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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Please use radian measure
In the diagram below, metal 1 is made of gold and metal 2 is aluminum. Both bars have the same length and area of cross-section but their thermal conductivities are different. The temperature Th is maintained at a constant 88.0°C at the end A while the temperature T, at the end B is maintained at 19.0°C. A. T metal 1 metal 2 T (a) What is the temperature T; at the junction of the two bars? The thermal conductivity of gold is 318 J/(s · m · °C) and that for aluminum is 220 J/(s• m · °C). °C (b) If metals 1 and 2 are now interchanged, but the values of Th and T, are the same as in part (a), what will be the temperature of the junction? °C
include diagram.
A thin bar of length L = 3 meters is situated along the x axis so that one end is at x = 0 and the other end is at x = 3. The thermal diffusivity of the bar is k = 0.4. The bar's initial temperature f(x) = 50 degrees Celsius. The ends of the bar (x = 0 and x = 3) are then put in an icy bath and kept at a constant 0 degrees C. Let u(x, t) be the temperature in the bar at x at time t, with t measured in seconds. Find u(x, t) and then u4 (2, 0.1). Put u4(2, 0.1) calculated accurately to the nearest thousandth (3 decimal places) in the answer box.
A thin bar of length L = 3 meters is situated along the x axis so that one end is at x = 0 and the other end is at x = 3. The thermal diffusivity of the bar is k = 0.4. The bar's initial temperature f(x) = 300 degrees Celsius. The ends of the bar (x = 0 and x = 3) are then put in an icy bath and kept at a constant O degrees C. Let u(x, t) be the temperature in the bar at x at timet, with t measured in seconds. Find u(x, t) and then u7 (2, 0.1). Put uz (2, 0.1) calculated accurately to the nearest thousandth (3 decimal places) in the answer box.
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)
A truncated solid cone is of circular cross section, and its diameter is related to the axial coordinate by an expression of the form D = ax3/2, where a = 2 m−1/2. The sides are well insulated, while the top surface of the cone at x1 is maintained at T1 and the bottom surface at x2 is maintained at T2. Conductivity k = 336 W/m-K (a) Obtain an expression for the temperature distribution T(x). (b) What is the rate of heat transfer across the cone if it is constructed of pure aluminum with x1 = 0.086 m, T1 = 113°C, x2 = 0.270 m, and T2 = 25°C?
Just want to understand this review example
= 27-30 Find the temperature distribution in a laterally insulated thin copper bar (c² K/po = 1.158 cm²/sec), 50 cm long and of constant cross section with endpoints at x = 0 and 50 kept at 0°C and initial temperature 28. f(x) = x(50 x(50 - x)
A circular cross-sectional rod made of AISI Type 303 Stainless Steel is normally operated at126oF. Length and radius of the rod are 1.5 ft and 1.75 in., respectively. What would be thechange in length of the rod, if it is subjected to a temperature of 214oF? Coefficient of thermal expansion of the rods’ material is 9.6 × 10^-6 in./in. Degrees Fahrenheit.
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