Problem 36 from Nagle Fundamentals Differential Equations 8th edition textbook A

Question

Problem 36 from Nagle Fundamentals Differential Equations 8th edition textbook

A building consists of two zones A and B (see Figure 5.5). Only zone A is heated by a furnace, which generates 80,000 Btu/hr. The heat capacity of zone A is 1/4oF per thousand Btu. The time constant for heat transfer between zone A and the outside is 4 hr, between the unheated zone B and the outside is 5 hr, and between the two zones is 2 hr. If the outside temperature stays at 0oF, how cold does it eventually get in the unheated zone B?

this is followed by question 37.

In Problem 36, if a small furnace that generates 1000 Btu/hr is placed in zone B, determine the coldest it would eventually get in zone B if zone B has a heat capacity of 2oF per thousand Btu.

Explanation / Answer

86000/3600 per sec=24 BTU/sec at B say the temperature is t and at A is s s>t then 5*3600*t=(s-t)*2*3600 and use 4*3600*s+(s-t)*2*3600=80000*4

solve this two linear equation to get s and t

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