Fins, or extended surfaces, commonly are used in a variety of engineering applications to enhance cooling. Common examples include a motorcycle engine head, a lawnmower engine head, heat sinks used in electronic equipment, and finned-tube heat exchangers in room heating and cooling applications. For long fins, the temperature distribution along the fin is given by the exponential relationship: T T = (T -T Je-ma ambient base ambient where T = temerature(K) hp m VkA h= the transfer coeficient (W/m2 · K) p= perimeter of the fin (m) A= cross-section area of the fin (m²) k= thermal onductivity of the fin material x= distance from the base of the fin (m) What is the appropriate unit for k if the preceding equation is to be homogeneous in units? Show all steps of your work.

Fins, or extended surfaces, commonly are used in a variety of engineering applications to enhance cooling. Common examples include a motorcycle engine head, a lawnmower engine head, heat sinks used in electronic equipment, and finned-tube heat exchangers in room heating and cooling applications. For long fins, the temperature distribution along the fin is given by the exponential relationship: T T = (T -T Je-ma ambient base ambient where T = temerature(K) hp m VkA h= the transfer coeficient (W/m2 · K) p= perimeter of the fin (m) A= cross-section area of the fin (m²) k= thermal onductivity of the fin material x= distance from the base of the fin (m) What is the appropriate unit for k if the preceding equation is to be homogeneous in units? Show all steps of your work.

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.

Chapter7: Forced Convection Inside Tubes And Ducts

Section: Chapter Questions

Problem 7.13P

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Fins, or extended surfaces, commonly are used in a variety of engineering applications to enhance cooling. Common examples include a motorcycle engine head, a lawn mower engine head, extended surfaces used in electronic equipment, and finned tube heat exchangers in room heating and cooling applications. Consider aluminum fins of a rectangular profile, which are used to remove heat from a surface whose temperature is100° C . The temperature of the ambient air is 20° C. We are interested in determining how the temperature of the fin varies along its length and plotting this temperature variation. For long fins, the temperaturedistribution along the fin is given by
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