7-28 A transformer that is 10-cm long, 6.2-cm wide, and 5-cm high is to be cooled by attaching a 10-cm x 6.2-cm-wide polished aluminum heat sink (emissivity = 0.03) to its top surface. The heat sink has seven fins, which are 5-mm high, 2-mm thick, and 10-cm long. A fan blows air at 25°C parallel to the passages between the fins. The heat sink heat sink is not to exceed 60°C. Assuming the fins and the base plate to be nearly isothermal and the radiation heat transfer to be negligible, determine the minimum free-stream velocity the fan needs to supply to avoid overheating. Assume the flow is laminar over the entire finned surface of the transformer. to dissipate 12 W of heat, and the base temperature of the FIGURE P7-28 Air 25°C 60°C -Fins 0.5 cm 10 cm Transformer 5 cm 12 W +6.2 cm -

400 circumferential fins of rectangular profile (k = 386 W/m °C) are installed on a tube having a diameter of 3 cm and 1 m length that is maintained at a temperature of 200°C. The single fin has a length of 2 cm and a thickness of 0.7 mm. The heat is transferred to the surrounding air at 100°C with a convection heat-transfer coefficient of 524 W/m2 °C. How many times is the heat transfer rate enhanced when the fins are installed on the tube?

Two parallel back disks are positioned coaxially with a distance of 0.25 m apart. The lower disk is 0.2 m in diameter and the upper disk is 0.4 m in diameter. If the lower disk is heated electrically at 20 W to maintain a uniform temperature of 500 K, determine the temperature of the upper disk.

Finned heat sinks are used to keep computer chips in an acceptable temperature range. The heat sink base is 53 mm x 57 mm, and the maximum allowable chip temperature is 75 C. An array of 54 aluminum fins (k = 237 W/m*K) which have a square cross-section (3 mm x 3 mm) are attached to the heat sink. The length of each fin is 30 mm. The cooling air supplied to the heat sink is 25 C. If the convection heat transfer coefficient is 125 W/m2*K, what is the heat transfer rate (in W) from the heat sink, assuming adiabatic fin tips? (Hint: heat transfer does not solely occur from the fins.)

Required information A cylindrical fuel rod (k = 30 W/m K) of 2 cm in diameter is encased in a concentric tube and cooled by water. The fuel rod generates heat uniformly at a rate of 100 MW/m³, and the average temperature of the cooling water is 80°C with a conveçtion heat transfer coefficient of 2500 W/m K. The operating pressure of the cooling water is such that the surface temperature of the fuel rod must be kept below 200°C to avoid the cooling water from reaching the critical heat flux (CHF). The critical heat flux is a thermal limit at which a boiling crisis can occur that cause overheating on the fuel rod surface and lead to damage. T(r.) é sen = 100 MW/m³ 3. Cooling water Fuel rod D=D2 cm 2500 W/m2-K Determine the temperature at the centerline of the rod. (Round your answer to the nearest whole number) (You must provide an answer before moving to the next part.) 5 6 18°C Clear へロ 註EN N

A thin board of 0.5 cm thickness is exposed to a fluid of T, = 22°C and h = 30 W/m².K from one side with an emissivity of 0.7 where it faces a surrounding whose temperature is Tsur = 30°C. A heat flux of q" = 3500 W/m? is applied to the other side. Each side has an area of 12cm×12cm. Tsur (a) If the board has the following properties: k = 15.1 W/m.K, c, = 480 J/kg.K and p = 8055 kg/m², express an equation for the variation of temperature with respect to time. (b) Find the initial time rate of change of the board temperature if the initial board temperature is q" h 50°C.

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

16-90 An electric heater with the total surface area of 0.25 m² and emissivity 0.75 is in a room where the air has a temperature of 20°C and the walls are at 10°C. When the heater consumes 500 W of electric power, its surface has a steady temperature of 120°C. Determine the temperature of the heater surface when it consumes 700 W. Solve the problem (a) assuming negligible radiation and (b) taking radiation into consideration. Based on your results, comment on the assumption made in part (a). We Too, h FIGURE P16-90 Ts Α, ε Qconv Qrad Tw

Consider an alumınum pan used to cook food on top of an electric range. The bottom section of the pan has thickness of L = 0.3 cm and diameter of D = 20 cm. The electric heating unit transfers 800 W of power to the pan. During steady operation. the temperature of the inner surface of the pan is measured to be 110 C. Which of the following boundary conditions is correct during this cooking process; Waler 4. a. Nore of the options D. 25.46 KW/m- T-1)= 110 C %3D Oc T,-o 110 °C & 4x=L 800 W m- %3D d. 9=0 = 800 Wm? To-03m)= 110°C