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6. (a) The temperature distribution across a wall of an aluminium cylin- der block, 4 mm thick at a certain instant of time is given as; T(x) = a +bx+ca², where T is in degrees Celsius, and x is in metres. The coefficents are; a = 200 °C, b=-10000 °C/m, and C= 1x106°C/m². = The area of the cylinder wall, normal to the direction of heat conduction is, A 20 mm². The cylinder block has material properties as follows; density, p = 2700 kg/m³, conductivity, K = 220W/m, and, specific heat capacity, c = 900J/kgK. i. Find the rate of heat transfer entering the wall, (r = 0), and leaving the wall, (r = 4x10-³ m). ii. What boundary conditions are implied at the surfaces of the wall, (r = 0), and, (x = 4x10-³ m). iii. Find the rate of change of energy storage in the wall. iv. Find the time rate of temperature change at .r = x = 4 mm. 1 mm, and

6. (a) The temperature distribution across a wall of an aluminium cylin- der block, 4 mm thick at a certain instant of time is given as; T(x) = a +bx+ca², where T is in degrees Celsius, and x is in metres. The coefficents are; a = 200 °C, b=-10000 °C/m, and C= 1x106°C/m². = The area of the cylinder wall, normal to the direction of heat conduction is, A 20 mm². The cylinder block has material properties as follows; density, p = 2700 kg/m³, conductivity, K = 220W/m, and, specific heat capacity, c = 900J/kgK. i. Find the rate of heat transfer entering the wall, (r = 0), and leaving the wall, (r = 4x10-³ m). ii. What boundary conditions are implied at the surfaces of the wall, (r = 0), and, (x = 4x10-³ m). iii. Find the rate of change of energy storage in the wall. iv. Find the time rate of temperature change at .r = x = 4 mm. 1 mm, and

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
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6. (a) The temperature distribution across a wall of an aluminium cylin- der block, 4 mm thick at a certain instant of time is given as; T(x) = a +bx+cr², where T is in degrees Celsius, and x is in metres. The coefficents are; a = 200 °C, b=-10000 °C/m, and c=1x106 C/m². = The area of the cylinder wall, normal to the direction of heat conduction is, A 20 mm². The cylinder block has material properties as follows; density, p = 2700 kg/m³, conductivity, K = 220W/m, and, specific heat capacity, c, = 900J/kgK. i. Find the rate of heat transfer entering the wall, (r = 0), and leaving the wall, (r = 4x10-³ m). -3 ii. What boundary conditions are implied at the surfaces of the wall, (r = 0), and, (x = 4x10-³ m). iii. Find the rate of change of energy storage in the wall. iv. Find the time rate of temperature change at r = 1 mm, and x = 4 mm.
Transcribed Image Text:6. (a) The temperature distribution across a wall of an aluminium cylin- der block, 4 mm thick at a certain instant of time is given as; T(x) = a +bx+cr², where T is in degrees Celsius, and x is in metres. The coefficents are; a = 200 °C, b=-10000 °C/m, and c=1x106 C/m². = The area of the cylinder wall, normal to the direction of heat conduction is, A 20 mm². The cylinder block has material properties as follows; density, p = 2700 kg/m³, conductivity, K = 220W/m, and, specific heat capacity, c, = 900J/kgK. i. Find the rate of heat transfer entering the wall, (r = 0), and leaving the wall, (r = 4x10-³ m). -3 ii. What boundary conditions are implied at the surfaces of the wall, (r = 0), and, (x = 4x10-³ m). iii. Find the rate of change of energy storage in the wall. iv. Find the time rate of temperature change at r = 1 mm, and x = 4 mm.
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