JNTU III B.Tech II Semester Supplimentary Examinations, Aug/Sep 2008
(Common to Mechanical Engineering and Automobile Engineering)
1. (a) Write Fourier‘s heat conduction equation and explain each term along with their units.
(b) A pipe with a diameter of 2 cm is kept at a surface temperature of 40 0C. Find the heat transfer rate per m length of this pipe if it is
i. Placed in an air flow in which the temperature is 50 0C and
ii. placed in a tank of water kept a temperature of 30 0C. The heat transfer coefficient in these two situations, which involve
A. forced convectiion in air and
B. free convection in water, are estimated to be 20 W/m2 K and 70 W/m2K respectively.
2. (a) Derive an expression for 1- Dimensional, steady state heat conduction state, with internal heat generation for plane wall.
(b) Nichrome, having a resistivity of 100?-cm is to be used as a heating element
in a 10kW heater. The Nichrome surface temperature should not exceed 12200C. Other design features include surrounding air temperature is 200C, Outside surface coefficient is 1.15 kW/m3k, Thermal conductivity of Nichrome =- 17 W/mk. Find out which diameter Nichrome wire is necessary for a 1meter long heater. Also find the rate of current flow.
3. (a) A long 20cm diameter cylindrical shaft made of stainless steel 304 comes out
of an oven at a uniform temperature of 6000C. The shaft is then allowed to cool slowly in an environment chamber at 2000C with an average heat transfer coefficient of h = 80 W/m2 0C. Determine the temperature at he centre of the shaft 45 min. after the start of the cooling process. Also, determine the heat transfer per unit length of the shaft during this time period.
(b) What are Biot number, Fourier number and Heisler charts?
4. (a) Define the local and average skin friction (drag) coefficient for a flat smooth plate at zero incidence.
(b) A thin flat plate has been placed longitudinally in a steam of air at 200C and while flows with undisturbed velocity of 7.5 m/s. The surface of plate is maintained at a uniform temperature of 1200C.
i. calculate the heat transfer coefficient 0.8m from the leading edge of the
ii. Also calculate the rate of heat transfer from one side of the plate to the air over the first 0.8 m length. Assume unit width of the plate.
5. (a) How is a modified Groshff number defined for a constant heat flux condition on a vertical plate?
(b) A metal plate 0.71 m in height and 1.02 m in width forms the vertical wall of an oven. The temperature of the plate is maintained at 230oC, where as the air outside the oven is at 23oC. Assuming the oven to be un-insulated, compute the convection heat loss from the wall to the outside air.
6. For laminar film condensation, what is the ratio of heat transfer to a horizontal tube
of large diameter to that to a vertical tube of the same size for the same temperature
difference? What L/D ratio will produce the same rate of heat transfer to a tube in both the vertical and horizontal orientations?
7. (a) Give a comparison of parallel flow and counter flow heat exchangers. Why are
counter flow exchangers are mostly used?
(b) Sketch the temperature distribution of hot and cold fluids along the length of heat exchanger for counter flow arrangement and derive the expression for LMTD.
8. (a) What is the shape factor with respect to itself if the surface is concave, convex
(b) Show that for two infinite parallel gray planes exchanging radiant energy, the mean emissivity is given by h1_???? 1″1 + 1″2? 1_i.