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A spherical tank is filled with ice slurry, where its inner surface is at 0°C. The tank has an inner diameter of 9 m, and its wall thickness is 20 mm. The tank wall is made of a material with a thermal conductivity given as
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HEAT+MASS TRANSFER:FUND.+APPL.
- Show that the rate of heat conduction per unit length through a long, hollow cylinder of inner radius ri and outer radius ro, made of a material whose thermal conductivity varies linearly with temperature, is given by qkL=TiTo(rori)/kmA where Ti = temperature at the inner surface To = temperature at the outer surface A=2(rori)/ln(ro/ri)km=ko[1+k(Ti+To)/2]L=lenthofcyclinderarrow_forwardyo lo:ll O %AV L. مرتضی نشط الآن Q5: The piston cylinder device (radius=10 cm) contains a liquid with a pressure 100 kpa and temperature of 20 ° C and has a liquid convection heat coefficient =93 WmK. Connect its fixed side to a cubic piece of aluminum (side length 15 cm) with a thermal conductivity coefficient of aluminum = 239 W mK. At the bottom of the aluminum piece there is a heat source with a temperature of 150 ° C, noting that the heat source is located in a vacuum chamber. Radiation thermal resistance = 3.17 K/W. Calculate the change in piston height during I sec. if you know that there is no change in the internal energy of the piston cylinder device. Note IK Watt 1KJ/s : Aaarrow_forwardThe temperature distribution across a wall 0.3 m thick at a certain instant of time is T(x) = a+ b+cx?, where T is in degrees Celsius and x is in meters, a = 200°C,b = -200°, and c = conductivity of 1 W /m · K. 30°C/m² . The wall has a thermal (a) On a unit surface area basis, determine the rate of heat transfer into and out of the wall and the rate of change of energy stored by the wall. (b) If the cold surface is exposed to a fluid at 100°C, what is the convection coefficient? k=1W/m•k T(x) =200-200x + 30x² 200°C- ĖST 142.7°C q"out | Fluid Too = 100°C,h 9"in |L-0.3marrow_forward
- Consider an apartment in a tower block as a cube of side L = 7.26 m. Since this apartment is designed to be rented by a student, it has no windows. The floor and ceiling are perfectly insulated, but the wall is made of concrete of thickness d = 19.1 cm. The thermal conductivity of the concrete is k = 0.567 Wm¬'K-1. Part 1) The outside temperature is stable at Tout = 35.6°C. What is the heat load (rate of heat transfer) on the air conditioner if the occupant wants to keep the inside temperature stable at Tn = 20.3°C? P = kW Part 2) A layer of insulation of thickness dins = 30.7 mm and thermal conductivity kins = 0.0105 Wm¬1K-l is added to the walls. What is the heat load now? P = kW Part 3) The occupant complains that the apartment is dank and dark, so the landlord is forced to install windows and a door. These are constructed, but then drafts from the gaps around the windows and doors allow the air in the apartment to change every 2 hours. How much additional heat load does changing…arrow_forwardThe ratio of heat flow through walls A and B (Q/Q,) having the same thickness having thermal conductivity k = 4k, for the temperature difference (AT), = 2(AT) will be Barrow_forwardIn a solid sphere of 0.2 m diameter, heat is generated at the rate of 1.2 x 106 W/m3. The center temperature is 300°C. Conductivity is 50 W/m-K. What is the surface temperature?arrow_forward
- Consider a large plane wall of thickness L = 0.4 m, thermal conductivity k=2.3 W/m °C,and surface area A= 20 m2. The left side of the wall at x= 0 is subjected of T1 = 80 C. while the right side losses heated by convection to the surrounding air at Too=15 C with a heat transfer coefficient of h=24 W/m2 .C. Assuming constant thermal conductivity and no heat generation in the wall, (a) express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the wall, (b) obtain a relation for the variation of temperature in the wall by solving the differential equation, and (c) evaluate the rate of heat transfer through the wallarrow_forwardConvection - Heat Transfer Coefficient (HTC) (1) The temperature of inner surface of insulation wall is t,=100°C, while the outer surface releases the heat by convection to surroundings air with temperature of -20°C. The thickness of the insulating layer is 5 cm and its thermal conductivity of 0,05 W/(m-K). What is the value of heat transfer coefficient on the outside this wall if its surface temperature t, is of 0°C.arrow_forward(b) 2- What is the temperature of the outer surface 3 cm of the steel plate? 0.6 cm Q2 : A hot surface at 100°C is to be cooled by attaching 0.25 3 cm long, 0.25 cm diameter aluminum pin fins (k =237 cm W/m.°C) to it, with a center-to-center distance of 0.6 cm. The temperature of the surrounding medium is 30 °C, and the heat transfer coefficient on the surfaces is 35 W/m2.°C. Determine the rate of heat transfer from the surface for a 1x1 m2 section of the plate. Also determine the overall effectiveness of the fins. Q3: Consider a 5-m-long constantan block (k 23 W/m °C) 30 cm high and 50 cm wide. The block tou ot 09C that i ffiaiontarrow_forward
- Q₁: Consider a large plane wall of thickness L = 0.4 m, thermal conductivity k-2.3 W/m °C, and surface area A= 20 m². The left side of the wall at x= 0 is subjected of T1 = 80°C. while the right side losses heated by convection to the surrounding air at T-15 °C with a heat transfer coefficient of h=24 W/m² °C. Assuming constant thermal conductivity and no heat generation in the wall, (a) express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the wall, (b) obtain a relation for the variation of temperature in the wall by solving the differential equation, and (c) evaluate the rate of heat transfer through the wall Ans: (c) 6030 Warrow_forward1. A residential building has height of 50 m and floor area (25 m x 30 m) as shown in figure below. It is occupied by 200 people. The external walls of the building has conductance ( C= 2 W/m?.°C ). The building has windows occupy about 25% from the outer area. The glass type of windows is clear with thickness of 6 mm. The overall heat transfer coefficient for the roof of the building is ( UR = 1.2 W/m?.°C ). The ventilation requirements is ( 36 m3/(hr. Person)) . The room design conditions is ( t; = 22 °C and RH= 40 %) and outside design conditions is (to = 0 °C and RH=70%). (neglect the heat loss to the ground and infiltration air) calculate the total heating load for the building. 30 m 25 m 50 marrow_forwardTwo walls of cold storage plant are composed of an insulating material (k = 0.25 kJ/hr-m-°C), 100mm thick at the outer layer and material (k = 3.5 kJ/hr-m-°C), 15mm thick at inner layer. If the surface temperature at the cold side is 30 °C and hot side is 250 °C, find the heat transmitted per square meter.arrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning