An aluminum heat sink (k = 240 W/m-K) used to cool an array of electronic chips consists of a square channel of inner width w =
30 mm, through which liquid flow may be assumed to maintain a uniform surface temperature of T1 = 25 °C. The outer width and length of the channel are W = 50 mm and L = 200 mm, respectively.
If N = 100 chips attached to the outer surfaces of the heat sink maintain an approximately uniform surface temperature of T2 = 60 °C and all of the heat dissipated by the chips is assumed to be transferred to the coolant, what is the heat dissipation per chip? If the contact resistance between each chip and the heat sink is R12 = 0.2 K/W, what is the chip temperature?
If N = 100 chips attached to the outer surfaces of the heat sink maintain an approximately uniform surface temperature of T2 = 60 °C and all of the heat dissipated by the chips is assumed to be transferred to the coolant, what is the heat dissipation per chip? If the contact resistance between each chip and the heat sink is R12 = 0.2 K/W, what is the chip temperature?
2 answers:
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Answer:
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Explanation:
Let suppose that fluid is incompressible and diffuser works at steady state. A diffuser reduces velocity at the expense of pressure, which can be modelled by using the Principle of Mass Conservation:
The following relation are found:
The new relationship is determined by means of linear interpolation:
After some algebraic manipulation, the following for the velocity as a function of position is obtained hereafter:
The acceleration can be calculated by using the following derivative:
The derivative of the velocity in terms of position is:
The expression for acceleration is derived by replacing each variable and simplifying the resultant formula.