An electrical heater 114 mm long and 7 mm in diameter is inserted into a hole drilled normal to the surface of a large block of material having a thermal conductivity of 9 W/m · K. Estimate the temperature reached by the heater when dissipating 54 W with the surface of the block at a temperature of 27°C.

Consider the base plate of a 850W household iron with a thickness of L= 0.5 cm, base area of A = 150 cm?, and thermal conductivity of k= 25 W/m°C. The inner surface of the base plate is subjected to uniform heat flux generated by the resistance heaters inside. When steady operating conditions are reached, the outer surface temperature of the plate is measured to be 85°C. Disregarding any heat loss through the upper part of the iron, a. express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the plate, b. obtain a relation for the variation of temperature in the base plate by solving the differential equation, c. evaluate the inner surface temperature. d. Base plate - 85°C Fig. 1– Base Plate

A thick-walled cylindrical tubing of hard rubber (k=0.151 W/m*K) having an inside radius of 5 mm and an outside radius of 20 mm is being used as a temporary cooling coil in a bath. Ice water is flowing rapidly inside, and the inside wall temperature is 275 K. The outside surface temperature is 300 K. A total of 20 W must be removed from the bath by the cooling coil. How many meter of tubing are needed?

Consider the base plate of a 750-W household iron with a thickness of L=0.6 cm, base area of A=170 cm2, and thermal conductivity of k=22 W/m.oC. The inner surface of the base plate is subjected to uniform heat flux generated by the resistance heaters inside. When steady operating conditions are reached, the outer surface temperature of the plate is measured to be 85 oC. Disregarding any heat loss through the upper part of the iron, (a) express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the plate, (b) obtain a relation for the variation of temperature in the base plate by solving the differential equation, and (c) evaluate the inner surface temperature.

40°C water with hwater = 800 W/m² K is flowing in a Pyrex tube. The inner and outer diameters of the tube are 25 mm and 35 mm. A thin metallic heater element bonded to the outer surface of the tube is being used to heat the water by transferring 600 W/m of thermal energy to the water flowing in the tube. The Pyrex tube and heater are covered with a 10-mm thick layer of foam insulation. The outer surface of the foam insulation is exposed to air at T = -5°C with hair = 12 W/m².K. The heater = air element must generate more than 600 W/m, because part of the heat being generated is lost to the air surrounding the foam insulation. Assume kp = 1.30 W/m K for Pyrex and k = 0.026 W/m K for the foam insulation. a) Find the temperature of the heater element needed to transfer 600 W/m of thermal energy to the water in the tube. b) Find the total rate at which the heater element must generate thermal energy. Water Pyrex tube, kp = 1.30 W/m.K = 40°C water hwater = 800 W/m².K Heater element Tair=…

based on a large 4 cm thick plate that is initially at a uniform temperature of 20°C that is heated by passing it through a space maintained at 500°C. The plate remains in the space for a period of 7 min. Take the heat transfer coefficient to be 120-W/m2°C. Example 4-4 [k = 110-W/m°C, r = 8530-kg/m³, C, = 0.380-kJ/kg°C, a = 33.9 x 10-6 m²/s] The dimensionless distance from center to a point 0.4-cm below the outer surface is 0.5 0.8 none of the above 0.2

A glass window with an area of 0.625 m² is installed in the wooden outside wall of a room. The wall dimensions are 25 x 3.05 m. The wood has a k of 0.151W/m.K and is 3.05 cm thick. The glass has a k of 0.692W/m.K and is 5.0 mm thick. The temperature of the inside room is 27°C and outside air temperature is 268K. (1)What is the heat loss through wooden wall and glass window q(W) ? (2) What are the total heat loss?

The 10-mm-thick bottom of a 200-mm-diameter pan may be made from aluminum (k = 240 W/m-K) or copper (k = 390 W/m-K). When used to boil water, the surface of the bottom exposed to the water is nominally at 110°C and heat is transferred from the stove to the pan at a rate of 1200 W. What is the temperature of the surface in contact with the stove for each of the two materials? Aluminum: T = i °C Copper: T = °C Physical Properties Mathematical Functions