2. A rectangular swimming pool is 1.5 m deep, 15 m wide, and 25 m long. Assume thebottom and sides of the swimming pool are insulated so that the pool exchanges heatwith its environment through the top surface only. The density of water is 1000 kg/m³, thespecific heat is 4180 J/kg-°C, and the heat transfer coefficient is 10 W/m²-°C.1.5 mHeat exchangethrough topsurface only25 mT(t)To15 mComplete the following.(a) Determine the thermal time constant of the pool and express your answer indays.(b) The swimming pool is being held at T0 = 30 °C when the power fails and externalheating stops. The air temperature around the pool (T) drops quickly and can beassumed to be 10 °C at time t = 0. Write a script file in MATLAB® that plots the pooltemperature for a duration of four thermal time constants.

Answered: Image /qna-images/answer/25e13b30-c6b3-49d8-8246-49b0fdaa2660.jpg

2. A rectangular swimming pool is 1.5 m deep, 15 m wide, and 25 m long. Assume the bottom and sides of the swimming pool are insulated so that the pool exchanges heat with its environment through the top surface only. The density of water is 1000 kg/m³, the specific heat is 4180 J/kg-°C, and the heat transfer coefficient is 10 W/m²-°C. 1.5 m Heat exchange through top surface only Too I 25 m T(1) 15 m Complete the following. (a) Determine the thermal time constant of the pool and express your answer in days. (b) The swimming pool is being held at T0 = 30 °C when the power fails and external heating stops. The air temperature around the pool (T∞) drops quickly and can be assumed to be 10 °C at time t = 0. Write a script file in MATLAB that plots the pool temperature for a duration of four thermal time constants. Ⓡ

2. A rectangular swimming pool is 1.5 m deep, 15 m wide, and 25 m long. Assume the bottom and sides of the swimming pool are insulated so that the pool exchanges heat with its environment through the top surface only. The density of water is 1000 kg/m³, the specific heat is 4180 J/kg-°C, and the heat transfer coefficient is 10 W/m²-°C. 1.5 m Heat exchange through top surface only Too I 25 m T(1) 15 m Complete the following. (a) Determine the thermal time constant of the pool and express your answer in days. (b) The swimming pool is being held at T0 = 30 °C when the power fails and external heating stops. The air temperature around the pool (T∞) drops quickly and can be assumed to be 10 °C at time t = 0. Write a script file in MATLAB that plots the pool temperature for a duration of four thermal time constants. Ⓡ

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter2: Steady Heat Conduction

Section: Chapter Questions

Problem 2.46P: 2.46 The wall of a liquid-to-gas heat exchanger has a surface area on the liquid side of with a...

