GET 227 Lecture 7 PDF

FUNDAMENTALS OF GET 227 LECTURE 7 Instructors: Dr. Petrus Nzerem, Engr. Abdulmojeed Oluogun, Engr. Seun Jesuloluwa  ENERGY TRANSFER BY HEAT Conduction Can take place in solids, liquids, and gas...

FUNDAMENTALS OF GET 227 LECTURE 7 Instructors: Dr. Petrus Nzerem, Engr. Abdulmojeed Oluogun, Engr. Seun Jesuloluwa  ENERGY TRANSFER BY HEAT Conduction Can take place in solids, liquids, and gas ̇ Heat conduction Qcond through a layer of constant thickness:...Eqn 8.1 Where: kt is the thermal conductivity of the material A is area normal to the direction of heat transfer ΔT is temperature difference across the layer Fig 8.8: Δ𝑥 is thickness of layer through which heat transfer is occurring. 2  ENERGY Historical TRANSFER Background on Heat BY HEAT Table 8.1 Conduction High kt are good heat (and electrical) conductors. Low kt are poor heat (and electrical) conductors. – In limiting cases of Δ𝑥 ⟶ 0,...Eqn 8.2 Fourier’s law of heat conduction 3  ENERGY Historical TRANSFER Background on Heat BY HEAT Convection – Rate of heat transfer by convection Q̇conv:...Eqn 9.1 Where: h is the convection heat transfer Fig 9.1: coefficient A is the surface area through which heat transfer takes place Ts is the surface temperature Tf is the bulk fluid temperature away from the surface. 4  ENERGY Historical TRANSFER Background on Heat BY HEAT Convection – Convection may be forced or free (natural) Forced convection: where a fluid is forced to flow in a tube or over a surface by external means, e.g., fan. Fig 9.2: Free (natural) convection: the fluid motion is caused by buoyancy forces induced by density differences due to the variation of temperature in the fluid 5  ENERGY Historical TRANSFER Background on Heat BY HEAT Convection Note: h is not a fluid property Experimentally derived and depends on Surface geometry Fluid properties Nature of fluid motion Bulk fluid velocity Table 9.1: Typical values of h Convection h, W/m2·K Free convection of gases 2–25 Free convection of liquids 50–1000 Forced convection of gases 25–250 Forced convection of liquids 50–20,000 Boiling and condensation processes 2500–100,000 6  ENERGY Historical TRANSFER Background on Heat BY HEAT Radiation Energy emitted by matter in the form of EM waves Does not require a medium for transfer Thermal radiation is due to temperature difference Associated with all solids, liquids Fig 9.3: and gases Unlike conduction and They emit, absorb, or transmit convection, heat transfer by radiation at varying degrees. radiation can occur between two bodies, even when they are separated by a medium colder than both of them. 7  ENERGY Historical TRANSFER Background on Heat BY HEAT Radiation A surface phenomenon for solids opaque to thermal radiation, e.g., metals, wood, rock Maximum rate of radiation that can be emitted from a ̇ surface, Qemit,max,at an absolute temperature (Ts)...Eqn 9.2 (Stefan–Boltzmann law) where A is the surface area σ is the Stefan–Boltzmann constant (5.67 ⨯ 10-8 W/m2·K4) Blackbody: an idealised surface that emits radiation at Q̇emit,max Blackbody radiation: radiation emitted by a blackbody 8  ENERGY Historical TRANSFER Background on Heat BY HEAT Radiation Radiation from real surfaces...Eqn 9.3 where e is the emissivity of the surface (0 ≤ e ≤ 1) – Absorptivity, a: the fraction of the radiation energy incident on a surface that is absorbed by the surface (0 ≤ a ≤ 1) For a blackbody, a = 1. – e and a depend on the temperature & wavelength of radiation. e and a of a surface equal at the same temperature and wavelength (kirchhoff’s law) 9  ENERGY Historical TRANSFER Background on Heat BY HEAT Radiation Table 9.2: Emissivity of some materials at 300 K Material Emissivity Material Emissivity Aluminium foil 0.07 White paper 0.92 – 0.97 Anodised aluminium 0.82 Asphalt pavement 0.85 – 0.93 Polished copper 0.03 Red brick 0.93 – 