of this system and (b) pressure drop across the tube bank. evaluate the air properties at an assumed mean temperature of -5°c and 1 atm. is this a good assumption?

Apiping systems consists of 6 m of 6-std type k and 12 m of 4-std type k, both drawn copper tubing. the system conveys ethylene glycol at a rate of 0.013 m3/s. the pressure drop across the system is to be calculated. there are two 90° elbows in the 6-in pipe, a reduction from the 6-in pipe to the 4-in pipe and four 90° elbows in the 4-in pipe. all fittings are soldered (same as flanged) and regular. the inlet and outlet of the system are at the same height.

Aparticle moves along a straight line such that its acceleration is a=(4t^2-2) m/s, where t is in seconds. when t = 0, the particle is located 2 m to the left of the origin, and when t = 2, it is 20 m to the left of the origin. determine the position of the particle when t=4s.