The fin array shown below is 8 rectangular fins on a 10-mm thick, 34-mm × 66-mm base plate. Each fin is 24 mm long with a 30-mm × 2-mm rectangular cross-section. The fin array is made of an aluminum alloy having $ k = 170 \, \text{W/m} \cdot \text{K} $. The array is installed in an insulated wall. The surface of the array with the fins is exposed to air with $ h_{\text{air}} = 40 \, \text{W/m}^2 \cdot \text{K} $.a) Find the fin efficiency (answer: $ \eta_f = 0.95103 $).b) Find the thermal resistance for convective heat transfer from the surface of the fin array to the air (answer: 1.798 K/W).**Diagram Explanation:**1. **Left Diagram:** - Shows the side view of one fin attached to the base plate. - The base plate is 10 mm thick. - The fin extends 24 mm out from the base plate. - The heat transfer coefficient $ h_{\text{air}} = 40 \, \text{W/m}^2 \cdot \text{K} $ is noted with arrows indicating the direction of heat transfer.2. **Right Diagram:** - Displays the top view of the fin array. - Each fin is 2 mm thick and 30 mm tall. - The overall base plate dimensions are 34 mm in height and 66 mm in width, accommodating 8 fins in total.

Answered: The fin array shown below is 8…

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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The fin array shown below is 8 rectangular fins on a 10-mm thick, 34-mm × 66-mm base plate. Each fin is 24 mm long with a 30-mm × 2-mm rectangular cross-section. The fin array is made of an aluminum alloy having $ k = 170 \, \text{W/m} \cdot \text{K} $. The array is installed in an insulated wall. The surface of the array with the fins is exposed to air with $ h_{\text{air}} = 40 \, \text{W/m}^2 \cdot \text{K} $.

a) Find the fin efficiency (answer: $ \eta_f = 0.95103 $).

b) Find the thermal resistance for convective heat transfer from the surface of the fin array to the air (answer: 1.798 K/W).

**Diagram Explanation:**

1. **Left Diagram:**
- Shows the side view of one fin attached to the base plate.
- The base plate is 10 mm thick.
- The fin extends 24 mm out from the base plate.
- The heat transfer coefficient $ h_{\text{air}} = 40 \, \text{W/m}^2 \cdot \text{K} $ is noted with arrows indicating the direction of heat transfer.

2. **Right Diagram:**
- Displays the top view of the fin array.
- Each fin is 2 mm thick and 30 mm tall.
- The overall base plate dimensions are 34 mm in height and 66 mm in width, accommodating 8 fins in total.

Expert Solution

Step 1

Introduction

The fins improve a surface's effective area, enhancing convective heat transmission. Straight fins include triangular and rectangular ones. Triangular fins are appealing because they require significantly less space than rectangular fins to conduct heat equally.

Given data:

$\begin{array}{rcl} number of rectangula fins (n) & = & 8 \\ thickness of the fins (t) & = & 10 mm \\ base area of the plate (A_{b}) & = & 34 mm \times 60 mm \\ cross sectional area of each fin & = & 30 mm \times 2 mm \\ length of each fin (L) & = & 24 mm \\ conductivity of fin (k) & = & 170 W / m K \\ convective heat transfer coefficient (h_{air}) & = & 40 W / m^{2} K \end{array}$

Find out:

(a). The fin efficiency $(η_{fin})$ .

(b). The thermal resistance for the convective heat transfer from the surface of the fin to the air.

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