The steady-state temperature distribution in a one-dimensional wall of thermal conductivity 50 W/m-K and thickness 50 mm is observed to be T(°C) = a + bx²,a = 200°C, b = -3,500°C/m2, and x is in meters.where Determine the heat fluxes at x = 50 mm in W/m-

4. 8.20 Engine oil flows through a 25-mm-diameter tube at a rate of 0.5 kg/s. The oil enters the tube at a temperature of 25°C, while the tube surface temperature is maintained at100°C. Determine the oil outlet temperature for a 5-m and for a 100-m long tube. For each case, compare the log mean temperature difference to the arithmetic mean temperature difference.

7.55 Consider a sphere with a diameter of 20 mm and a surface temperature of 60°C that is immersed in a fluid at a temperature of 30°C and a velocity of 2.5 m/s. Calculate the heat rate when the fluid is (a) water and (b) air at atmospheric pressure. Explain why the results for the two fluids are so different.

A drying oven consists of a long semicircular duct of diameter D = 1 m (Surface1). Materials to be dried cover the base of the oven (Surface 2). The wall(Surface 1) of the oven (81=0.8) is maintained at T1 = 1200 K, while the materials to be dried are considered a black body (82=1.0) is maintained at a temperature T2 = 325 K during the process. a. Calculate the view factor F12; b. Calculate the net radiation heat transfer rate from the oven wall to the material to be dried. Given: o = !5.67x108 W/m2-K and for a two-surface enclosure it is known

2. 7.42 Hot water at 50°C is routed from one building in which it is generated to an adjoining building in which it is used for space heating. Transfer between the buildings occurs in a steel pipe (k = 60 W/m-K) of 100-mm outside diameter and 8-mm wall thickness. During the winter, representative environmental conditions involve air at T =-5°C and V = 3 m/sin cross flow over the pipe. a. If the cost of producing the hot water is $0.10/kWh, what is the representative daily cost of heat loss from an uninsulated pipe to the air per meter of pipe length? The convection resistance associated with water flow in the pipe may be neglected. b. Determine the savings associated with application of a 10-mm-thick coating of urethane insulation (k = 0.026 W/m-K) to the outer surface of the pipe.

Consider an airplane cruising at altitude of 10 km where standard atmospheric conditions are -50°C and 26.5 kPa at a speed of 800 km/h. Each wing of the airplane can be modeled as a 25-m x 3-m flat plate, and the friction coefficient of the wings is o.0016. Using the momentum-heat transfer analogy, determine the heat transfer coefficient for the wings at cruising conditions.

3. A co generation power plant operating in a thermodynamic cycle at steadystate. The plant provides electricity to a community at a rate of 80 MW.The energy discharges from the power plant by heat transfer is denoted on the figure by Q out: Of this, 70 MW is provided to the community for water heating and the remainder is discarded to the environment without use.The electricity is valued at $0.08 / kW-hr. If the cycle thermal efficiency is40%, determine: a) The rate energy is added by heat transfer Q in MW.in b) The rate energy is discarded to the environment, in MW c) The value of the electricity generated in $ per year.

1 m^3 of saturated liquid water at 473 K is expanded isothermally in a closed system until its quality is 80 percent. Determine the total work produced by this expansion, in kJ.

A5-m x 5-m flat plate maintained at a constant temperature of 80°C is subjected to parallel flow of air at 1 atm, 20°C, and 10 m/s. The total drag force acting on the upper surface of the plate is measured to be 2.4 N. Using the momentum-heat transfer analogy, determine the average convection heat transfer coefficient and the rate of heat transfer between the upper surface of the plate and the air. Evaluate the air properties at 50°C and 1 atm.

In a counter-flow heat exchanger, 2 kg/s of hot water flows through the tubes and8 kg/s of cold water flows on the shell side. Which flow will experience the largesttemperature change? O Cold water O Hot water The change will be the same for both