Consider a solid body having mass m, volume V, density = 10000 kg/m3 , specific heat...
Consider a solid body having mass m, volume V, density = 10000 kg/m3 , specific heat capacity at constant pressure Cp = 600 J/(kg.K), and its initial temperature Ti = 200oC. Assume the system losses heat to the environment by convection at temperature T = 40oC and heat transfer coefficient h = 12 W/(m2 .K). (a) Start with applying the energy balance, and use the concept of the simplified lumped system analysis to derive an expression for the change of the system temperature T with time t. (b) If the system is a spherical ball having a diameter D = 10 cm and thermal conductivity k = 10 W/(m.K), can the simplified lumped system analysis be applicable to determine the change of the temperature of the ball with time? If the answer is yes, what is the temperature of the spherical ball after 30 min and 2.0 hour?
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Consider a solid body having mass m, volume V, density = 10000
kg/m3 , specific heat...
5. A flaked cereal is of thickness 2L=1.2 mm (or the characteristic length Lc = V/A=...
5. A flaked cereal is of thickness 2L=1.2 mm (or the characteristic length Lc = V/A= 0.6 mm). The density, specific heat, and thermal conductivity of the flake are p 700 kg/m3,cp = 2400J/kg K, and k = 0.34 W/m K, respectively. The product is to be baked by increasing its temperature from Ti = 20 °C to Tr = 220 °C in a convection oven, through which the product is carried on a conveyor. If the oven is Lo...
A long cylinder of diameter D 0.012 m, thermal conductivity k 358 W/(mK), density p -...
A long cylinder of diameter D 0.012 m, thermal conductivity k 358 W/(mK), density p - 7614 kg/m3, specific heat c 418 J/(kgK) is initially at a uniform temperature of Ti-74°C. The cylinder is suddenly exposed to a gas at T,-18 ℃ The convection coefficient is h -17 W/(m2K). Verify that a lumped capacitance analysis can be used for the transient response of the cylinder temperature. What is the time t in seconds for the cylinder temperature to become Tf-32...
Thermal energy storage systems commonly involve a packed bed of solid spheres through which a hot...
Thermal energy storage systems commonly involve a packed bed of solid spheres through which a hot gas flows when the system is being charged. In the charging process heat is transferred from the hot gas to the spheres and it increases the thermal energy stored in the spheres. Here are some variables that are important - the convection coefficient between the particle surface and the gas is h (W/m2 K) and the particle thermophysical properties are k (W/m K), Cp...
Consider an oil of density p 800 kg/m3, viscosity u 0.01 Pa.s (10 times the viscosity of water), ...
Consider an oil of density p 800 kg/m3, viscosity u 0.01 Pa.s (10 times the viscosity of water), heat capacity of Cp 2 k]/(kg K) and thermal conductivity of Koll -0.15 W/(mk). This oil flows at mass flowrate of 30 kg/minute through a copper pipe of d- 2 cm inner diameter, with wall thickness of t-1 mm. At the relevant conditions, copper has thermal conductivity of ke 400 W/(m.K). The copper pipe loses heat to the surroundings of Tsurr 20°C...
QUESTION 1 (10 marks) a) Write the Newton's law of heat convection in fluid using convection heat transfer coef...
QUESTION 1 (10 marks) a) Write the Newton's law of heat convection in fluid using convection heat transfer coefficient, h (Wm2.K). Please explain the equation in terms of its driving force and resistancC (2 marks) (POUCOI/C2) b) Define the heat transfer rate, q,by inside and outside convection and wall conduction considering a stainless steel cylindrical pipe (inside radius, ri and outer radius, ) with fiberglass insulator (radius, s) in ą steady state condition as shown in Figure Q11 Steam with...
A large wall made of 10-cm-thick solid brick (k = 0.8 W/m.K, p 2000 kg/m3, and p 800 J/kg.K) is o...
Heat transfer question.
A large wall made of 10-cm-thick solid brick (k = 0.8 W/m.K, p 2000 kg/m3, and p 800 J/kg.K) is originally at a uniform temperature of 30°C. The wall is adiabatic (well insulated) on one side as shown in the figure. The other surface is suddenly exposed to convection air flow at 10°C, resulting in a heat transfer coefficient h=40W/m2.K. Fluid (4.1) Determine the temperature of both surfaces Gr 0 and x 10 cm) after 5 hr...
There is a small sphere with volume, V, surface area, As, and specific heat, c. The sphere was in...
There is a small sphere with volume, V, surface area, As, and specific heat, c. The sphere was initially was at T, and was placed in liquid with temperature To and heat transfer coefficient h. Show the governing equation and temperature as a function of time when (i) Ti > To and (ii) Ti < T. You can use the lumped capacitance analysis. (20 pt) 3.
There is a small sphere with volume, V, surface area, As, and specific heat,...
The temperature distribution across a wall 0.2 m thick at a certain instant of time is...
The temperature distribution across a wall 0.2 m thick at a certain instant of time is T(x) = a + bx + cxº, where T is in degrees Celsius and x is in meters, a = 200°C, b = -190°c/m, and c = 30°C/m2. The wall has a thermal conductivity of 1 W/m.k. (a) On a unit surface area basis, determine the rate of heat transfer into and out of the wall and the rate of change of energy stored...
The temperature distribution across a wall 1 m thick at a certain instant of time is...
