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Assignment heat transfer, Exercises of Heat and Mass Transfer

Universiti Teknologi MaraHeat and Mass Transfer

5 questions for this exercise.

Typology: Exercises

2018/2019

Uploaded on 10/18/2019

arnurul
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UNIVERSITI TEKNOLOGI MARA
ASSIGNMENT 1
COURSE CODE : CHE 463
HEAT TRANSFER
EXAMINATION : JANUARY2020
TIME
NAME/ ID NO
: WEEK
STUDENT 1:
STUDENT 2:
STUDENT 3:
QUESTION 1;TOPIC: Conduction: Rate equation for conduction
When a long section of a compressed air line passes through the outdoors, it is observed that
the moisture in the compressed air freezes in cold weather, disrupting and even completely
blocking the air flow in the pipe. To avoid this problem, the outer surface of the pipe is
wrapped with electric strip heaters and then insulated. Consider a compressed air pipe of
length L = 6 m, inner radius r1 = 3.7 cm, outer radius r2 = 4.0 cm, and thermal conductivity
k = 14 W/m · °C equipped with a 300-W strip heater.
Air is flowing through the pipe at an average temperature of -10°C, and the average
convection heat transfer coefficient on the inner surface is h =30 W/m2 · °C. Assuming 15
percent of the heat generated in the strip heater is lost through the insulation,
(a) express the differential equation and the boundary conditions for steady one-dimensional
heat conduction through the pipe
(b) obtain a relation for the variation of temperature in the pipe material by solving the
differential equation
(c) evaluate the inner and outer surface temperatures of the pipe.
(d) by using an excel spreadsheet and relation obtained for the variation of temperature in the
pipe material, plot the temperature as a function of the radius r in the range of r = r1 to r = r2.
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Download Assignment heat transfer and more Exercises Heat and Mass Transfer in PDF only on Docsity!

UNIVERSITI TEKNOLOGI MARA

ASSIGNMENT 1

COURSE CODE : CHE 463

HEAT TRANSFER

EXAMINATION : JANUARY

TIME

NAME/ ID NO

: WEEK

STUDENT 1:

STUDENT 2:

STUDENT 3:

 QUESTION 1;TOPIC: Conduction: Rate equation for conduction When a long section of a compressed air line passes through the outdoors, it is observed that the moisture in the compressed air freezes in cold weather, disrupting and even completely blocking the air flow in the pipe. To avoid this problem, the outer surface of the pipe is wrapped with electric strip heaters and then insulated. Consider a compressed air pipe of length L = 6 m, inner radius r 1 = 3.7 cm, outer radius r 2 = 4.0 cm, and thermal conductivity k = 14 W/m · °C equipped with a 300-W strip heater. Air is flowing through the pipe at an average temperature of -10°C, and the average convection heat transfer coefficient on the inner surface is h =30 W/m2 · °C. Assuming 15 percent of the heat generated in the strip heater is lost through the insulation, (a) express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the pipe (b) obtain a relation for the variation of temperature in the pipe material by solving the differential equation (c) evaluate the inner and outer surface temperatures of the pipe. (d) by using an excel spreadsheet and relation obtained for the variation of temperature in the pipe material, plot the temperature as a function of the radius r in the range of r = r 1 to r = r 2.

QUESTION 2;TOPIC: Thermal contact resistance Steam exiting the turbine of a steam power plant at 40°C is to be condensed in a large condenser by cooling water flowing through copper pipes (k = 386W/m.oC) of inner diameter 1 cm and outer diameter 1.5cm at an average temperature of 200 C. The heat of vaporization of water at 40° C is 2407 kJ/kg. The heat transfer coefficients are 8500W/m^2 · °C on the steam side and 200 W/m^2 · °C on the water side. (a) Determine the length of the tube required to condense steam at a rate of 54 kg/h. (b) Determine the length of the tube if 0.025cm thick layer of mineral deposit (k = 0.87W/m^0 C) has formed on the inner surface of the pipe. (c) by using an excel spreadsheet, investigate the effects of the thermal conductivity of the pipe material and the outer diameter of the pipe on the length of the tube required. Let the thermal conductivity vary from 20W/m.C to 700 W/m.C and the outer diameter from 1.25cm to 2.3cm (with no mineral deposit). Plot the length of the tube as functions of pipe conductivity and the outer pipe diameter,.

QUESTION 3;TOPIC: 2-D steady state finite different method Hot combustion gases of a furnace are flowing through a concrete chimney (k = 1.4 W/m°C) of rectangular cross section. The flow section of the chimney is 20 cm x 40 cm, and the thickness of the wall is 10 cm. The average temperature of the hot gases in the chimney is Ti= 280°C, and the average convection heat transfer coefficient inside the chimney is hi = W/m2 · °C. The chimney is losing heat from its outer surface to the ambient air at To=15°C by convection with a heat transfer coefficient of ho=18 W/m2.°C and to the sky by radiation. The emissivity of the outer surface of the wall is ɛ=0.9, and the effective sky temperature is estimated to be 250 K. Using the finite difference method with Δx=Δy=10 cm and taking full advantage of symmetry, (a) obtain the finite difference formulation of this problem for steady two dimensional heat transfer (b) determine the temperatures at the nodal points of a cross section (c) evaluate the rate of heat loss for a 1-m-long section of the chimney. (d) Repeat a,b and c by disregarding radiation heattransfer from the outer surfaces of the chimney. (f) by using an excel spreadsheet, investigate the effects of hot-gas temperature and the outer surface emissivity on the temperatures at the outer corner of the wall and the middle of the inner surface of the right wall, and the rate of heat loss. Let the temperature of the hot gases vary from 200°C to 400°C and the emissivity from 0.1 to 1.0. Plot the temperatures and the rate of heat loss as functions of the temperature of the hot gases and the emissivity

QUESTION 4;TOPIC: Lumped capacitance method A plane wall of a furnace is fabricated from plain carbon steel (k = 60 W/m. K, ῤ= kg/m3, c = 430 J/kg. K) and is of thickness L=10 mm. To protect it from the corrosive effects of the furnace combustion gases, one surface of the wall is coated with a thin ceramic film that, for a unit surface area, has a thermal resistance of R= 0.01 m^2. K/W. The opposite surface is well insulated from the surroundings. At furnace start-up the wall is at an initial temperature of Ti = 300 K, and combustion gases at Tꝏ = 1300 K enter the furnace, providing a convection coefficient of h = 25 W/m^2 .K at the ceramic film. Assuming the film to have negligible thermal capacitance, (a)how long will it take for the inner surface of the steel to achieve a temperature of Ts,i= 1200 K. (b) Determine the temperature of the exposed surface of the ceramic film at this time. QUESTION 5;TOPIC: Transient Heat Conduction with Spatial Effects A 35cm diameter cylindrical shaft made of stainless steel (k= 14.9 W/m · °C, ῤ=7900 kg/m3, Cp =477J/kg°C, and α= 3.95x 10_6^ m2/s) comes out of an oven ata uniform temperature of 400°C. The shaft is then allowed to cool slowly in a chamber at 150°C with an average convection heat transfer coefficient of h = 60 W/m2 · °C. (a) determine the temperature at the center of the shaft 20 min after the start of the cooling process. (b) determine the heat transfer per unit length of the shaft during this time period (c) by using an excel spreadsheet, investigate the effect of the cooling time on the final center temperature of the shaft and the amount of heat transfer. Let the time vary from 5 min to 60 min. Plot the center temperature and the heat transfer as a function of the time.