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A procedure for determining the thermal conductivity of a solid material involves embedding a thermocouple in a thick slab of the solid and measuring the response to a prescribed change in temperature at one surface. Consider an arrangement for which the thermocouple is embedded from a surface that is suddenlybrought to a temperature of
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Fundamentals of Heat and Mass Transfer
- VI.2 A coolant is transported in a pipe with external wall temperature of -30 °C and with outer diameter of 10 cm. The tube is thermally isolated by two layers: 1) an internal layer of foamed polypropylene with thermal conductivity of 0.08 W.m.K and thickness of 10 cm, and 2) an external felt layer with thermal conductivity of 0.05 W.m.K and thickness of 5 cm. Temperature of the outer surface is 25 °C. Calculate the heat flow from the surroundings to the tube with length of 100 m. What is the temperature on the boundary between polypropylene and felt layers? Result: The heat flow from the surroundings is approx. 1.77 kW. Temperature between layers of isolation is 8.8 °C.arrow_forwardQuestion 5: A copper bar 35 cm long, with square cross-section 2 cm x 2 cm is fitted with a resistive heater at one end, and a large heat sink at the other. The bar itself is ideally thermally lagged. (i) (ii) Sketch how you think the two thermometers would behave when the heater is switched on; (ii) Calculate the thermal conductivity if in the steady-state, T1=64.7 deg C and T2=40.0 deg C. Hint: rate of flow of heat = k*A*AT/X V=6 V, I=2.5A heater T1 25 cm T2 Heat sinkarrow_forwardA long insulated tube is doped with an exothermic ma- terial which generates steady and uniform heat at rate of è [W/m³]. The tube has an inner radius r₁ and outer radius r₂. The temperature of the outer insulated sur- face is T₂. This tube is used to heat a liquid flowing through it. (a) Write the governing differential equation and boundary conditions to determine the tempera- ture distribution inside the tube. (b) What is the heat flux supplied to the liquid by the tube? e (√₂²-1₁²) / 21₁ 1 Fluid Figure 2: Schematic Insulation T₂ Narrow_forward
- Let's say a 3.0 gram copper wafer is dropped from a height of 50.0 meters. If 60% of the potential energy lost in the drop could be converted to thermal energy used to heat the copper from an initial temperature of 25 degrees celsius, what would the final temperature of the copper wafer? Would the answer be different if the wafer has a mass greater than 3 grams? Note: the specific heat of copper is 387 J/(kg*K). The temperature is between 25.8 and 26.0 degrees celsius, yes the bigger the mass the greater the energy. O The temperature is between 25.6 and 25.8 celsius, answer does not depend on mass. O The temperature is between 25.0 and 25.2 celsius, answer does not depend on mass. O The temperature is 25.5 and of course the more mass something has the greater energy will be needed to raise the temperature. The temperature is 26.2 and if the mass is doubled so will be the change in temperature. O The temperature is 25.9 degrees celsius and the answer does not depend on mass. O The…arrow_forwardConsider a solid sphere of radius R with a fixed surface temperature, TR. Heat is generated within the solid at a rate per unit volume given by q = ₁ + ₂r; where ₁ and ₂ are constants. (a) Assuming constant thermal conductivity, use the conduction equation to derive an expression for the steady-state temperature profile, T(r), in the sphere. (b) Calculate the temperature at the center of the sphere for the following parameter values: R=3 m 1₁-20 W/m³ TR-20 °C k-0.5 W/(m K) ₂-10 W/m³arrow_forwardA mechanic needs to remove a tight fitting pin of material A from a hole in a block made of material B. The machinist heats both the pin and the block to the same high temperature and removes the pin easily. What statement relates the coefficient of thermal expansion of material A to that of material B?arrow_forward
- In this question, we are concerned with the evolution of the temperature u(x, t) in a homogeneous thin heat conducting rod of length L = 1. We can consider that the rod is laterally insulated as to have a one-dimensional problem. The evolution of the temperature is governed by the one-dimensional heat equation ди 0 0 = K Ət Əx2' Assume that this equation is subject to the following initial conditions u(x,0) = f(x) and boundary conditions (0, t) = 0 and ди (1,t) + и(1,t) — 0 (i) Discuss briefly the physical meaning of the boundary conditions.arrow_forward1. Saturated steam at 500 K flows in a 0.20 m inside diameter, 0.21 m outside diameter pipe. The pipe is covered with 0.08 m of insulation with a thermal conductivity of 0.10 W/m-K. The pipe's conductivity is 52 W/m-K. The ambient temperature is 300 K. The unit convective coefficients are h; = 18,000 W/m²-K and ho = 12 W/m²-K. Determine the heat loss (kJ/min) from 4 m of pipe. • show conversions, units, and box in your final answersarrow_forwardAnswer correctly and quickly as possible please.arrow_forward
- Please include a fbd of the problemarrow_forwardBuild a spreadsheet to do the step by step method for estimating the temperature of unprotected steel work exposed to the ASTM E119 Standard Fire. Assume a convective heat transfer coefficient of 25 W/m2K and an emissivity of 0.5. Assume the specific heat to remain constant at 600 J/kgK. Use a time step of 30 seconds and an ambient temperature of 20°C. Provide an Excel plot showing the curves of the fire and a steel member through a time of 60 minutes with F/V ratios of: a)25 m-1 b)100 m-1 c)200 m-1 d)300 m-1 Note your plot should contain 5 curves. One for the fire and one for each of the F/V values. Also on the spreadsheet, highlight in green, the cells identifying the temperature of the unprotected steel member with an F/V of 200m-1 at the following times: a)3 minutes b)10 minutes c)20 minutes d)50 minutesarrow_forwardThe 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 + bx, where a = 200 °C, b=-2000 °C/m², and x is in meters. i. ii. What is the heat generation rate in the wall? (8) Determine the heat fluxes at the two wall faces. In what manner are these heat fluxes related to the heat generation rate? (arrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning