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Eq(1) Here T is temperature, p ,C and K are density, heat capacity and...
12. The temperature at the inner and outer surfaces of a hollow cylindrical pipe with wall...
12. The temperature at the inner and outer surfaces of a hollow cylindrical pipe with wall thickness L are held at constant values of T and T, respectively, where T, <To. The wall material has thermal conductivity that varies linearly according to k = k,(1 +BT), where k, and ß are constants. Draw a schematic of the system. Define and label a coordinate system. State assumptions and boundary conditions. b. Derive the governing differential equation for the heat transport and...
(1) A sphere of decaying radioactive material of radius ro produces heat at a rate of q"" (W/m3)....
(1) A sphere of decaying radioactive material of radius ro produces heat at a rate of q"" (W/m3). The sphere is contained in a spherical shell of graphite of outside radius r1. The outside surface of the graphite is cooled uniformly by flowing air of temperature To. The heat transfer coefficient at the outside surface is h. The constant thermal conductivities of the radioactive material and the graphite are ko and ki, respectively. Densities and heat capacities are ρο, co...
Two large parallel plates with surface conditions approximating those of a blackbody are maintained at 800°C...
Two large parallel plates with surface conditions approximating those of a blackbody are maintained at 800°C and 100°C, respectively. Determine the rate of heal transfer by radiation between the plates in Wim and the radiative heat transfer coefficient in W/m K ) 12 Write down the one-dimensional sent heal conduction equation for a plane wall with constant thermal conductivity and heat generation in its simplest form, and indicate what each variable represents 13 Write down the one-dimensional transient heat conduction...
Problem 2(30 points) Consider the steady-state temperature distribution in a square plate with dimensions 2 m...
Problem 2(30 points) Consider the steady-state temperature distribution in a square plate with dimensions 2 m x 2 m. There is a heat generation of ġ(x.y)=6x [W/my], and the thermal conductivity of k=1[W/(m-°C)]. The temperature on the top boundary is given by a piecewise function, f(x), which is defined below. x(4- x²)+10 0<x<1 | x(4- x?) + 20, 1<x<2 The bottom boundary is insulated. The temperatures on left-handed and right-handed boundary are maintained at constants 10[°C] and 20 [°C] as...
Question 1. Substitution of given form of solution and hyperbolic functions. The non-linear ordinary differential equat...
Question 1. Substitution of given form of solution and hyperbolic functions. The non-linear ordinary differential equation describing the smooth shape of a structural arch of constant thickness in mechanical equilibrium under its own weight per unit length w, and a horizontal compressive force T, is (y")2 = k2(1 + (y')"). Here k is a known constant and y(x) is the vertical height of the arch at position x, the horizontal distance from a given reference point. (a) Using hyperbolic function...
please provide me with full working solution. Any help is appreciated. thank you in advance Consider the diffusion equation, au(x,t u(x,t) Here u(x,t) > 0 is the concentration of some diffusing...
please provide me with full working solution. Any help is
appreciated. thank you in advance
Consider the diffusion equation, au(x,t u(x,t) Here u(x,t) > 0 is the concentration of some diffusing substance, the spatial variable is x, time is t and D is a constant called the diffusivity with dimensions [LT-11. We will consider the diffusion equation on a finite spatial domain (0<x< 1) and an infinite time horizon (t > 0). To solve the diffusion equation we must include...
1) 2) 3) PROJECT #1 (2.5 Marks): The heat that is conducted through a body must...
1)
2)
3)
PROJECT #1 (2.5 Marks): The heat that is conducted through a body must frequently be removed by other heat transter processes. For example, the heat generated in an electronic device must be dissipated to the surroundings through convection by means of fins. Consider the one-dimensional aluminum fin (thickness t 3.0 mm, width Z 20 cm, length L) shown in Figure 1, that is exposed to a surrounding fluid at a temperature 1. The conductivity of the aluminum...
LT An aluminum rod of diameter D 2.5 cm and of length from a wall maintained at T, 300"C. The.coovective heat coefficient h 17 W/m2-K with an ambie.t air temperature T Thermal conductivity k =...
LT An aluminum rod of diameter D 2.5 cm and of length from a wall maintained at T, 300"C. The.coovective heat coefficient h 17 W/m2-K with an ambie.t air temperature T Thermal conductivity k = 204 WmK. Assume there is e luid by convection from the end of the rod, which is at temperature Ta. Using 2. -38c. nergy transfer to the a finite difference method, with Ax = 5 cm, the fo be derived for the solution of the...
1. 1.08x106 grams/h of a superheated fluid flows through a pipe in a power plant. The...
