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[10] 5. A solid sphere is initially at temperature f(r) = 1, and its surface r...
Consider a spherical fuel particle with radius R. Within sphere heat is produced which varies with...
Consider a spherical fuel particle with radius R. Within sphere heat is produced which varies with temperature according to the relation: S=S, [1-a(T-T.)] So is the heat produced per unit volume per unit time and "a" is a constant. Surface temperature of the sphere is kept constant at To a. By constructing a shell balance obtain an O.D.E. describing steady state temperature profile. b. By using dimensionless temperature @= T-TO S.R?/k and dimensionless position x= t/R bring the O.D.E to...
Let us denote the volume and the surface area of an n-dimensional sphere of adius R as V(OR)-VR a...
We were unable to transcribe this imageLet us denote the volume and the surface area of an n-dimensional sphere of adius R as V(OR)-VR and S(R)-S.),respectively (a) Find the relation between V(0) and S 1) (b) Calculate the Gaussian integral 3. (c) Calculate the same integral in spherical coordinates in terms of the gamma function re)-e'd (d) Obtain the closed forms of S,,(1) and V(1) (e) Calculate r5) and S.,0), p.(1) for n-1, 2, 3. (40 points)
Let us denote...
1. A solid sphere of radius a is concentric with a hollow sphere of radius b,...
1. A solid sphere of radius a is concentric with a hollow sphere of radius b, where b>alf the solid sphere has a charge +Qand the hollow sphere a charge of see figure. The electric field at radius , where r>b, is: A) KOR; B) 2KQ/R; C) MQ/#; D) AQB; E) zero.) 1. A solid sphere of radius a is concentric with a hollow sphere of radius b, where b>alf the solid sphere has a charge +Qand the hollow sphere...
i need help on number3 lelmperaturein the luid as a function of r, the distance from...
i need help on number3
lelmperaturein the luid as a function of r, the distance from the descne t re? What are the boundary conditions? The thermal conductivity k of the fluid is considered center of the sphe constant. The temperature of the sphere constant at Ta boundary is constant at Tr. and the temperature far from the fluid is (b) Determine the temperature profile in the fluid. (c) From the temperature profile, obtain an expression for the heat flux...
Suppose that a scalar field is constant on a surface As shown in the lectures. there are two methods that one might use to obtain the normal to the surface, and they give the same direction (a) Let r...
Suppose that a scalar field is constant on a surface As shown in the lectures. there are two methods that one might use to obtain the normal to the surface, and they give the same direction (a) Let r(u, v) be a parametric form for the surface S. Use the vector identity to show that Our ar-λ▽u where λ is a scalar field. [Note: no marks will be awarded for simply stating that a term is zero. If it is...
1. Let V be the solid region in R3 that lies within the sphere 2+y+z2-4, above the zy-plane, and ...
please help with Q1 and 3
1. Let V be the solid region in R3 that lies within the sphere 2+y+z2-4, above the zy-plane, and below the cone z -Vx2 + y2 (a) Sketch the region V (b) Calculate the volume of V by using spherical coordinates. (c) Find the surface area of the part of V that lies on the sphere z2 y 24, by calculatinga surface integral. (d) Verify your solution to (c) by calculating the surface integral...
1. A solid sphere with mass M- 10 kgand radius R 20 cmexperiences a tangential force F-200 N at i...
1. A solid sphere with mass M- 10 kgand radius R 20 cmexperiences a tangential force F-200 N at its surface. Find the angular acceleration of the sphere. (Hint the moment of inertia of a solid sphere about its center of massisMR?)
1. A solid sphere with mass M- 10 kgand radius R 20 cmexperiences a tangential force F-200 N at its surface. Find the angular acceleration of the sphere. (Hint the moment of inertia of a solid sphere about...
2. Heat equation Let ult, 2) satisfy the equation 4472(t, 2) +1, 0<r <1, t>0 with...
2. Heat equation Let ult, 2) satisfy the equation 4472(t, 2) +1, 0<r <1, t>0 with initial condition u(0,2) = 0, 0<x<1, and boundary conditions u(t,0) = 0, u(t,1)= 0, t> 0. This equation describes the temperature in a rod. The rod initially has a temperature of 0 (zero degree Celsius), and is then heated at a uniform rate 1. However, its two endpoints are kept at the temperature of 0 at all times. The unknown function u(t, x) describes...
(35pt) A new process for treatment of a special material is to be evaluated. A sphere...
(35pt) A new process for treatment of a special material is to be evaluated. A sphere of radius R (-5mm) is made of this special material. The physical properties of the materials are p 3000 kg/m k20Wm K), C, 1000 J(kgx K). 3. First step: An electric current is applied to the sphere to produce a total constant heat generation rate, S, (Unit: W), which can be considered spatially uniformly distributed through the sphere. And the surface of the spherical...
