A Zamboni is a multi-step mechanical ice rink resurfacer. The first step is shaving the ice surface with an auger conveyor, pictured below. In an experimental conveyor design, a stream of warm water is piped through the conveyor tube. This design can be modeled as an array of annular fins, illustrated on the right. Assume steady state. In this auger conveyor, you are asked to calculate the amount of heat needed to maintain the air and ice temperature in the chamber at T ¥ = 0°C, with convection coefficient h = 25 W/m2 ·K. The conveyor inside wall tube temperature is T b = 40°C. The annular fin array dimensions are: r 1 = 2 cm, r 2 = 10 cm, t = 2 mm, and S = 8 cm. There are N = 16 fins, with the first and last fins attached to the ends. The auger conveyor assembly is made of stainless steel (ksteel = 15 W/m·K). (a) Using the annular fin efficiency plot on the next page, approximate the fin efficiency of a single annular fin, h f . Answer: [%] Continued on the back side b) From the single fin efficiency obtained in Part (a), calculate the overall fin efficiency of the entire device, h o . First, obtain the total area of the fin array, At . Answer: [%] (c) Assuming that the stainless steel conveyor tube wall thickness is 1 cm, obtain the total heat rate, q needed to support this temperature difference. First, obtain the overall fin array thermal resistance, Rt,o . Then, obtain the tube wall thermal resistance, Rt,w . Answer: [W]

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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A Zamboni is a multi-step mechanical ice rink resurfacer. The first step is shaving the ice surface
with an auger conveyor, pictured below. In an experimental conveyor design, a stream of warm
water is piped through the conveyor tube. This design can be modeled as an array of annular fins,
illustrated on the right. Assume steady state.
In this auger conveyor, you are asked to calculate the amount of heat needed to maintain the air
and ice temperature in the chamber at T ¥ = 0°C, with convection coefficient h = 25 W/m2 ·K. The
conveyor inside wall tube temperature is T b = 40°C. The annular fin array dimensions are:
r 1 = 2 cm, r 2 = 10 cm, t = 2 mm, and S = 8 cm. There are N = 16 fins, with the first and last fins
attached to the ends. The auger conveyor assembly is made of stainless steel (ksteel = 15 W/m·K).
(a) Using the annular fin efficiency plot on the next page, approximate the fin efficiency of a single
annular fin,
h f .
Answer: ____________________________ [%]
Continued on the back side

b) From the single fin efficiency obtained in Part (a), calculate the overall fin efficiency of the
entire device,
h o . First, obtain the total area of the fin array, At .
Answer: ____________________________ [%]
(c) Assuming that the stainless steel conveyor tube wall thickness is 1 cm, obtain the total heat
rate, q needed to support this temperature difference. First, obtain the overall fin array thermal
resistance, Rt,o . Then, obtain the tube wall thermal resistance, Rt,w .
Answer: ____________________________ [W]

(%) Fu
100
80
60
40
20
ak
12
0.5
2c = √₂+1/2
L = L + 1/2
A₂ = Let
1.0
13/2 (h/kA)¹/2
1 = √₂c/r₁
2 -3
5
1.5
2.0
2.5

Zamboni
ice resurfacer
Auger conveyor
2
Ico
-Tb

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