Consider the thermal system shown below. The temperature of the inflow liquid is kept constant, and the liquid inflow rate G kg/s is also kept constant. For t<0 the system is at steady state, wherein the heat input from the heater is U kcal/s and the temperature of the liquid in tank 2 is 0,°C. At t 0 the heat input is changed from U to U + u where u is small. This change will cause the temperature of the liquid in tank 2 to change from 02 to 02 +82. Taking the change in the heat input from the heater to be the input to the system and the change in the temperature of the liquid in tank 2 to be the output, obtain the transfer function 02(s)/U(s). Assume that the thermal capacitances of tanks 1 and 2 are Ci kcal/°C and C2 kcal/C, respectively, and that the specific heat of the liquid is c kcal/kg°C. The steady-state heat flow rates from tanks 1 and 2 are the same, Q kcal/s. The changes in heat flow rates from tanks 1 and 2 are qi and q2, respectively. %3D Ū+u \b + 0 Tank 1 + 0, O+0, Q+ 42 Tank 2

Consider the thermal system shown below. The temperature of the inflow liquid is kept constant, and the liquid inflow rate G kg/s is also kept constant. For t<0 the system is at steady state, wherein the heat input from the heater is U kcal/s and the temperature of the liquid in tank 2 is 0,°C. At t 0 the heat input is changed from U to U + u where u is small. This change will cause the temperature of the liquid in tank 2 to change from 02 to 02 +82. Taking the change in the heat input from the heater to be the input to the system and the change in the temperature of the liquid in tank 2 to be the output, obtain the transfer function 02(s)/U(s). Assume that the thermal capacitances of tanks 1 and 2 are Ci kcal/°C and C2 kcal/C, respectively, and that the specific heat of the liquid is c kcal/kg°C. The steady-state heat flow rates from tanks 1 and 2 are the same, Q kcal/s. The changes in heat flow rates from tanks 1 and 2 are qi and q2, respectively. %3D Ū+u \b + 0 Tank 1 + 0, O+0, Q+ 42 Tank 2

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Pressure and Stress

Question

Consider the thermal system shown below. The temperature of the inflow liquid is kept
constant, and the liquid inflow rate G kg/s is also kept constant. For t <0 the system is at
steady state, wherein the heat input from the heater is U kcal/s and the temperature of the
liquid in tank 2 is 0,°C. At t 0 the heat input is changed from U to U + u where u is
small. This change will cause the temperature of the liquid in tank 2 to change from 02 to
02 +82. Taking the change in the heat input from the heater to be the input to the system
and the change in the temperature of the liquid in tank 2 to be the output, obtain the transfer
function 02(s)/U(s). Assume that the thermal capacitances of tanks 1 and 2 are Ci
kcal/°C and C2 kcal/C, respectively, and that the specific heat of the liquid is c kcal/kg°C.
The steady-state heat flow rates from tanks 1 and 2 are the same, Q kcal/s. The changes in
and
heat flow rates from tanks 1 and 2 are
q2, respectively.
U +u
G
Tank 1
O+ 0,
O+ 0,
O+ 42
Tank 2

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