2. The diagram shows a conical section fabricated from pure aluminum. It is of circular crosssection having diameter D = ax¹/2, where a = 0.5 m¹/2. The small end is located at x1 = 25 mm andthe large end at x2 = 125 mm. The end temperatures are T₁ = 600 K and T₂ = 400 K, while thelateral surface is well insulated.(a) Derive an expression for the temperature distribution T(x) in symbolic form, assuming onedimensional conditions. Sketch the temperature distribution.(b) Calculate the heat rate qx.Answer: Pure Aluminum (500K): k= 236 W/m·K. (b). 5.76kW

Answered: 2. The diagram shows a conical section…

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter3: Transient Heat Conduction

Section: Chapter Questions

Problem 3.4P

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3.39 The diagram shows a conical section fabricated from pure aluminum. It is of circular cross section having diameter D = ax2, where a = 0.5 m². The small end is located at x₁ = 25 mm and the large end at x₂ = 125 mm. The end temperatures are T₁ = 600 K and T₂ = 400 K, while the lateral surface is well insulated. +1.x₂ ·X₂² (a) Derive an expression for the temperature distribution T(x) in symbolic form, assuming one-dimensional conditions. Sketch the temperature distribution. (b) Calculate the heat rate q.. 3.4 3.4
include diagram.
A short bar of copper, 25 mm in diameter, is enclosed centrally within a steel tube of external diameter 36 mm and thickness 3 mm. At 0°C the ends of the bar and tube are rigidly fastened together and the complete assembly heated to 80°C. Calculate the stress in the bar and in the tube if E for copper is 100 000 N/mm?, E for steel is 200 000 N/mm? and the coefficients of linear expansion of copper and steel are 0.000 01/°C and 0.000 006/°C, respectively.
2. A rectangular block has thickness B in the x-direction. The side at x = 0 is held at temperature T, while the side at x = B is held at T2. The other four sides are well insulated. Heat is generated in the block at a uniform rate per unit volume of [. (a) Use the conduction equation to derive an expression for the steady-state temperature profile, T(x). Assume constant thermal conductivity. (b) Use the result of part (a) to calculate the maximum temperature in the block for the following values of the parameters: T₁-120 °C k-0.2 W/(m K) B-1.0 m T₂-0 F-100 W/m³
The diagram (below) illustrate an object of a thermal conductivity 236 W/m-K. The circular cross section is having a radius r = ax, where a = 0.4. The small end is located at x1= 24 mm and the large end at x2 = 124 mm. End temperatures are Ti= 600 K and T2 = 400 K (as shown by figure), while lateral surface is well insulated. (1) Please find the temperature distribution equation (in terms of temperature (T) and distance (x)). (2) Calculate conduction heat rate (q.) in kW.
2. A brass ring of diameter 10.00 cm at 20.0°C is heated and slipped over an aluminum rod of diameter 10.01 cm at 20.0°C. Assuming the average coefficients of linear expansion are constant, a. to what temperature must the combination be cooled to separate the two metals? b. What if the aluminum rod were 10.02 cm in diameter? (- 179°C, - 374°C]
Please clearly show all steps so your approach is easy to follow
Rigid bar ABCD is supported by a pin connection at A and by two axial bars (1) and (2). Bar (1) is a 30-in.-long bronze [E = 15900 ksi, 9.4x 10-6/°F] bar with a cross-sectional area of 1.00 in.?. Bar (2) is a 48-in-long aluminum alloy [E = 9200 ksi, a = 12.6 x 10-6/°F] bar with a cross-sectional area of 2.50 in.?. Both bars are unstressed before the load Pis applied. Assume L1=30 in., L2=48 a = %3D in., a=32 in., b=44 in., and c=14 in. If a concentrated load of P = 29 kips is applied to the rigid bar at Dand the temperature is decreased by 120°F, determine: (a) the normal stresses in bars (1) and (2). (b) the normal strains in bars (1) and (2). (c) the deflection of the rigid bar at point D. (2) L2 A B D L1 (1)
H= 55mm A= 40mm R1 R2 B= 55mm C= 50mm R1=13mm H P=2000 N R2= 15mm A B Figure QI: A rectangular plate with holes
A square piece is initially at 10 degrees Celsius everywhere. Each side is 0.05 m long. Then the four sides are instantly heated up to 25 degrees Celsius, 50 degrees Celsius, 30 degrees Celsius, and 0 degrees Celsius. a. Find how long it takes for the temperature profile of this square to become steady if the material is copper. What is the final temperature at the center of the square? b. Find how long it takes for the temperature profile of this square to become steady if the material is air. What is the final temperature at the center of the square? c. Which material takes longer to reach steady state and why?
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