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The Plane Wall: Assumptions For This Chapter: 1-D Heat Conduction 1. Steady-State Situation 2

This document discusses one-dimensional steady-state heat conduction through a plane wall. It assumes 1D heat conduction, steady-state conditions, and no internal heat sources or sinks. The document defines the temperature boundary conditions of the hot and cold fluids on either side of the wall and the governing equation used. It then discusses determining the temperature profile through the wall using these conditions and equation. Additional sections cover thermal resistance, composite walls, contact resistance, and provide a sample problem to demonstrate the calculations.

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AMARTYA MONDAL
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66 views10 pages

The Plane Wall: Assumptions For This Chapter: 1-D Heat Conduction 1. Steady-State Situation 2

This document discusses one-dimensional steady-state heat conduction through a plane wall. It assumes 1D heat conduction, steady-state conditions, and no internal heat sources or sinks. The document defines the temperature boundary conditions of the hot and cold fluids on either side of the wall and the governing equation used. It then discusses determining the temperature profile through the wall using these conditions and equation. Additional sections cover thermal resistance, composite walls, contact resistance, and provide a sample problem to demonstrate the calculations.

Uploaded by

AMARTYA MONDAL
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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One-Dimensional Steady-State Heat Conduction

Thursday, August 20, 2020 8:52 AM

Assumptions for this chapter:

1. 1-D Heat Conduction


2. Steady-state situation
The Plane Wall
Objective: Use governing equation, initial condition, and
boundary conditions to find the steady-state temperature profile.

A plane wall separates two fluids of different temperatures. Heat


transfer occurs by convection from the hot fluid at 𝑇 , to one surface
of the wall at 𝑇 , , by conduction through the wall, and by convection
from the other surface of the wall at 𝑇 , to the cold fluid at 𝑇 , .

Additional assumptions:

3. No source or sink

1D Heat Conduction Page 1


Hence, for one-dimensional, steady-state conduction in a plane wall with no heat
generation, the heat flux is a constant, independent of x.

Let us say, we only knew the temperature of the fluids and not at the solid boundary.

1D Heat Conduction Page 2


Thermal Resistance

1D Heat Conduction Page 3


The Composite Wall

Where U is the overall heat transfer coefficient.

1D Heat Conduction Page 4


Where U is the overall heat transfer coefficient.

Composite walls may also be characterized by series–parallel


configurations, such as that shown in Figure below. Although
the heat flow is now multidimensional, it is often reasonable to
assume one-dimensional conditions. Subject to this
assumption, two different thermal circuits may be used.
(a) it is presumed that surfaces normal to the x direction are
isothermal

(b) it is assumed that surfaces parallel to the x direction are


adiabatic.

Different results are obtained for 𝑅 , and the corresponding

values of q bracket the actual heat transfer rate.

These differences increase with increasing |𝑘 − 𝑘 |, as

Multidimensional effects become more significant.

Contact Resistance

1D Heat Conduction Page 5


Contact Resistance

(for a unit area of the interface)

1D Heat Conduction Page 6


Sample Problem

1D Heat Conduction Page 7


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