**Problem 5.78**Spheres of 40-mm diameter, heated to a uniform temperature of 400°C, are suddenly removed from the oven and placed in a forced-air bath operating at 25°C with a convection coefficient of 300 W/m²·K on the sphere surfaces. The thermophysical properties of the sphere material are:- Density $ \rho = 3000 \, \text{kg/m}^3 $- Specific heat capacity $ c = 850 \, \text{J/kg·K} $- Thermal conductivity $ k = 15 \, \text{W/m·K} $**(a)** How long must the spheres remain in the air bath for 80% of the thermal energy to be removed?**(b)** The spheres are then placed in a packing carton that prevents further heat transfer to the environment. What uniform temperature will the spheres eventually reach?

The spheres remain in the air bath for 80% is 98.6 second Uniform temperature will be 1000C

Spheres of 40-mm diameter heated to a uniform temperature of 400°C are suddenly removed from the oven and placed in a forced-air bath operating at 25°C with a convection coefficient of 300 W/m² K on the sphere surfaces. The thermophysical properties of the sphere material are p = 3000 kg/m³, c = 850 J/kg-K, and k = 15 W/m.K. (a) How long must the spheres remain in the air bath for 80% of the thermal energy to be removed?

Spheres of 40-mm diameter heated to a uniform temperature of 400°C are suddenly removed from the oven and placed in a forced-air bath operating at 25°C with a convection coefficient of 300 W/m² K on the sphere surfaces. The thermophysical properties of the sphere material are p = 3000 kg/m³, c = 850 J/kg-K, and k = 15 W/m.K. (a) How long must the spheres remain in the air bath for 80% of the thermal energy to be removed?

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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Question

**Problem 5.78**

Spheres of 40-mm diameter, heated to a uniform temperature of 400°C, are suddenly removed from the oven and placed in a forced-air bath operating at 25°C with a convection coefficient of 300 W/m²·K on the sphere surfaces. The thermophysical properties of the sphere material are:
- Density $ \rho = 3000 \, \text{kg/m}^3 $
- Specific heat capacity $ c = 850 \, \text{J/kg·K} $
- Thermal conductivity $ k = 15 \, \text{W/m·K} $

**(a)** How long must the spheres remain in the air bath for 80% of the thermal energy to be removed?

**(b)** The spheres are then placed in a packing carton that prevents further heat transfer to the environment. What uniform temperature will the spheres eventually reach?

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