1. 1.08x106 grams/h of a superheated fluid flows through a pipe in a power plant. The pipe is 1000 cm long, has an inner diameter of 0.05m and a wall thickness of 0.6 cm. The pipe has a thermal conductivity of 0.0017 kW/mK, and the inner pipe surface is at a uniform temperature of 393K. The temperature drop between the inlet and exit of the pipe is 7K, and the constant pressure specific heat of vapor is 2190 J/kgK. If...
A long wire with circular cross section and diameter D = 1 mm is submerged in an oil bath with temperature To 20。C. The wire is initially at temperature T = 20。C, the same temperature as the oil. A...
A long wire with circular cross section and diameter D = 1 mm is submerged in an oil bath with temperature To 20。C. The wire is initially at temperature T = 20。C, the same temperature as the oil. A current is passed through the wire, resulting in a volumetric heat generation of q - 1.5 x 108 W/m3. The convection coefficient is h - 500 W/m2 - K, and the properties of the wire are ρ-8000 kg/m3, Cp-500 J/kg-K, and...
12. The temperature at the inner and outer surfaces of a hollow cylindrical pipe with wall thickness L are held at constant values of T and T, respectively, where T, <To. The wall material has thermal conductivity that varies linearly according to k = k,(1 +BT), where k, and ß are constants. Draw a schematic of the system. Define and label a coordinate system. State assumptions and boundary conditions. b. Derive the governing differential equation for the heat transport and...
(1) A sphere of decaying radioactive material of radius ro produces heat at a rate of q"" (W/m3). The sphere is contained in a spherical shell of graphite of outside radius r1. The outside surface of the graphite is cooled uniformly by flowing air of temperature To. The heat transfer coefficient at the outside surface is h. The constant thermal conductivities of the radioactive material and the graphite are ko and ki, respectively. Densities and heat capacities are ρο, co...
Two large parallel plates with surface conditions approximating those of a blackbody are maintained at 800°C and 100°C, respectively. Determine the rate of heal transfer by radiation between the plates in Wim and the radiative heat transfer coefficient in W/m K ) 12 Write down the one-dimensional sent heal conduction equation for a plane wall with constant thermal conductivity and heat generation in its simplest form, and indicate what each variable represents 13 Write down the one-dimensional transient heat conduction...
Problem 2(30 points) Consider the steady-state temperature distribution in a square plate with dimensions 2 m x 2 m. There is a heat generation of ġ(x.y)=6x [W/my], and the thermal conductivity of k=1[W/(m-°C)]. The temperature on the top boundary is given by a piecewise function, f(x), which is defined below. x(4- x²)+10 0<x<1 | x(4- x?) + 20, 1<x<2 The bottom boundary is insulated. The temperatures on left-handed and right-handed boundary are maintained at constants 10[°C] and 20 [°C] as...
Question 1. Substitution of given form of solution and hyperbolic functions. The non-linear ordinary differential equation describing the smooth shape of a structural arch of constant thickness in mechanical equilibrium under its own weight per unit length w, and a horizontal compressive force T, is (y")2 = k2(1 + (y')"). Here k is a known constant and y(x) is the vertical height of the arch at position x, the horizontal distance from a given reference point. (a) Using hyperbolic function...
please provide me with full working solution. Any help is
appreciated. thank you in advance
Consider the diffusion equation, au(x,t u(x,t) Here u(x,t) > 0 is the concentration of some diffusing substance, the spatial variable is x, time is t and D is a constant called the diffusivity with dimensions [LT-11. We will consider the diffusion equation on a finite spatial domain (0<x< 1) and an infinite time horizon (t > 0). To solve the diffusion equation we must include...
1)
2)
3)
PROJECT #1 (2.5 Marks): The heat that is conducted through a body must frequently be removed by other heat transter processes. For example, the heat generated in an electronic device must be dissipated to the surroundings through convection by means of fins. Consider the one-dimensional aluminum fin (thickness t 3.0 mm, width Z 20 cm, length L) shown in Figure 1, that is exposed to a surrounding fluid at a temperature 1. The conductivity of the aluminum...
LT An aluminum rod of diameter D 2.5 cm and of length from a wall maintained at T, 300"C. The.coovective heat coefficient h 17 W/m2-K with an ambie.t air temperature T Thermal conductivity k = 204 WmK. Assume there is e luid by convection from the end of the rod, which is at temperature Ta. Using 2. -38c. nergy transfer to the a finite difference method, with Ax = 5 cm, the fo be derived for the solution of the...
A long wire with circular cross section and diameter D = 1 mm is submerged in an oil bath with temperature To 20。C. The wire is initially at temperature T = 20。C, the same temperature as the oil. A current is passed through the wire, resulting in a volumetric heat generation of q - 1.5 x 108 W/m3. The convection coefficient is h - 500 W/m2 - K, and the properties of the wire are ρ-8000 kg/m3, Cp-500 J/kg-K, and...
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