Concept explainers
In a cylindrical fuel rod of a nuclear reactor, heat is generated internally according to the equation
where
Calculate the temperature drop from the centerline to the surface for a 2.5-cm-diameter rod having a thermal conductivity of
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Chapter 2 Solutions
Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
- The left side of this equation tells how much energy Q the cylinder gives to the water while it cools. The right side of this equation tells how much energy Q the water and aluminum cup absorb from the cylinder to warm up. Because it is the same energy, they are equal. What is known in this equation? Mcyl 411.7 g, malum 46.5 g, malum+water = 175 g Can you find: mwater =? g Twater = Talum = 20°C (water and cup of room temperature) 90°C, T; = 35°C (hot cylinder and cool "cylinder+cup+water" temperatures) Tcyl kCal Calum = 0.22, Cwater 1 (specific heat of water and aluminum, measured in units kg-°C What are we looking for is Ccul - How we find it? Plug all the numbers into the equation (1), Ccul will be one unknown which you can calculate from the equation. Important, convert all the masses from grams to kilograms! After you find Ccyl, compare it to known value for the copper 0.093(our cylinder is made out of copper). |Ceyl -0.093| % : · 100% 0.093arrow_forwarda. True/False Given 1-D steady-state conduction through a wall with uniform heat generation, the heat transfer (Q. W) is constant throughout the wall. TRUE FALSE b. True/False Consider convection heat transfer acting on an object that is in contact with a fluid at temperature T-. Ifh (the convection coefficient) gets very large. it tends to drive the surface temperature of that object to the fluid temperature T-. TRUE FALSE c. Short answer You need to calculate the temperature at the free end (tip) of a long fin. The boundary condītion you should NOT use is: Circle one! Convective tip Adiabatic tip Infinite finarrow_forwardProblem 5. Heat is generated uniformly at a rate of Se in a copper wire of radius re having thermal conductivity k where the ambient temperature is T. and the heat transfer coefficient is ho. At steady state; i. ii. iii. find an expression for the temperature distribution at steady-state and draw a T vs. r graph. Substituting; S₂ = 125 kW/m³, k = 390 W/m.K, rc = 2 mm, T = 20°C and hoc=25W/m²K, find the steady state surface and center temperatures and the heat transfer rate to the surroundings. Repeat part i and ii when the wire is covered with an insulation of thickness ti and ki which are 0.1 mm and 0.2 W/m.K, respectively.arrow_forward
- The rate of heat flow per unit length q/L through a hollow cylinder of inside radius ri and outside radius ro is q/L=(AkT)/(rori) where A=2/(rori)/ln(ro/ri). Determine the percent error in the rate of heat flow if the arithmetic mean area (ro+ri) is used instead of the logarithmic mean area A for ratios of outside-to-inside diameters (Do/Dj) of 1.5, 2.0, and 3.0. Plot the results.arrow_forwardAn elastic string is fixed at one end and is wound on a drum of diameter 0.2m so that the tension in the string increases as the angle through which the drum turns increases. The torque Ton the drum then varies according to the law: T = Sr20 where S = stiffness of elastic string (S=120KN/m) r = radius of drum As the drum starts at 0 = 0, the work done can be calculated using calculus, for any given value of 0, as shown: ST de Determine the work done by the drum if it rotates through an angle of 0 = 2/3,arrow_forwardQ3: Consider evaluation of different temperatures of solar photovoltaic/thermal system (PVT) as shown in Figure 1(a). The following set of differential equations represent energy balance equations to be solve using matrices and eigenvalues dTglass = -0.75Tglass + 0.75TPVT (1) dt - 1.18Tglass – 22TpyT + 237wax (2) dt dTwax 12Tglass + 18TpyT – 19 Twax (3) dt Where, Tptass, TPVT, and Twax, are temperatures illustrated in Figure 1(b). At time t-0 the initial conditions are Tglass = 35 , Tpyr = 33, and Twax = 31 °C. Cold sappty In frem water Tank Glass PVT Enpann Nane-PCMPVT Collector Wax Tubes Sterg Tank Mat Nanofluid Heat Exchanger Tepe Contalner Tuek et Pump for drainarrow_forward
- 5 Problem = How long should it take to boil an egg? Model the egg as a sphere with radius of 2.3 cm that has properties similar to water with a density of ρ 1000 kg/m³ and thermal conductivity of k = 0.606 Watts/(m.°C) and specific heat of c = 4182 J/(kg.° C). Suppose that an egg is fully cooked when the temperature at the center reaches 70° C. Initially the egg is taken out of the fridge at 4° C and placed in the boiling water at 100° C. Since the egg shell is very thin assume that it quickly reaches a temperature of 100° C. The protein in the egg effectively immobilizes the water so the heat conduction is purely conduction (no convection). Plot the temperature of the egg over time and use the data tooltip in MATLAB to make your conclusion on the time it takes to cook the egg in minutes. Figure 1: Image source: [Link]arrow_forwardK). average NUSseit Number. 2. A slab of iron with temperature, T1=48 deg C is used to heat a flat glass plate that has an initial temperature of Tg1=18 deg C. Assuming no heat is lost to the environment, and the masses are m;=0.49 kg for the slab and mg=310g for the plate, what is the amount of heat transferred when the two have reached equal temperature? Assume C;=0.11 kcal/kg-deg C for iron and cg=0.20 kcal/kg-deg C for glass.arrow_forwardSuppose that we have a wire (or a thin metal rod) of length that is insulated except at the endpoints. Let L denote the position along the wire and let t denote time. The 1- D heat equation is * temperature u 3 insulation O (a^2 u)/(at^2)=c^2 (a^2 u)/(ax^2) (a^2 u)/(at^2 )=c^2 du/əx au/Ət=c^2 (a^2 u)/(ðx^2 ) au/at=c^2 au/Əx nonearrow_forward
- 2: The first law of thermodynamics can be written as: TdS = dU + PdV = dU = TdS – PdV. Moreover, we also use some other thermodynamic potentials. Most common three are: Helmholtz free energy: F = U – TS, Gibbs free energy: G = F + PV, Enthalpy: H = U + PV. From here prove the following: dF = -SdT – PdV, dG = -SdT +VdP, %3D dH = TdS + VdP. %3Darrow_forwardAn electric heater producing 260 W of heat is used to warm up a room containing 7 m3 of air. If we assume the room is perfectly sealed and there is no heat loss through the room boundaries, such that all of the heater output goes into increasing the air temperature, how long will it take to heat up the air in the room from 5.0 °C to 24.1 °C? Give your answer to the nearest minute and assume that the specific volume (v = 0.85 m3/kg) and specific heat capacity at constant volume (cv = 1.005 kJ/(kg K)) remain constant throughout the heating process.arrow_forwardIn a concentrated solar power plant, molten salt tank is used to store the thermal energy from the sun during the day. The tank wall thickness is 3cm containing molten salt at a temperature of 390 degree Celsius. There is atmospheric air outside the tank at a temperature of 30 degree Celsius. Suppose heat is lost as a result of heat transfer from the molten salt to the atmospheric air. What is the mode of heat transfer in this condition? conduction then convection convection then conduction convection then conduction then convection conduction then convection then conductionarrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning