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this is a laplace equation in cylinder coordinates: ） 1. (10 points) A solid cylinder of radius a and height h has...
10. (21 pts]Find the steady-state temperature distribution in a solid cylinder with radius R and height...
10. (21 pts]Find the steady-state temperature distribution in a solid cylinder with radius R and height H, if the boundary temperatures are set as 0 on the bottom surface, ugra/R? on the top surface and Uz/H on the curved surface 1 [4 pts) Write the governing equation and boundary conditions 2) [17 pts]Solve the problem
Steady, 2-D conduction takes place in a rectangular solid having height (in the y-direction), H, and...
Steady, 2-D conduction takes place in a rectangular solid having height (in the y-direction), H, and width (in the X-direction), W. The bottom of the rectangle, from x-0 to x=W, is insulated. The left boundary, x0, 0 s ys H, is held at a temperature of 500 K, as is the top boundary, y=H, 0 sxs W. The right boundary, x=W and0 Sys H, has a steady temperature distribution given by TOy,x W) 500 (1-sin(ny/H) Find the temperature distribution, T(x,...
Steady, 2-D conduction takes place in a rectangular solid having height (in the y-direction), H, and...
Steady, 2-D conduction takes place in a rectangular solid having height (in the y-direction), H, and width (in the X-direction), W. The bottom of the rectangle, from x-0 to x-W, is insulated. The left boundary, x0, 0 ys H, is held at a temperature of 500 K, as is the top boundary, y=H, 0 sxs W. The right boundary, x=W and0 Sys H, has a steady temperature distribution given by TOy,x W) 500 (1-sin(ny/H) Find the temperature distribution, T(x, y),...
Steady, 2-D conduction takes place in a rectangular solid having height (in the y-direction), H, and...
Steady, 2-D conduction takes place in a rectangular solid having height (in the y-direction), H, and width (in the X-direction), W. The bottom of the rectangle, from x-0 to x-W, is insulated. The left boundary, x0, 0 ys H, is held at a temperature of 500 K, as is the top boundary, y=H, 0 sxs W. The right boundary, x=W and0 Sys H, has a steady temperature distribution given by TOy,x W) 500 (1-sin(ny/H) Find the temperature distribution, T(x, y),...
Steady, 2-D conduction takes place in a rectangular solid having height (in the y-direction), H, and...
Steady, 2-D conduction takes place in a rectangular solid having height (in the y-direction), H, and width (in the X-direction), W. The bottom of the rectangle, from x=0 to x-W, is insulated. The left boundary x-0, 0 y s H, is held at a temperature of 500 K, as is the top boundary, y=H, 0 s x sW. The right boundary, x=W and 0 Sys H, has a steady temperature distribution given by Ty,x W) 500 (1-sin(ny/H) Find the temperature...
4. Find the total charge of a solid cylinder of height H and radius R. The...
4. Find the total charge of a solid cylinder of height H and radius R. The charge density of the cylinder is given by p k, where k is a constant.
teger Type Questions A transparent cylinder of radius R and height H made from a material...
teger Type Questions A transparent cylinder of radius R and height H made from a material of refractive index n 1.5 is placed on a horizontal table top with the base of the cylinder on contact with the table. A point light source is placed at a height h above the centre of the top circular face of the cylinder. The unilluminated area on the table top outside the cylinder is given by A then find the value of k
3. (Cotal: 30 pts) Consider a cylinder of radius R and length L. The thermal "Gonductivity ofthe eyǐnaeris R. The temperature is fixed at the left end at TO and the other end is subject to co...
3. (Cotal: 30 pts) Consider a cylinder of radius R and length L. The thermal "Gonductivity ofthe eyǐnaeris R. The temperature is fixed at the left end at TO and the other end is subject to convective heat transfer with heat transfer coefficient h and environment temperature of To. The side surface of the cylinder is subject to radiative heat transfer to environment of To. Assume there is no heat generation in the cylinder. (10 pts) starting with energy balance,...
A cylinder of height L and radius L has a charge Q> 0 located in the...
A cylinder of height L and radius L has a charge Q> 0 located in the center of the base. Find the electrical flow through: a) the lateral surface of the cylinder b) Cylinder top cover c) the lower cylinder cover
1. A cylinder of mass m, height h and radius r floats partially submerged in a...
1. A cylinder of mass m, height h and radius r floats partially submerged in a liquid of density ρ. One third of the height of the cylinder is above the surface of the water. Johnny pushes the cylinder down by a small distance x<h/3, then he releases it from rest. A) prove that the resulting motion of the cylinder is a simple harmonic motion. B) Find the period of the small oscillations in terms of the given quantities (m,r,h,ρ)
10. (21 pts]Find the steady-state temperature distribution in a solid cylinder with radius R and height H, if the boundary temperatures are set as 0 on the bottom surface, ugra/R? on the top surface and Uz/H on the curved surface 1 [4 pts) Write the governing equation and boundary conditions 2) [17 pts]Solve the problem
Steady, 2-D conduction takes place in a rectangular solid having height (in the y-direction), H, and width (in the X-direction), W. The bottom of the rectangle, from x-0 to x=W, is insulated. The left boundary, x0, 0 s ys H, is held at a temperature of 500 K, as is the top boundary, y=H, 0 sxs W. The right boundary, x=W and0 Sys H, has a steady temperature distribution given by TOy,x W) 500 (1-sin(ny/H) Find the temperature distribution, T(x,...
Steady, 2-D conduction takes place in a rectangular solid having height (in the y-direction), H, and width (in the X-direction), W. The bottom of the rectangle, from x-0 to x-W, is insulated. The left boundary, x0, 0 ys H, is held at a temperature of 500 K, as is the top boundary, y=H, 0 sxs W. The right boundary, x=W and0 Sys H, has a steady temperature distribution given by TOy,x W) 500 (1-sin(ny/H) Find the temperature distribution, T(x, y),...
Steady, 2-D conduction takes place in a rectangular solid having height (in the y-direction), H, and width (in the X-direction), W. The bottom of the rectangle, from x-0 to x-W, is insulated. The left boundary, x0, 0 ys H, is held at a temperature of 500 K, as is the top boundary, y=H, 0 sxs W. The right boundary, x=W and0 Sys H, has a steady temperature distribution given by TOy,x W) 500 (1-sin(ny/H) Find the temperature distribution, T(x, y),...
Steady, 2-D conduction takes place in a rectangular solid having height (in the y-direction), H, and width (in the X-direction), W. The bottom of the rectangle, from x=0 to x-W, is insulated. The left boundary x-0, 0 y s H, is held at a temperature of 500 K, as is the top boundary, y=H, 0 s x sW. The right boundary, x=W and 0 Sys H, has a steady temperature distribution given by Ty,x W) 500 (1-sin(ny/H) Find the temperature...
4. Find the total charge of a solid cylinder of height H and radius R. The charge density of the cylinder is given by p k, where k is a constant.
teger Type Questions A transparent cylinder of radius R and height H made from a material of refractive index n 1.5 is placed on a horizontal table top with the base of the cylinder on contact with the table. A point light source is placed at a height h above the centre of the top circular face of the cylinder. The unilluminated area on the table top outside the cylinder is given by A then find the value of k
3. (Cotal: 30 pts) Consider a cylinder of radius R and length L. The thermal "Gonductivity ofthe eyǐnaeris R. The temperature is fixed at the left end at TO and the other end is subject to convective heat transfer with heat transfer coefficient h and environment temperature of To. The side surface of the cylinder is subject to radiative heat transfer to environment of To. Assume there is no heat generation in the cylinder. (10 pts) starting with energy balance,...
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