1 (a) Explain why there is no electic field inside an uncharged, or statically charged, [2]...
1 (a) Explain why there is no electic field inside an uncharged, or statically charged, [2] conductor (b) An uncharged perfectly conducting solid sphere of radius a is placed with its centre at the origin in a region of uniform electric field E = E02. The presence of the sphere modifies the electric field (and the potential) i. Show that the initial potential in spherical coordinates is Vinit (T, 0, )Eor cos 0 everywhere (i.e. before the sphere was placed...
Consider a spherical fuel particle with radius R. Within sphere heat is produced which varies with temperature according to the relation: S=S, [1-a(T-T.)] So is the heat produced per unit volume per unit time and "a" is a constant. Surface temperature of the sphere is kept constant at To a. By constructing a shell balance obtain an O.D.E. describing steady state temperature profile. b. By using dimensionless temperature @= T-TO S.R?/k and dimensionless position x= t/R bring the O.D.E to...
We were unable to transcribe this imageLet us denote the volume and the surface area of an n-dimensional sphere of adius R as V(OR)-VR and S(R)-S.),respectively (a) Find the relation between V(0) and S 1) (b) Calculate the Gaussian integral 3. (c) Calculate the same integral in spherical coordinates in terms of the gamma function re)-e'd (d) Obtain the closed forms of S,,(1) and V(1) (e) Calculate r5) and S.,0), p.(1) for n-1, 2, 3. (40 points)
Let us denote...
1. A solid sphere of radius a is concentric with a hollow sphere of radius b, where b>alf the solid sphere has a charge +Qand the hollow sphere a charge of see figure. The electric field at radius , where r>b, is: A) KOR; B) 2KQ/R; C) MQ/#; D) AQB; E) zero.) 1. A solid sphere of radius a is concentric with a hollow sphere of radius b, where b>alf the solid sphere has a charge +Qand the hollow sphere...
i need help on number3
lelmperaturein the luid as a function of r, the distance from the descne t re? What are the boundary conditions? The thermal conductivity k of the fluid is considered center of the sphe constant. The temperature of the sphere constant at Ta boundary is constant at Tr. and the temperature far from the fluid is (b) Determine the temperature profile in the fluid. (c) From the temperature profile, obtain an expression for the heat flux...
Suppose that a scalar field is constant on a surface As shown in the lectures. there are two methods that one might use to obtain the normal to the surface, and they give the same direction (a) Let r(u, v) be a parametric form for the surface S. Use the vector identity to show that Our ar-λ▽u where λ is a scalar field. [Note: no marks will be awarded for simply stating that a term is zero. If it is...
please help with Q1 and 3
1. Let V be the solid region in R3 that lies within the sphere 2+y+z2-4, above the zy-plane, and below the cone z -Vx2 + y2 (a) Sketch the region V (b) Calculate the volume of V by using spherical coordinates. (c) Find the surface area of the part of V that lies on the sphere z2 y 24, by calculatinga surface integral. (d) Verify your solution to (c) by calculating the surface integral...
1. A solid sphere with mass M- 10 kgand radius R 20 cmexperiences a tangential force F-200 N at its surface. Find the angular acceleration of the sphere. (Hint the moment of inertia of a solid sphere about its center of massisMR?)
1. A solid sphere with mass M- 10 kgand radius R 20 cmexperiences a tangential force F-200 N at its surface. Find the angular acceleration of the sphere. (Hint the moment of inertia of a solid sphere about...
2. Heat equation Let ult, 2) satisfy the equation 4472(t, 2) +1, 0<r <1, t>0 with initial condition u(0,2) = 0, 0<x<1, and boundary conditions u(t,0) = 0, u(t,1)= 0, t> 0. This equation describes the temperature in a rod. The rod initially has a temperature of 0 (zero degree Celsius), and is then heated at a uniform rate 1. However, its two endpoints are kept at the temperature of 0 at all times. The unknown function u(t, x) describes...
(35pt) A new process for treatment of a special material is to be evaluated. A sphere of radius R (-5mm) is made of this special material. The physical properties of the materials are p 3000 kg/m k20Wm K), C, 1000 J(kgx K). 3. First step: An electric current is applied to the sphere to produce a total constant heat generation rate, S, (Unit: W), which can be considered spatially uniformly distributed through the sphere. And the surface of the spherical...
1 (a) Explain why there is no electic field inside an uncharged, or statically charged, [2] conductor (b) An uncharged perfectly conducting solid sphere of radius a is placed with its centre at the origin in a region of uniform electric field E = E02. The presence of the sphere modifies the electric field (and the potential) i. Show that the initial potential in spherical coordinates is Vinit (T, 0, )Eor cos 0 everywhere (i.e. before the sphere was placed...
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