FUND OF ENG THERMODYN-WILEYPLUS NEXT GEN
9th Edition
ISBN: 9781119840589
Author: MORAN
Publisher: WILEY
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4. Find the equivalent spring constant and equivalent viscous-friction coefficient for the systems shown
below.
@
B₁
B₂
H
B3
(b)
5. The cart shown below is inclined 30 degrees with respect to the horizontal. At t=0s, the cart is released
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900 kg and b 44.145 Ns²/m².
Mg
-bx 2
от
9₁
A
Insulated boundary
Insulated boundary
dx
Let's begin with the strong form for a steady-state one-dimensional heat
conduction problem, without convection.
d dT
+ Q =
dx dx
According to Fourier's law of heat conduction, the heat flux q(x), is
dT
q(x)=-k
dx. x
Q is the internal heat source, which heat is generated per unit time per unit
volume. q(x) and q(x + dx) are the heat flux conducted into the control
volume at x and x + dx, respectively. k is thermal conductivity along the x
direction, A is the cross-section area perpendicular to heat flux q(x). T is the
temperature, and is the temperature gradient.
dT
dx
1. Derive the weak form using w(x) as the weight function.
2. Consider the following scenario: a 1D block is 3 m long (L = 3 m), with
constant cross-section area A = 1 m². The left free surface of the block
(x = 0) is maintained at a constant temperature of 200 °C, and the right
surface (x = L = 3m) is insulated. Recall that Neumann boundary
conditions are naturally satisfied…
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