2. ME0223 SEM-IV Applied Thermodynamics & Heat Engines Example 1 A 3-mm-diameter and 5 m long electric wire is tightly wrapped with a 2 mm thick plastic cover whose thermal conductivity is k = 0.15 W/m·°C. Electrical measurements indicate that a current of 10 A passes through the wire and there is a voltage drop of 8 V along the wire. If the insulated wire is exposed to a medium at T 2 = 30 °C with a heat transfer coefficient of h = 12 W/m2·°C, determine the temperature at the interface of the wire and the plastic cover in steady operation. Also determine whether doubling the thickness of the plastic cover will increase or decrease this interface temperature. Heat is generated in the wire and its temperature rises as a result of resistance heating. In steady operation, the rate of heat transfer becomes equal to the heat generated within the wire, which is determined to be : The thermal resistance network for this problem involves a conduction resistance for the plastic cover and a convection resistance for the outer surface in series.

3. Example 1….contd Interface temperature can be detected as; ME0223 SEM-IV Applied Thermodynamics & Heat Engines Thus; R Total = R Plastic +R Convection = 0.76 + 0.18 = 0.94 ºC/W … .Ans

4. To answer the second part of the question, we need to know the Critical Radius of Insulation of the plastic cover. Example 1….contd ME0223 SEM-IV Applied Thermodynamics & Heat Engines which is larger than the radius of the plastic cover. Therefore, increasing the thickness of the plastic cover will enhance heat transfer until the outer radius of the cover reaches 12.5 mm. … .Ans

5. Example 2 A reversible heat engine operating between a source temperature of 1000 K and a sink temperature of 300 K The engine drives a reversible heat pump which operates between 250 K to 300 K .The engine is supplied with 600 kW heat from source. All the work produced by engine is used for running the heat pump. Calculate the heat removed by the heat pump from cold body at 250 K. Q 3 = COP X W = 6 X 420 = 2520 kW ME0223 SEM-IV Applied Thermodynamics & Heat Engines T 1 = 1000 K Q 1 = 600 kW Heat Engine Heat Pump T 2 = 300 K Q 4 T 3 = 250 K Q 3 = Q 4 + W η max = 1 - T 2 = 1 - T 1 300 1000 = 0.7 W Q 1 = 0.7 W = 0.7 X 600 = 420 kW COP max = T 2 T 2 – T 3 300 300 - 250 = = 6 COP max = Q 3 W = 6 Q 4 = Q 3 - W = 2520 - 420 = 2100 kW … .Ans

6. Example 3 A counter-flow double-pipe heat exchanger is to heat water from 20 °C to 80 °C at a rate of 1.2 kg/s. The heating is to be accomplished by geothermal water available at 160 °C at a mass flow rate of 2 kg/s. The inner tube is thin-walled and has a diameter of 1.5 cm. If the overall heat transfer coefficient of the heat exchanger is 640 W/m 2 ·°C, determine the length of the heat exchanger required to achieve the desired heating. The outlet temperature of the geothermal water is determined to be, ME0223 SEM-IV Applied Thermodynamics & Heat Engines The rate of heat transfer in the heat exchanger can be determined from,

7. Knowing the inlet and outlet temperatures of both fluids, the logarithmic mean temperature difference (LMTD) for this counter-flow heat exchanger becomes, Example 3….contd ME0223 SEM-IV Applied Thermodynamics & Heat Engines The surface area of the heat exchanger is determined to be, To provide this much heat transfer surface area, the length of the tube must be, … .Ans

9. ME0223 SEM-IV Applied Thermodynamics & Heat Engines Example 5 Nitrogen gas at 300 K, 101 kPa and 0.1 m 3 is compressed slowly in an isothermal process to 500 kPa. Calculate the work done during the process. .… Ans And, Now,

10. ME0223 SEM-IV Applied Thermodynamics & Heat Engines Example 6 1.2 kg of liquid water initially at 15 °C is to be heated to 95 °C in a teapot equipped with a 1200 W electric heating element inside. The teapot is 0.5 kg and has an average specific heat of 0.7 kJ/kg·°C. Taking the specific heat of water to be 4.18 kJ/kg·°C and disregarding any heat loss from the teapot, determine how long it will take for the water to be heated. Taking the teapot and the water in it as the system, which is a closed system (fixed mass). The energy balance in this case can be expressed as;

11. Example 6….contd ME0223 SEM-IV Applied Thermodynamics & Heat Engines The 1200-W electric heating unit will supply energy at a rate of 1.2 kW or 1.2 kJ per second. Therefore, the time needed for this heater to supply 429.3 kJ of heat is determined as, … .Ans

12. ME0223 SEM-IV Applied Thermodynamics & Heat Engines Example 7 Engine oil at 60 °C flows over the upper surface of a 5 m long flat plate whose temperature is 20 °C with a velocity of 2 m/s. Determine the rate of heat transfer per unit width of the entire plate. The properties of engine oil at the film temperature of T f = ( T s + T ∞ )/2 = (20 + 60)/2 = 40 °C: ρ = 876 kg/m 3 , Pr = 2870 k = 0.144 W/m.°C, ν = 242 X 10 -6 m 2 /sec. which is less than the critical Reynolds number. Thus we have Laminar Flow over the entire plate. Noting that L = 5 m , the Reynolds number at the end of the plate is, The Nusselt number is determined using the laminar flow relations for a flat plate,

13. Example 7….contd ME0223 SEM-IV Applied Thermodynamics & Heat Engines This leads to, And, … .Ans

14. ME0223 SEM-IV Applied Thermodynamics & Heat Engines Show that the Reynolds number for flow in a circular tube of diameter D can be expressed as Re = Example … .Ans