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Laplace transform to find T (t)

Laplace transform to find T (t)

Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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1. Hot water at a temperature of Th is supplied to the jacket of a tank, shown in Figure-1 below. Heat is transferred at a rate of UA(Th – T(t)) from the jacket to the tank content. This input causes a change in the liquid temperature, T(t). Qin Cp T(t) Figure-1: Water jacket heating system where Qin is the heat transfer from jacket to the tank, T(t) is liquid temperature in the tank. The tank is insulated and therefore the energy balance over the system is governed by: Answer the following questions: dT (t) UA(Th T (t)) = mcp dt (a) Use Laplace transform to find T(t) with an initial condition of T(0) = 0 °C in terms of the variables given in this problem. (b) How long does it take for 500 kg of liquid from 0 °C to reach 55 °C if hot water at 90 °C circulates around the tank? The heat surface area (A) and overall heat transfer coefficient (U) are 20 m² and 1.7 kWm-²K-¹, respectively (Cp = 0.7 kJkg-¹K-¹).
Transcribed Image Text:1. Hot water at a temperature of Th is supplied to the jacket of a tank, shown in Figure-1 below. Heat is transferred at a rate of UA(Th – T(t)) from the jacket to the tank content. This input causes a change in the liquid temperature, T(t). Qin Cp T(t) Figure-1: Water jacket heating system where Qin is the heat transfer from jacket to the tank, T(t) is liquid temperature in the tank. The tank is insulated and therefore the energy balance over the system is governed by: Answer the following questions: dT (t) UA(Th T (t)) = mcp dt (a) Use Laplace transform to find T(t) with an initial condition of T(0) = 0 °C in terms of the variables given in this problem. (b) How long does it take for 500 kg of liquid from 0 °C to reach 55 °C if hot water at 90 °C circulates around the tank? The heat surface area (A) and overall heat transfer coefficient (U) are 20 m² and 1.7 kWm-²K-¹, respectively (Cp = 0.7 kJkg-¹K-¹).
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