Reference no: EM13181110
Problem 1:
Heat is being generated uniformly throughout a sphere at volumetric rate 4. The radius of the sphere is R and the sphere is made of a material having thermal conductivity k. The surface of the sphere is exposed to a convection environment with fluid temperature Tx and convection heat transfer coefficient h. Assume one-dimensional steady conduction in the radial direction and do the following:
a) Use the equation for V2T in spherical coordinates and the heat diffusion equation to produce the differential equation that models the conduction in the sphere.
b) Find the general form of the solution for T(r) answer : T(r) = 47-2 C + 6kr
c) Find the temperature at the center of the sphere ( 4R2/4R answer : T(0) =__ +___ +T 6k 3h
Problem 2
A 6-mm thick steel plate will be heated from 300°C to 600°C by exposing both sides of the plate to 700°C air having h = 100 W/m2- K . The density, heat capacity, and thermal conductivity of the steel are, respectively, 7900 kg/m" , 640 J/kg • K , and
30 W/m K
a) Verify that heating the steel plate may be treated as a lumped-capacity process.
b) Find how long it will take to heat the plate.
Problem 3, Heat Transfer, Spring 2014
The surface of a long 1-mm diameter aluminum wire is exposed to 15°C ambient air having h = 25 W/m2- K . The temperature of the wire is initially the same as the temperature of the ambient air. The wire has an electrical resistance per unit length of
= 0.034 K)/m and at time t = 0 a 20 ampere current begins flowing through the wire.
a) Verify that heating the wire may be treated as a lumped-capacity process.
b) Find the steady-state temperature of the wire.
c) Find how long it takes for the temperature of the wire to reach 100°C.
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