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(a) An experiment was conducted to analyze temperature distribution T(x) at a 2. distance x, measured from one side along a plate having length L. The result is given by the following function 1 w...
Consider a uniform bar of length L having an initial temperature distribution given by f(x), 0...
Consider a uniform bar of length L having an initial temperature distribution given by f(x), 0 < x < L. Assume that the temperature at the end x=0 is held at 0°C, while the end x=L is thermally insulated. Heat is lost from the lateral surface of the bar into a surrounding medium. The temperature u(x, t) satisfies the following partial differential equation and boundary conditions aluxx – Bu = Ut, 0<x<l, t> 0 u(0,t) = 0, uz (L, t)...
Find the temperature function u(x,t)u(x,t) (where xx is the position along the rod in cm and...
Find the temperature function u(x,t)u(x,t) (where xx is the
position along the rod in cm and tt is the time) of a 1818 cm rod
with conducting constant 0.10.1 whose endpoint are insulated such
that no heat is lost, and whose initial temperature distribution is
given by:
u(x,0)={5 if 6≤x≤12
{0 otherwise
To start, we have L=18 0.1 Because the rods are insulated, we will use the cosine Fourier expansion. 22 Ac + =1 A cos(" )e| A cos( u(x,...
1) 2) 3) PROJECT #1 (2.5 Marks): The heat that is conducted through a body must...
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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...
Consider a uniform bar of length L having an initial temperature distribution given by f(x), 0 < x < L. Assume that the temperature at the end x=0 is held at 0°C, while the end x=L is thermally insulated. Heat is lost from the lateral surface of the bar into a surrounding medium. The temperature u(x, t) satisfies the following partial differential equation and boundary conditions aluxx – Bu = Ut, 0<x<l, t> 0 u(0,t) = 0, uz (L, t)...
Find the temperature function u(x,t)u(x,t) (where xx is the
position along the rod in cm and tt is the time) of a 1818 cm rod
with conducting constant 0.10.1 whose endpoint are insulated such
that no heat is lost, and whose initial temperature distribution is
given by:
u(x,0)={5 if 6≤x≤12
{0 otherwise
To start, we have L=18 0.1 Because the rods are insulated, we will use the cosine Fourier expansion. 22 Ac + =1 A cos(" )e| A cos( u(x,...
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...
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