POLYTECHNIC UNIVERSITY OF PUERTO RICOHATO REY, PUERTO RICO

DEPARTMENT OF CHEMICAL ENGINEERINGSPRING 2014

LINEAR CONDUCTION

Agenda• Introduction• Objectives• Theory• Equipment• Procedure• Data• Calculations• Expected Results• Safety Rules• References

Introduction• Heat Transfer

Introduction• Modes of heat transfer• Conduction • Convection • Radiation

Objectives• To understand the use of the Fourier Rate Equation in determining rate of heat flow through solid materials for one-dimensional steady flow of heat.

• To measure the temperature distribution for steady-state conduction of energy through a composite plane wall and determine the Overall Heat Transfer Coefficient for the flow of heat through a combination of different materials in series

• To determine the thermal conductivity k (the constant of proportionality) of a metal specimen (good conductor)

• To demonstrate that temperature gradient is inversely proportional to the cross-sectional area for one-dimensional flow of heat in a solid material of constant thermal conductivity

Theory

Conduction – One dimensional heat conduction analysis

J. P. Holman. Heat Transfer Tenth Edition. (2009)

𝑄=−𝑘𝐴 𝑑𝑡𝑑𝑥

Where,

k is the thermal conductivity of the material

A is the cross sectional area normal to direction of heat flow

is the temperature gradient of the selection

Theory

𝑞𝑥=(𝑇 2−𝑇 1)

𝑥𝑘𝐴

=(𝑇 2−𝑇1 )𝑅 h𝑡

Conduction – One dimensional heat conduction analysis

J. P. Holman. Heat Transfer Tenth Edition. (2009)

Theory

• Thermal conductivity of various materials at 0°C

J. P. Holman. Heat Transfer Tenth Edition. (2009)

𝑘=𝑞∆ 𝑥𝐴∆𝑇

Theory

J. P. Holman. Heat Transfer Tenth Edition. (2009)

Conduction – One dimensional heat conduction analysis using more than one material

𝑞=𝑇1−𝑇 4

∆ 𝑥𝐴

𝑘𝐴 𝐴+∆𝑥𝐵

𝑘𝐵𝐴+∆ 𝑥𝐶

𝑘𝐶 𝐴

Theory

Overall Heat Transfer Coefficient

• Where, • +

Theory

Conduction – one dimensional heat flow through a cylinder

Equiment

Procedure

Data

Calculus

Safety

References