The temperature distribution across a wall 1 m thick at a certain instant of time is T(x) = a + box + cx", where T is in Kelvin and x is in meters, a = 350 K, b = -100 K/m, and c=50 K/m". The wall has a thermal conductivity of 2 W/m.K. (a) On a unit surface area basis, determine the rate of heat transfer into and out of the wall and the rate of change of energy stored...
Problem 3 (20 points) A cross-flow heat exchanger consists of a bundle of 32 tubes in a long duct. Hot water at 150°C and a mean velocity of 0.5 m/s enters the tubes having inner and outer diameters...
Problem 3 (20 points) A cross-flow heat exchanger consists of a bundle of 32 tubes in a long duct. Hot water at 150°C and a mean velocity of 0.5 m/s enters the tubes having inner and outer diameters of 10.2mm and 12.5mm and has to be cooled to 136°C. The tubes are made of steel of thermal conductivity k-40 W/m.K. Air at 10°c enters the exchanger (unfinned) with a volumetric flow rate of 1.0 m3/s. The convective heat transfer coefficient...
5. A flaked cereal is of thickness 2L=1.2 mm (or the characteristic length Lc = V/A= 0.6 mm). The density, specific heat, and thermal conductivity of the flake are p 700 kg/m3,cp = 2400J/kg K, and k = 0.34 W/m K, respectively. The product is to be baked by increasing its temperature from Ti = 20 °C to Tr = 220 °C in a convection oven, through which the product is carried on a conveyor. If the oven is Lo...
A long cylinder of diameter D 0.012 m, thermal conductivity k 358 W/(mK), density p - 7614 kg/m3, specific heat c 418 J/(kgK) is initially at a uniform temperature of Ti-74°C. The cylinder is suddenly exposed to a gas at T,-18 ℃ The convection coefficient is h -17 W/(m2K). Verify that a lumped capacitance analysis can be used for the transient response of the cylinder temperature. What is the time t in seconds for the cylinder temperature to become Tf-32...
Thermal energy storage systems commonly involve a packed bed of solid spheres through which a hot gas flows when the system is being charged. In the charging process heat is transferred from the hot gas to the spheres and it increases the thermal energy stored in the spheres. Here are some variables that are important - the convection coefficient between the particle surface and the gas is h (W/m2 K) and the particle thermophysical properties are k (W/m K), Cp...
Consider an oil of density p 800 kg/m3, viscosity u 0.01 Pa.s (10 times the viscosity of water), heat capacity of Cp 2 k]/(kg K) and thermal conductivity of Koll -0.15 W/(mk). This oil flows at mass flowrate of 30 kg/minute through a copper pipe of d- 2 cm inner diameter, with wall thickness of t-1 mm. At the relevant conditions, copper has thermal conductivity of ke 400 W/(m.K). The copper pipe loses heat to the surroundings of Tsurr 20°C...
QUESTION 1 (10 marks) a) Write the Newton's law of heat convection in fluid using convection heat transfer coefficient, h (Wm2.K). Please explain the equation in terms of its driving force and resistancC (2 marks) (POUCOI/C2) b) Define the heat transfer rate, q,by inside and outside convection and wall conduction considering a stainless steel cylindrical pipe (inside radius, ri and outer radius, ) with fiberglass insulator (radius, s) in ą steady state condition as shown in Figure Q11 Steam with...
Heat transfer question.
A large wall made of 10-cm-thick solid brick (k = 0.8 W/m.K, p 2000 kg/m3, and p 800 J/kg.K) is originally at a uniform temperature of 30°C. The wall is adiabatic (well insulated) on one side as shown in the figure. The other surface is suddenly exposed to convection air flow at 10°C, resulting in a heat transfer coefficient h=40W/m2.K. Fluid (4.1) Determine the temperature of both surfaces Gr 0 and x 10 cm) after 5 hr...
There is a small sphere with volume, V, surface area, As, and specific heat, c. The sphere was initially was at T, and was placed in liquid with temperature To and heat transfer coefficient h. Show the governing equation and temperature as a function of time when (i) Ti > To and (ii) Ti < T. You can use the lumped capacitance analysis. (20 pt) 3.
There is a small sphere with volume, V, surface area, As, and specific heat,...
The temperature distribution across a wall 0.2 m thick at a certain instant of time is T(x) = a + bx + cxº, where T is in degrees Celsius and x is in meters, a = 200°C, b = -190°c/m, and c = 30°C/m2. The wall has a thermal conductivity of 1 W/m.k. (a) On a unit surface area basis, determine the rate of heat transfer into and out of the wall and the rate of change of energy stored...
The temperature distribution across a wall 1 m thick at a certain instant of time is T(x) = a + box + cx", where T is in Kelvin and x is in meters, a = 350 K, b = -100 K/m, and c=50 K/m". The wall has a thermal conductivity of 2 W/m.K. (a) On a unit surface area basis, determine the rate of heat transfer into and out of the wall and the rate of change of energy stored...
Problem 3 (20 points) A cross-flow heat exchanger consists of a bundle of 32 tubes in a long duct. Hot water at 150°C and a mean velocity of 0.5 m/s enters the tubes having inner and outer diameters of 10.2mm and 12.5mm and has to be cooled to 136°C. The tubes are made of steel of thermal conductivity k-40 W/m.K. Air at 10°c enters the exchanger (unfinned) with a volumetric flow rate of 1.0 m3/s. The convective heat transfer coefficient...
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