(a) Explanation Given information: The length of wire is 6 m , maximum energy stored is 2 kW , the diameter of the wire is 0 .2 cm .the thermal conductivity is 15 .1 W / m ⋅ k , environment temperature is 20 ° C , heat transfer coefficient is 175 W / m 2 ⋅ K . Write the expression for heat generation per unit volume. q ˙ g e n = E V ...... (I) Here, the heat generation per unit volume q ˙ g e n , the maximum energy stored is E , volume of wire is V . Write the expression for surface temperature. T s = T ∞ + q ˙ g e n r 2 h ...... (II) Here, surface temperature is T s . Write the relation between radius and diameter. r = d 2 ...... (III) Here, diameter is d and radius is r . Write the expression for volume of wire. V = π 4 d 2 L ...... (IV) Here, the diameter is d and the length of the pipe is L . Calculation: Substitute 0 .2 cm for d in Equation (III) r = 0.2 cm 2 = ( 0.1 cm ) ( 1 m 100 cm ) = 1 × 10 − 3 m Substitute 1 × 10 − 3 m for r and 6 m for length of wire L Equation (IV). V = π ( 1 × 10 − 3 m ) 2 6 m = 1.88 × 10 − 5 m 3 Substitute 2 kW for E , 1 (b) To determine The surface temperature of wire by using differential equation.

6th Edition

ISBN: 9781260913217

Author: CENGEL

Publisher: INTER MCG

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Question

Chapter 2, Problem 103P

(a)

To determine

The surface temperature of wire by using relations.

(b)

To determine

The surface temperature of wire by using differential equation.

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Chapter 2, Problem 102P

Chapter 2, Problem 104P

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