(a) Explanation Given: The density of aluminum wire is 2702 kg / m 3 . Thermal conductivity of aluminum wire is 236 W / m ⋅ K . Specific heat of the aluminum rod is 0.896 kJ / kg ⋅ K . Diameter of aluminum wire is 3 mm . Heat transfer coefficient is 35 W / m 2 ⋅ K . Initial temperature of aluminum wire is 350 ° C . Final temperature of aluminum wire is 50 ° C . Temperature of surrounding air is 3 0 ° C . Concept used: Write the expression for the characteristics length. L = V A ....... (1) Here, L is the characteristics length, V is the volume and A is the surface area. Write the expression for the volume of wire. V = 1 4 π d 2 l Here, d is the diameter of wire and l is the length of the wire. Write the expression for the surface area of wire. A = π d l Substitute 1 4 π d 2 l for V and π d l for A in equation (1). L = 1 4 π d 2 l π d l L = d 4 Write the expression for the Biot number. B i = h L k Here, B i is the Biot number, h is the heat transfer coefficient and k is the thermal conductivity. Substitute d 4 for L in above equation. B i = h d 4 k Substitute 35 W / m 2 ⋅ K for h , 3 mm for d and 236 W / m ⋅ K for k in above equation. B i = ( 35 ) ( 3 mm ( 1 m 1000 mm ) ) 4 ( 236 ) = ( 35 ) ( 0.003 ) 4 ( 236 ) = 0.00011 Here, Biot number is less than 0.1 . Write the expression for the variation of temperature with time by Lumped capacitance. T f − T 0 T i − T 0 = e − ( h A t ρ V c P ) Here, T f is the final temperature, T i is the final temperature, T 0 is the surrounding temperature, ρ is the density, c P is the specific heat of the aluminum wire and t is the time (b). To determine The distance travel by the wire during the temperature drop to 50 ° C . (c). To determine The heat transfer to the extrusion room from the aluminum wire.

6th Edition

ISBN: 9781265896676

Author: CENGEL

Publisher: MCG CUSTOM

See similar textbooks

Question

Chapter 4, Problem 144P

(a)

To determine

The time duration so that the temperature drop to 50°C .

(b).

To determine

The distance travel by the wire during the temperature drop to 50°C .

(c).

To determine

The heat transfer to the extrusion room from the aluminum wire.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4, Problem 143P

Chapter 4, Problem 145P

Students have asked these similar questions

"11-17 The shaft shown in Figure P11-3 was designed in Problem 10-17. For the data in the row(s) assigned from Table P11-1, and the corresponding diameter of shaft found in Problem 10-17, design suitable bearings to support the load for at least 1E8 cycles at 1800 rpm. State all assumptions. (a) Using hydrodynamically lubricated bronze sleeve bearings with Ox = 15, 11d=0.75, and a clearance ratio of 0.001. ✓ ✓ cast-iron roller FIGURE P11-3 Shaft Design for Problems 11-17 b gear key assume bearings act as simple supports 11-19 The shaft shown in Figure P11-4 was designed in Problem 10-19. For the data in the row(s) assigned from Table P11-1, and the corresponding diameter of shaft found in Problem 10-19, design suitable bearings to support the load for at least 5E8 cycles at 1200 rpm. State all assumptions. (a) Using hydrodynamically lubricated bronze sleeve bearings with Oy = 40, 1/d=0.80, and a clearance ratio of 0.002 5. gear gear key FIGURE P11-4 Shaft Design for Problems 11-19 and…

For the frame below calculate the bending moment at point R. Take P=40 and note that this value is used for both the loads and the lengths of the members of the frame. 2.5P- A Q B R С 45 degrees ✗ ✗ P i 19 Кур -2P- 4PRN -P- -

Calculate the bending moment at the point D on the beam below. Take F=79 and remember that this quantity is to be used to calculate both forces and lengths. 15F 30F A с