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Summer2022-VM335 Homework 2

代写机械工程作业 A hole of diameter D = 0.25 m is drilled through the center of a solid block of square cross section with w= 1m on a side.

3.126 Turbine blades mounted to a rotating disc in a gas turbine engine are exposed to a gas stream that is at T_∞= 1200°C and maintains a convection coefficient of h = 250 W/m2. K over the blade.  代写机械工程作业

The blades，which are fabricated from Inconel,k≈20 W/m.K, have a length of L= 50 mm. The blade profile has a uniform cross-sectional area of A_c=6×10^-4m2 and a perimeter of P= 110 mm. A proposed blade-cooling scheme, which involves routing air through the supporting disc, is able to maintain the base of each blade at a temperature of T_b= 300°C.

(a) If the maximum allowable blade temperature is 1050°C and the blade tip may be assumed to be adi-abatic, is the proposed cooling scheme satisfactory?  代写机械工程作业

(b) For the proposed cooling scheme, what is the rate at which heat is transferred from each blade to the coolant?

3.146 As more and more components are placed on a single integrated circuit (chip), the amount of heat that is dissipated continues to increase.

However,this increase is limited by the maximum allowable chip operating temperature, which is approximately 75°C. To maximize heat dissipation, it is proposed that a 4 X 4 array of copper pin fins be metallurgi-cally joined to the outer surface of a square chip that is 12.7 mm on a side.

(a) Sketch the equivalent thermal circuit for the pin-chip-board assembly, assuming one-dimensional,steady-state conditions and negligible contact resistance between the pins and the chip. In vari-able form, label appropriate resistances, tempera-tures, and heat rates.

(b) For the conditions prescribed in Problem 3.27,what is the maximum rate at which heat can be dissipated in the chip when the pins are in place? That is, what is the value ofqc for T。= 75°C? The pin diameter and length are D。= 1.5 mm and Lp= 15 mm.

4.27 A hot fuid passes through circular channels of a cast poor contact with the cover plates (B) of thickness L_A= 7.5 mm.  代写机械工程作业

The channels are of diameter D = 15 mm with a centerline spacing of L。= 60 mm. The thermal with a centerline spacing of L_B= 60 mm. The thermal kp = 75 W/m.K, while the contact resistance between the two materials is R”_t,s= 2.0 × 10^-4m². K/W. The hot fluid is at T_i= 150°C, and the convection coefient is 1000 W/m2.K. The cover plate is exposed to ambient air at T_∞= 25°C with a convection coefient of  200 W/m?.K. The shape factor between one channel and the platen top and bottom surfaces is 4.25.

(a) Determine the heat rate from a single channel per unit length of the platen normal to the page, q’_!.

(b) Determine the outer surface temperature of the cover plate,T_s.  代写机械工程作业

(c) Comment on the effects that changing the center-line spacing will have on q’_! and Ts. How would insulating the lower surface affect q’_! and T_s?

4.31 A hole of diameter D = 0.25 m is drilled through the center of a solid block of square cross section with w= 1m on a side.

The hole is drilled along the length, l= 2m, of the block, which has a thermal conductivity of k = 150 W/m.K. The four outer sur- faces are exposed to ambient air, with T_∞,2= 25°C and h₂= 4 W/m². K, while hot oil flowing through the hole is characterized by T_∞,1= 300°C and h₁ = 50 W/m².K.Determine the corresponding heat rate and surface temperatures.

4.46 Derive the nodal finite- difference equations for the fol-lowing configurations.

(a) Node (m, n) on a diagonal boundary subjected to convection with a fuid at T_∞ and a heat transfer coefficient h. Assume△r= △y. 代写机械工程作业

(b) Node (m, n) at the tip of a cutting tool with the upper surface exposed to a constant heat flux q”_o and the diagonal surface exposed to a convection cooling process with the fuid at T_∞ and a heat transfer coefficient h. Assume△x=△y.

4.61 The steady-state temperatures (°C) associated with selec-ted nodal points of a two-dimensional system having a Ithermal conductivity of 1.5 W/m*K are shown on the accompanying grid.

(a) Determine the temperatures at nodes 1, 2, and 3.

(b) Calculate the heat transfer rate per unit thickness normal to the page from the system to the fluid.

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