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2.46 The wall of a liquid-to-gas heat exchanger has a surface area on the liquid side of with a heat transfer coefficient of . On the other side of the heat exchanger wall flows a gas, and the wall has 96 thin rectangular steel fins 0.5 cm thick and 1.25 cm high as shown in the accompanying sketch. The fins are 3 m long and the heat transfer coefficient on the gas side is . Assuming that the thermal resistance of the wall is negligible, determine the rate of heat transfer if the overall temperature difference is .
3.17 A 1.4-kg aluminum household iron has a 500-W heating element. The surface area is . The ambient temperature is 21°C, and the surface heat transfer coefficient is . How long after the iron is plugged in does its temperature reach 104°C?
2.2 A small dam, which is idealized by a large slab 1.2 m thick, is to be completely poured in a short Period of time. The hydration of the concrete results in the equivalent of a distributed source of constant strength of 100 W/m3. If both dam surfaces are at 16°C, determine the maximum temperature to which the concrete will be subjected, assuming steady-state conditions. The thermal conductivity of the wet concrete can be taken as 0.84 W/m K.
3.16 A large, 2.54-cm.-thick copper plate is placed between two air streams. The heat transfer coefficient on one side is and on the other side is . If the temperature of both streams is suddenly changed from 38°C to 93°C, determine how long it takes for the copper plate to reach a temperature of 82°C.
A steel tube with a thermal conductivity of 55 W/m.K carries a fluid at 175°C, with a convection heat transfer coefficient of 190 W/m²./K. The tube has an external diameter of 5 cm, a wall thickness of 1 cm and a length of 1.5 m. The ambient air and surroundings are at 27°C, with a convection heat transfer coefficient of 20 W/m².K. Neglecting the effects of radiation, determine:a) The new heat transfer rate, considering the effects of radiation, if an additional layer of 15 mm thick foam with a conductivity of 0.03 W/m.K is added to the system. b) The critical insulation radius of the system after the addition of this insulating layer.
Suppose that the 10 cm thick concrete wall of a commercial building measures 30 mby 4 m. The energy impinging on the surface is 700 W/m^2. Under these conditionsthe external air temperature is 25ºC, and the internal and external surfacetemperatures of the concrete wall are 17ºC and 40ºC, respectively. Calculate the net amount of thermal energy radiated by the wall answer = 41,880 W Data for wall: Heat transfer coefficient of air at 25ºC = 5 W/m^2KThermal conductivity of concrete = 1.2 W/mKEmissivity of concrete = 0.85Stefan’s constant = 5.7 x 10^-8 W/m^2K^4
A steel tube with a thermal conductivity of 45 W/m.K carries a fluid at 200°C, with a convection heat transfer coefficient of 210 W/m2./K. The tube has an external diameter of 5 cm, a wall thickness of 1 cm and a length of 2 m. The ambient air and surroundings are at 25°C, with a convection heat transfer coefficient of 25 W/m2.K. Neglecting the effects of radiation, determine: 1) The total resistance considering the effects of radiation only on the outside, with the coefficient hr = 2W/m2.K 2) The new heat transfer rate, considering the effects of radiation, if an additional layer of 15 mm thick foam with a conductivity of 0.03 W/m.K is added to the system. 3) The critical insulation radius of the system after adding this insulating layer.
: A spherical container ( k= 30 W/moC ) with inner radius r1 = 2 m and outer radius ro=2.1 m is is filled with ice water T= 0 oC subjected to the convection on the outer surface T∞2 = 25 oC , h∞2= 18 W/m2 oC .For steady one-dimensional heat transfercalculate a) The mathematical formulation b) the variation of temperature, and c) therate of heat transfer are to be determined fo
A steel tube with a thermal conductivity of 55 W/mK carries a fluid at 175°C, with a convection heat transfer coefficient of 190 W/m 2 ./K. The tube has an external diameter of 5 cm, a wall thickness of 1 cm and a length of 1.5 m. The ambient air and surroundings are at 27°C, with a convection heat transfer coefficient of 20 W/m 2 .K. Neglecting the effects of radiation, determine: a) the resistance by conduction through the tube wall b) the convection resistance inside the tube c) The total rate of heat transfer d) The temperature of the outer surface of the tube e) The total resistance considering the effects of radiation only on the outside, with the coefficient h r = 2W/m 2 .K f) The new heat transfer rate, taking into account the effects of radiation, if an additional layer of 15 mm thick foam with a conductivity of 0.03 W/mK is added to the system. g) The critical insulation radius of the system after the addition of this insulating layer.
An electric motor is to be connected by a horizontal steel shaft (k - 42.56 W/m.K), 25 mm in diameter to an impeller of a pump, circulating liquid metal at a temperature of 540°C. If the temperature of electric motor is limited to a maximum value of 52°C with the ambient air at 27°C and heat transfer coefficient of 40.7 W/m?K, what length of shaft should be specified between the motor and pump ?
5.17 In the liquid heating tank shown in the figure below, density = 0.8g/cm^3, V=500cm^3, Cp=0.5cal/(g C), the total heat transfer area of the heating coil is 20cm^2, and the total heat transfer coefficient is 10cal/ (cm^2 hr C). Inside the coil, hot oil flows with a temperature of Tq. Find the temperature T(t) of the fluid when the temperature of the oil changes as shown in the figure at any moment, ignoring the temperature difference between the surface of the heating coil and the oil.
Given a plaster of paris (PoP) slab with L = 0.052 cm, W = 0.052 cm, and H = 0.0095 cm, what is the heat transfer coefficient if the biot number is 0.19682? Other data (if necessary):Initial Temperature: 328.2 CSurrounding Temperature: 27.9 CPoP Density: 680 kg/m^3Heat Capacity: 1090 J/kgKThermal Conductivity: 0.1185 W/mK