0.96 Polished gold 0.03 Human skin 0.95 Polished silver 0.02 Wood 0.82 – 0.92 Polished stainless steel 0.17 Soil 0.93 – 0.96 Black paint 0.98 Water 0.96 White paint 0.90 Vegetation 0.92 – 0.96 10  ENERGY Historical TRANSFER Background on Heat BY HEAT Radiation Rate at which a surface absorbs radiation...Eqn 9.4 where ,rate at which radiation Fig 9.4: The absorption of is incident on a surface and a is the radiation incident on an absorptivity of the surface. opaque surface of – Net radiation heat transfer absorptivity α. by a surface: Fig 9.5: Radiation heat 𝑸ሶ 𝒓𝒂𝒅 = 𝑸ሶ 𝒂𝒃𝒔 − 𝑸ሶ 𝒆𝒎𝒊𝒕 transfer between a body & the inner surfaces of a – Special case: much larger enclosure that completely surrounds it....Eqn 9.5 11  ENERGY Historical TRANSFER Background on Heat BY HEAT Class work Consider a person standing in a breezy room at 20oC. Determine the total rate of heat transfer from this person if the exposed surface area and the average outer surface temperature of the person are 1.6 m2 and 29oC, respectively, and the convection heat transfer coefficient is 6 W/m2·oC. Fig 9.6: Heat transfer from a person standing in a breezy room at 20oC 12  ENERGY Historical TRANSFER Background on Heat BY HEAT Class work The inner and outer surfaces of a 5-m × 6- m brick wall of thickness 30 cm and thermal conductivity 0.69 W/m·oC are maintained at temperatures of 20oC and 5oC, respectively. Determine the rate of heat transfer through the wall, in W. Fig 9.7: Heat transfer through a brick wall 13 ENERGY TRANSFER BY WORK Work: The energy transfer associated with a force acting through a distance.  A rising piston, a rotating shaft, and an electric wire crossing the system boundaries are all associated with work interactions  The work done during a process between states 1 and 2 is denoted by W12, or simply W Work done per unit mass:...Eqn 8.1 Power: work done per unit time Ẇ.. (kJ/s or kW)...Eqn 8.2 Fig 8.1: Relationship btw w, W & W 14 ENERGY TRANSFER BY WORK Sign convention: Heat and work are directional quantities, thus both magnitude and direction have to be specified. Energy Direction Formal Alternative (+) Heat (Q) input + Qin (–) Heat (Q) output – Qout Work (W) input – Win (–) Work (W) output + Wout (+) Heat vs. Work Fig 8.2: Specifying the directions of heat & work. Both are boundary phenomena. Systems possess energy, but not heat or work. Both are associated with a process, not a state. Both are path functions 15  ENERGY TRANSFER BY WORK Point functions have exact differentials (d )....Eqn 8.3 Path functions have inexact differentials ( )...Eqn 8.4 FIGURE 8.3: 16  ENERGY TRANSFER BY WORK Consider the following processes Is there any heat transfer during the burning process? Is there any change in the internal energy of the system? Fig 8.5: Baking in Microwave oven Fig 8.4: Burning candle in a well insulated room Is there any heat transfer during the baking process? 1 2 What type of energy interaction is taking place in electric ovens 1 and 2? Fig 8.6: Electric ovens 17  ENERGY TRANSFER BY WORK Electrical Work,We...Eqn 8.5 V is potential difference; N is electric charge Electrical Power, Ẇe...Eqn 8.6 FIGURE 8.7: I, current, is the number of electrical charges flowing per unit time. In general, V and I vary with time: ∴...Eqn 8.7 When V and I remain constant with time:...Eqn 8.8 18 MECHANICAL FORMS OF WORK Work = Force  Distance (kJ)... Eqn. 6 When force is not constant Fig 8.8: The work done is proportional to the force applied (F) & the distance travelled (s). (kJ)...Eqn. 7 There are two requirements for a work interaction between a system and its surroundings to exist:  there must be a force acting on the boundary.  