Concept explainers
A thin electrical heating element provides a uniformheat flux
(a) At a particular location, the air temperature is 30°Cand the convection heat transfer coefficientbetween the air and inner surface of the duct is
(b) For the conditions of part (a), what is the temperature
(c)With
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Fundamentals of Heat and Mass Transfer
- A plane wall, 7.5 cm thick, generates heat internally at the rate of 105 W/m3. One side of the wall is insulated, and the other side is exposed to an environment at 90C. The convection heat transfer coefficient between the wall and the environment is 500 W/m2 K. If the thermal conductivity of the wall is 12 W/m K, calculate the maximum temperature in the wall.arrow_forward2.2 A small dam, which is idealized by a large slab 1.2 m thick, is to be completely poured in a short Period of time. The hydration of the concrete results in the equivalent of a distributed source of constant strength of 100 W/m3. If both dam surfaces are at 16°C, determine the maximum temperature to which the concrete will be subjected, assuming steady-state conditions. The thermal conductivity of the wet concrete can be taken as 0.84 W/m K.arrow_forward2.15 Suppose that a pipe carrying a hot fluid with an external temperature of and outer radius is to be insulated with an insulation material of thermal conductivity k and outer radius . Show that if the convection heat transfer coefficient on the outside of the insulation is and the environmental temperature is , the addition of insulation actually increases the rate of heat loss if , and the maximum heat loss occurs when . This radius, is often called the critical radius.arrow_forward
- 2.30 An electrical heater capable of generating 10,000 W is to be designed. The heating element is to be a stainless steel wire having an electrical resistivity of ohm-centimeter. The operating temperature of the stainless steel is to be no more than 1260°C. The heat transfer coefficient at the outer surface is expected to be no less than in a medium whose maximum temperature is 93°C. A transformer capable of delivering current at 9 and 12 V is available. Determine a suitable size for the wire, the current required, and discuss what effect a reduction in the heat transfer coefficient would have. (Hint: Demonstrate first that the temperature drop between the center and the surface of the wire is independent of the wire diameter, and determine its value.)arrow_forward1.10 A heat flux meter at the outer (cold) wall of a concrete building indicates that the heat loss through a wall of 10-cm thickness is . If a thermocouple at the inner surface of the wall indicates a temperature of 22°C while another at the outer surface shows 6°C, calculate the thermal conductivity of the concrete and compare your result with the value in Appendix 2, Table 11.arrow_forwardA domestic refrigerator with inner dimensions of 0,7 m by 0,7 m at the base and height 1m was designed to maintain a set temperature of 6 degrees Celsius. The bodies consist of two 10 mm thick layers of Aluminum (k=225 W/mK) separated by a 30 mm polyurethane insulation (k=0,028 W/mK). If the convection heat transfer coefficient at the inner and outer surfaces are 11,6 W/m²K and 14,5 W/m²K respectively, calculate the outer surface temperature of Aluminum in degrees Celsius to 2 decimal places. 2)calculate the resistance (R) for the insulation layer in K/W to 4 decimal places. 3)calculate the steady rate of heat transfer from the interior to maintain the specified temperature in the kitchen at 25 degrees Celsius in W to 2 decimal places. 4)calculate the total resistance (R) for the refrigerator in K/W to 4 decimal placesarrow_forward
- A domestic refrigerator with inner dimensions of 0.7 m by 0.7 m at the base and height 1 m was designed to maintain a set temperature of 6 ˚C. The bodies consist of two 10-mm-thick layers of Aluminium (k = 225 W/mK) separated by a 30 mm polyurethane insulation (k=0.028 W/mK). If the average convection heat transfer coefficient at the inner and outer surfaces are 11.6 W/m2K and 14.5 W/m2K respectively, calculate: Data: Hgt = , W = , L1 = L3 = = m, k1= k3 = , L2 = = , k2 = , T∞1 = , T∞2 = , ho= , hi = .arrow_forwardPin fins are provided to increase the heat transfer from a hot surface. The perimeter of each fin is 4cm and its cross section area is 2 cm². The thermal conductivity of fin material is 200 W / mK. The fin base temperature is 230 ° C, the ambient air temperature is 30 ° C and the heat transfer coefficient is 20 W / (m²K). The fins are assumed of negligible end loss Which of the following arrangements will give higher heat transfer rate? (1) 6 fins of 10 cm length. (2) 12 fins of 5 cm lengtharrow_forwardA steel pipe (k = 48 W/m∙K) of a heating system carries wet steam at 125 °C. The inner and outer diameters of the pipe are 15 cm and 17 cm respectively. The pipe is insulated on the outside with rockwool insulation (k = 0.05 W/m∙K) of thickness 8 cm. The ambient air temperature is 30 °C. The outside heat transfer coefficient is 22 W/m2∙K. The thermal resistance between the inner pipe surface and the steam is negligible. Calculate the rate of heat flow (in W) from the steam to the ambient over a 7 m length of pipe. calculate the temperature (in °C) of the outer surface of the insulation. calculate the rate of condensation of steam (in kg/hr) over the 7-m length of pipe if the latent heat of steam is 2189 kJ/kg.arrow_forward
- A domestic refrigerator with inner dimensions of 0.7 m by 0.7 m at the base and height 1 m was designed to maintain a set temperature of 6 ˚C. The bodies consist of two 10-mm-thick layers of Aluminium (k = 225 W/mK) separated by a 30 mm polyurethane insulation (k=0.028 W/mK). If the average convection heat transfer coefficient at the inner and outer surfaces are 11.6 W/m2K and 14.5 W/m2K respectively, calculate: the resistance(R) for the insulation thermal layer in K/W to 4 decimal places.arrow_forwardA domestic refrigerator with inner dimensions of 0.7 m by 0.7 m at the base and height 1 m was designed to maintain a set temperature of 6 ˚C. The bodies consist of two 10-mm-thick layers of Aluminium (k = 225 W/mK) separated by a 30 mm polyurethane insulation (k=0.028 W/mK). If the average convection heat transfer coefficient at the inner and outer surfaces are 11.6 W/m2K and 14.5 W/m2K respectively, calculate: the resistance(R) for the insulation thermal layer in K/W to 4 decimal places thermodynamicsarrow_forwardGiven a plaster of paris (PoP) slab with L = 0.052 cm, W = 0.052 cm, and H = 0.0095 cm, what is the heat transfer coefficient if the biot number is 0.19682? Attached is the Heisler Chart below. Other data (if necessary):Initial Temperature: 328.2 CSurrounding Temperature: 27.9 CPoP Density: 680 kg/m^3Heat Capacity: 1090 J/kgKThermal Conductivity: 0.1185 W/mKarrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning