tutorial#5 solutions.pptx
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A thermocouple junction is approximated as a sphere to measure the temperature of a gas stream. With given properties and a convection coefficient of 400 W/m2-K, the junction diameter needed for a time constant of 1 second is calculated. If the junction at 25°C is placed in a 200°C gas stream, it will take approximately 6 minutes to reach 199°C.
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This document contains multiple heat transfer problems involving pipes, fins, and composite walls. The first problem involves calculating the overall heat transfer coefficient and dominant resistance for a steel pipe with water flowing inside at 500 W/m2K and the outside exposed to 12 W/m2K. The second problem involves calculating the maximum possible heat generation rate for electric heater wires in a solid wall to keep the temperature below 300°C with boundary conditions of 50 W/m2K and 75 W/m2K. The third problem involves determining the increase in heat transfer from adding fins to steam tubes in a heating system.
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The document contains 10 problems related to heat transfer and thermodynamics. The problems involve calculating temperatures, time required to reach a temperature, temperature distributions, and deriving governing equations for heat transfer. Lumped system analysis, transient and steady-state heat conduction, convection, and thermal resistances are concepts used.
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Tutorial#2.pptx
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Tutorial#2.pptx
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Analysis of Temperature loss of Hot Metal during Hot Rolling Process at Steel...
Hot metal is travelling a long distance (around 126 m) between roughing mill and a Steckel
finishing mill during hot rolling process in a steel plant which resulted in heat loss. Since, the
metallurgical qualities of finished product are closely related to the accurate control of temperature of
the material during the hot rolling process, the heat in the furnaces maintains the slab temperature at
high level at the cost of more fossil fuels. Temperature of the work piece influences spread appreciably.
Lower the temperature of raw material input, greater is the spread. Similarly, higher the temperature,
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resistance to radiation heat flow. Because radiation is a major source of heat loss at the temperatures
involved (around 1060° C.) Thermal shields may be fixed over the path of the hot strip to reduce heat
loss and in particular such heat shields can be employed to reduce the head-to-tail temperature
variation along the length of a transfer bar. The result of this study is the development of an effective
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tutorial#5 solutions.pptx
- 2. A thermocouple junction, which may be approximated as a sphere, is to be used for temperature measurement in a gas stream. The convection coefficient between the junction surface and the gas is h = 400 W/m2-K, and the junction thermophysical properties are k = 20 W/m-K, c = 400 J/kg-K, and ρ = 8500 kg/m3. Determine the junction diameter needed for the thermocouple to have a time constant of 1 s. If the junction is at 25°C and is placed in a gas stream that is at 200°C, how long will it take for the junction to reach 199°C?
- 4. An electronic device, such as a power transistor mounted on a finned heat sink, can be modeled as a spatially isothermal object with internal heat generation and an external convection resistance. (a) Consider such a system of mass M, specific heat c, and surface area As, which is initially in equilibrium with the environment at T∞. Suddenly, the electronic device is energized such that a constant heat generation Eg(W) occurs. Show that the temperature response of the device is 𝜃 𝜃𝑖 = 𝑒𝑥𝑝 − 𝑡 𝑅𝐶 where θ = T - T(∞) and T(∞) is the steady-state temperature corresponding to t → ∞ ; θi = Ti - T(∞); Ti = initial temperature of device; R = thermal resistance ; and C = thermal capacitance Mc. (b) An electronic device, which generates 60 W of heat, is mounted on an aluminum heat sink weighing 0.31 kg and reaches a temperature of 100°C in ambient air at 20°C under steady-state conditions. If the device is initially at 20°C, what temperature will it reach 5 min after the power is switched on?
- 6. A thermal energy storage unit consists of a large rectangular channel, which is well insulated on its outer surface and encloses alternating layers of the storage material and the flow passage. Each layer of the storage material is an aluminum slab of width W = 0.05 m, which is at an initial temperature of 25°C. Consider conditions for which the storage unit is charged by passing a hot gas through the passages, with the gas temperature and the convection coefficient assumed to have constant values of T∞ = 600°C and h =100 W/m2-K throughout the channel. How long will it take to achieve 75% of the maximum possible Storage material energy storage? What is the temperature of the aluminum at this time?
- 8. Thermal energy storage systems commonly involve a packed bed of solid spheres, through which a hot gas flows if the system is being charged, or a cold gas if it is being discharged. In a charging process, heat transfer from the hot gas increases thermal energy stored within the colder spheres; during discharge, the stored energy decreases as heat is transferred from the warmer spheres to the cooler gas. Consider a packed bed of 75-mm-diameter aluminum spheres (ρ = 2700 kg/m3, c = 950 J/kgK, k= 240 W/m K) and a charging process for which gas enters the storage unit at a temperature of Tg,i = 300°C. If the initial temperature of the spheres is Ti = 25°C and the convection coefficient is h = 75 W/m2 K, how long does it take a sphere near the inlet of the system to accumulate 90% of the maximum possible thermal energy? What is the corresponding temperature at the centre of the sphere? Is there any advantage to using copper instead of aluminum?