the boundary must move. 17 19 MECHANICAL FORMS OF WORK Fig 8.9: If there is no movement , no work is done 17 20  MECHANICAL FORMS OF WORK Shaft Work, Wsh Work done to rotate a shaft connected to a system Common in engineering practice Energy transmission in a car Energy transmission in a ship 21  MECHANICAL FORMS OF WORK Shaft Work, Wsh A force F acting through a moment arm r generates a torque T...Eqn. 8 Fig 8.10: F, force acts through a distance s which is related to r as follows: ∴ (kJ)...Eqn. 9 where n is no of revolutions & ṅ (kW)...Eqn. 10 is no of revolutions per unit time 22  MECHANICAL FORMS OF WORK Shaft Work, Wsh Class work Determine the power transmitted through the shaft of a car when the torque applied is 200 N·m and the shaft rotates at a rate of 4000 revolutions Fig 8.11: Diagram to Class work per minute (rpm). 23  MECHANICAL FORMS OF WORK Shaft Work, Wsh 8.11 24  MECHANICAL FORMS OF WORK Spring Work When the length of the spring changes by a differential amount d𝑥 under the influence of a force F, the work done is...Eqn. 10 For linear elastic springs, the displacement, 𝑥, is proportional to the force applied...Eqn. 11 where k is the spring constant (kN/m) Substituting and integrating yield...Eqn. 12 x1 and x2: the initial and the final displacements 25  MECHANICAL FORMS OF WORK Work Done on Elastic Solid Bars Fig 8.12: Solid bars behave as springs (kJ)...Eqn. 13 under the influence of a force. σn is normal stress (F/A); A is cross-sectional area Work Associated with the Stretching of a Liquid Film...Eqn. 14 σs is surface tension per unit length (N/m) F = σs 2b dA = 2b d𝑥 (for the 2 surfaces of the film) Fig 8.13: Stretching a liquid film with a U-shaped wire, and the forces acting on the movable wire of length b. 26  MECHANICAL FORMS OF WORK Work Done to Raise or to Accelerate a Body 1. The work transfer needed to raise a body is equal to the change in the potential energy of the body. 2. The work transfer needed to accelerate a body is equal to the change in the kinetic energy of the body. Nonmechanical Forms of Work Electrical work Fig 8.14: Magnetic work: Electrical polarization work: 27  MECHANICAL FORMS OF WORK Homework 1. Consider a 1200-kg car cruising steadily on a level road at 90 km/h. Now the car starts climbing a hill that is sloped 30o from the horizontal. If the velocity of the car is to remain constant during climbing, determine the additional Fig 8.15: Diagram to homework 1 power that must be delivered by the engine. 2. Determine the power required to accelerate a 900-kg car shown in the diagram from rest to a velocity Fig 8.16: Diagram to homework 2 of 80 km/h in 20 s on a level road. 28  MECHANICAL FORMS OF WORK Homework 3. Determine the work required to deflect a linear spring with a spring constant of 70 kN/m by 20 cm from its rest position. 4. A spherical soap bubble with a surface-tension of 0.073 N/m is expanded from a diameter of 1.27 cm to 7.62 cm. How much work, in kJ, is required to expand this bubble? 5. The force F required to compress a spring a distance x is given by F − F0 = kx where k is the spring constant and F0 is the preload. Determine the work required to compress a spring whose spring constant is k =35 kN/m a distance of one inch starting from its Fig 8.17: Diagram to homework 2 free length where F0 = 0 N. 29  MECHANICAL FORMS OF WORK Homework 6. A gas in a piston-cylinder device is compressed, and as a result its temperature rises. Is this a heat or work interaction? 7. A room is heated by an iron that is left plugged in. Is this a heat or work interaction? Take the entire room, including the iron, as the system. 8. A room is heated as a result of solar radiation coming in through the windows. Is this a heat or work interaction for the room? 9. An insulated room is heated by burning candles. Is this a heat or work interaction? Take the entire room, including the candles, as the system. 10. A small electrical motor produces 5 W of mechanical power. What is this power in (a) N, m, and s units; and (b) kg, m, and s units? 30