Exercise 4.6.8 A plane wall (k = 10 W/m C) of thickness 50 cm has its exterior surface subjected to a convection environment of 30°C with a surface heat transfer coefficient of 600 W/m2 C. Determine the temperature distribution in the plane wall using (a) four lin- ear elements (b) one quadratic element and (c) one modified quadratic element with only two nodes. Compare the results with the analytical solution. If the heat transfer coefficient increases to 10,000 W/m C, what happens to the temperature of the exterior surface? %3D

Exercise 4.6.8 A plane wall (k = 10 W/m C) of thickness 50 cm has its exterior surface subjected to a convection environment of 30°C with a surface heat transfer coefficient of 600 W/m2 C. Determine the temperature distribution in the plane wall using (a) four lin- ear elements (b) one quadratic element and (c) one modified quadratic element with only two nodes. Compare the results with the analytical solution. If the heat transfer coefficient increases to 10,000 W/m C, what happens to the temperature of the exterior surface? %3D

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.

Chapter1: Basic Modes Of Heat Transfer

Section: Chapter Questions

Problem 1.50P: A steam pipe 200 mm in diameter passes through a large basement room. The temperature of the pipe...

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Concept explainers

Conduction and Convection

When energy travels from one object to another it is said to have undergone heat transfer. Heat transfer is nothing but the transfer of thermal energy or internal energy from one thing to another, like e.g., when a vessel with water, kept on top of a burner, heats up because of the flame underneath it.

Question

Exercise 4.6.8 A plane wall (k = 10 W/m C) of thickness 50 cm has its exteriar surface
subjected to a convection environment of 30°C with a surface heat transfer coefficient of
600 W/m2 C. Determine the temperature distribution in the plane wall using (a) four lin-
ear elements (b) one quadratic element and (c) one modified quadratic element with only
two nodes. Compare the results with the analytical solution. If the heat transfer coefficient
increases to 10,000 W/m C, what happens to the temperature of the exterior surface?

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An electronic device that internally generates 600 mW of heat has a maximum permissible operating temperature of 70C. It is to be cooled in 25C air by attaching aluminum fins with a total surface area of 12cm2. The convection heat transfer coefficient between the fins and the air is 20W/m2K. Estimate the operating temperature when the fins are attached in such a way that (a) there is a contact resistance of approximately 50 K/W between the surface of the device and the fin array and (b) there is no contact resistance (in this case, the construction of the device is more expensive). Comment on the design options.
The handle of a ladle used for pouring molten lead is 30 cm long. Originally the handle was made of 1.9cm1.25cm mild steel bar stock. To reduce the grip temperature, it is proposed to form the handle of tubing 0.15 cm thick to the same rectangular shape. If the average heat transfer coefficient over the handle surface is 14 W/m K, estimate the reduction of the temperature at the grip in air at 21C.
2.29 In a cylindrical fuel rod of a nuclear reactor, heat is generated internally according to the equation where = local rate of heat generation per unit volume at r = outside radius = rate of heat generation per unit volume at the centerline Calculate the temperature drop from the centerline to the surface for a 2.5-cm-diameter rod having a thermal conductivity of if the rate of heat removal from its surface is 1.6 .
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1.10 A heat flux meter at the outer (cold) wall of a concrete building indicates that the heat loss through a wall of 10-cm thickness is . If a thermocouple at the inner surface of the wall indicates a temperature of 22°C while another at the outer surface shows 6°C, calculate the thermal conductivity of the concrete and compare your result with the value in Appendix 2, Table 11.
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