A hot reservoir with a temperature of 721 K is 0.15 m away from a cold reservoir

Question

A hot reservoir with a temperature of 721 K is 0.15 m away from a cold reservoir with a temperature of 316 K. The two reservoirs are insulated from each other except for a rod of brass (k = 109 W/m-K) that has a cross-sectional area of 0.015 m2. The entire system is allowed to reach a steady-state condition.

1.

How much energy is transferred by heat between the hot reservoir and the cold reservoir in ten minutes?

2.

Assume that you need to transfer 6501700 J of energy in ten minutes between the two reservoirs. To enhance the rate of energy transfer, a steel rod (k = 43 W/m-K) of the same length is added between the two reservoirs. What should the cross-sectional area of the steel rod be in order to achieve the proper rate of energy transfer?

Explanation / Answer

1) Energy transfer rate=-k × A × dT/dx
k=thermal conductivity=109W/m.K
A=cross sectional area=0.015m^2
dt=temperature difference=(316-721)K
dx=distance between the reservoirs=0.15m
Time=10minutes=10 × 60=600 seconds
Heat transfer rate=-109 × 0.015 × (316-721)/0.15=4414.5W= 4414.5 J/second.
Energy transfer=energy transfer rate × time=4414.5×600=2648700J

2) 6501700/600 = energy transfer rate

10836.16 =- 43*A* (316-721)/0.15

A = -252*0.15/(316-721) =0.093m^2

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.