Heat transfer
Numerical practice
Conduction
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Find the heat loss per square meter through a brick wall 0.5 m thick. let the inner and outer surface
temperature are 400 and 300 K. the thermal conductivity of brick is 0.7 W/m K.
A plane wall is laid from fireclay brick. The wall thickness is 250 mm. the temperature of inside and
outside surfaces are 50 and 1350 oC respectively. Find the heat flux through the wall if the thermal
conductivity of brick k = 0.838 W/m oC.
A furnace is constructed with 229 mm thick of fire brick, 115 mm of insulation brick and again 229 mm of
building brick. The inside temperature is 1223 K and the temperature at the outermost wall is 323 K. The
thermal conductivities of fire brick, insulating brick and building brick are 6.05, 0.581 and 2.33 W/m.K.
Find the heat loss per unit area and temperature at the interface.
A hollow sphere has an inside and outside temperature is 573 and 303 K. The inside and outside diameter
of sphere is 500 and 1500 mm. find the heat loss if the thermal conductivity of material is 17.45 W/m.K.
A 300 mm o.d. pipe is covered with two layers of insulation having thermal conductivities are 0.105 and
0.07 W/m.K. the better insulating material is on the outside and is 40 mm thick. The other insulating
material is of 50 mm thickness. The inner and outer surface temperatures of the insulation are 623 K and
323 K. Estimate: (i) heat loss per meter length (ii) heat loss per square meter of outer insulation surface.
(ii) Temperature of the surface b/w two layers insulation.
Calculate the rate at which heat is being lost to the surrounding per unit length of an insulated steam pipe
having following dimensions and specifications: I. D. = 30 mm ; thickness of pipe
= 2 mm. thickness
of insulation = 10mm; hi and ho = 11.63 W/m2. K. Temperature of steam = 373 K. surrounding
temperature = 298 K ; thermal conductivities are 17.44 W/m.K for pipe and 0.58 W/m.K for insulation.
Find the critical radius for pipe and sphere if heat transfer coefficient h = 250 W/m2 k and thermal
conductivity k =2000 W/ m. K.
A furnace is constructed with 229 mm thick of fire brick, 115 mm of insulation brick and again 229 mm of
building brick. The inside temperature is 1223 K and the temperature at the outermost wall is 323 K. The
thermal conductivities of fire brick, insulating brick and building brick are 6.05 , 0.581 and 2.33 W/m.K.
Find the heat loss per unit area and temperature at the interface.
A special thermobox is made of 20 mm thick stainless steel plate [k = 60 w/m.k], insulated with 20 mm
thick asbestos layer [ k = 0.10 w/m .k] . If the inner wall of the plate is exposed to hot gas at 798 K with a
heat transfer coefficient of 100 w/m2.k and outer surface of asbestos is in contact with cool air at 298 K
with heat transfer coefficient of 25W/m2.K. Calculate (i) Q/A ; (ii) the interfacial temperatures between
the layers.
Calculate the rate at which heat is being lost to the surrounding per unit length of an insulated steam pipe
having following dimensions and specifications: I. D. = 30 mm; thickness of pipe
= 2 mm. thickness
of insulation = 10mm; hi and ho = 11.63 W/m2. K. Temperature of steam = 373 K. surrounding
temperature = 298 K ; thermal conductivities are 17.44 W/m.K for pipe and 0.58 W/m.K for insulation.
A thick walled tube of stainless steel [k= 19 W/m.k] with 2 cm ID and 4 cm OD is covered with a 3 cm
layer of insulation [k=0.2 W/m.k]. If the inside wall temp. is 333 K , calculate the heat transfer per meter
length.
An ice box has walls constructed of a 10 cm layer of cork board contained between two wooden walls
each 2 cm thick. Find the rate of heat removal in Kcal/ m 2.hr. If the inner wall surface is kept at -10oC
while the outer surface temperature is 30 oC . Find the in the wall where the temperature is 20 oC. Thermal
l conductivities of cork board and wood respectively are 0.035 and 0.09 Kcal/hr.m. o C.
A cylindrical hot gas duct, 0.5 m inside radius has an inner layer of fireclay bricks (k =1.3 W/m.k) of 0.27
m thickness. The outer layer 0.14 m thick, is made of special bricks (k= 0.92 W/m.k). The brick work is
enclosed by an outer steel cover which has a temperature of 338 K . The inside temperature of the
composite cylindrical wall of the duct is 673 K. Neglecting the thermal resistance of the steel cover,
calculate the heat loss per meter length of the duct and also the interface temperatures of the different
layers.
Practice make perfect
Radiation
1. Two concentric tubes A and B with diameters 30 cm and 25 cm resp. are maintained at
temperature of 540 oC and 200 oC. The emissivity of tube A is 0.87 nad that of tube B is 0.26.
Determine the net heat transfer by radiation between the surfaces of the tubes (σ = 4.875 x 10-8
kcal/hr m2 K4)
2. Two large parallel plates having emissivity 0.2 and 0.3 respectively are maintained at
temperatures of 600 oC and 100 oC. Calculate heat flux between them.
Convection
1. determine the heat transfer coefficient for water flowing in a tube of 16 mm dia at a velocity of
3 m/s. the temp of the tube is 297 K and water enters at 353 K and leaves at 309 K. Use (i) the
dittus- Boelter equation (ii) Sieder – tate equation. Data: properties of water at 331 K are:
density= 984.1 Kg/m3 , sp heat capacity= 4187 j/kg.K , µ= 485 *10-6 Pa.s , k = 0.657 W/m.K,
viscosity of water at 297 K , µw =920 x 10-6 Pa. s.
2. Fuel oil in a tank is to be heated from 288.5 K to 316 K by means of steam coil. The coil has a
pour point below 288.5 K. this oil stands in the tank and circulates only by natural convection.
Exhaust steam is used and it leaves the coil at atmospheric pressure but not cooled to below
373 K. the heat transfer coeff. for fuel oil is 18.26 and for steam is 4070 w/m2 k. the fouling
factor for oil and steam are 0.123 and 0.215 m2 K/W resp. the coil is required to heat 2250 kg/h
of fuel oil of sp heat= 3.35 kJ/kg.K. the inside and outside dia of pipe are 40 and 48 mm.
Calculate (a) The overall coeff. of heat transfer
(b) heat transfer surface area.
3. In counter current flow double pipe heat exchanger , oil (m= 2 kg/s ,CP = 2.1 kJ/kg K) is cooled
from 363 K to 313 K by water (m = 1kg/s, Cp = 4.2 kJ/kg K) which enters the inner pipe at 283 K.
the radius of inner pipe is 3 cm and length is 5 m. neglecting the wall resistance , the overall
heat transfer coefficient based on inner radius.
Practice make perfect