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
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.
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.
Please what is the correct option
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
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.
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]
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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?
EXAMPLE 5.1 Calculate nodal temperatures of four elements - A= 1m?, L= 1m, k= 10W/m/°C Q =-200W T 200 °C T3 T - - > 1 2 3 4 Q = 500W Q = 0 Q = 0 Element conduction equation What is Q;? 1 -11(T, 10 -1 1 -11(T, 10 -1 (2) = 1 T, (1) 1 T, (2) -11[T, (3) -1(T, (4)' 1 10 -1 1 10 -1 4 = 1 (3) 1 T. 12

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