## Abstract

The aim of this report is to look at the different modes of heat transfer. Specifically, heat transfer through walls will be clearly outlined and the different equations associated with the same discussed. The report will also cover conduction, radiation and convection as modes of heat transfer.

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## Introduction

Heat can be defined as energy in transition brought about by a difference in temperature.If there is a greater temperature difference, then the heat is transferred more rapidly. The rate of heat transfer is what defines the situation while discussing heat transfer models. There are three distinct modes of heat transfer:

- Conduction
- Radiation and
- convection

Heat transfer is only possible for all the above mentioned modes in the existence of a temperature difference (Incropera 75)

### Conduction

In this mode of heat transfer, heat energy is transferred without any movement of macroscopic particles but on a molecular scale with vibration of the body molecules. Fourier’s law was developed on the basis of heat transfer by conduction.

### Convection

In this mode, heat is transferred by mixing of one part of fluid with another of different temperature. The movement of the fluid portion could be caused by a density gradient due to temp difference or due to natural convection. It could also be due to a pump as in a heat exchanger; a phenomenon called forced convection (Incropera 78)

### Radiation

In this mode, heat energy is transferred in the form of electromagnetic waves and does not therefore require a medium of transfer (Incropera 80).

## Heat transfer through walls

Heat transfer by conduction through walls is mainly due to vibration of the molecular particles and energy transfer to the adjacent walls. Fourier’s law of heat conduction states that “The rate of heat flow *Q *is proportional to the area through which it flows *A *and the temperature difference *dt *across the layer and inversely proportional to the thickness *dx*. The law is expressed as below.

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*QαAdt/ dx*

Equation i. above expression is then expressed as an equation by introducing a constant *k *(thermal conductivity) to give:

*Q = – k(dt/ dx)*

The negative sign in the equation ii is an indication of direction i.e. heat flow is positive in the direction of the temperature fall.

Fourier’s law of conduction is based on one dimensional steady heat flow through a solid. One dimensional flow is whereby the temperature is constant over surfaces perpendicular to the direction of heat flow.

Steady state implies that *Q _{in }= Q_{out }= Q_{intermediate}*

Where *Q *represents the Heat energy.

Assuming that the heat changes from *t*_{1 }to *t _{2}*, equation ii can be integrated with t

_{1}and t

_{2 }as the lower and upper limts respectively to obtain:

*Q = – kA (t*_{1 }− t_{2})/x

### Newton’s law of cooling

This states that heat transfer of a solid surface of area, *A *at a temp *t*_{w }to a fluid of temperature *t *is given by

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*QαA (t*_{w}−t)*QhA (t*_{w}−t)

Where h=heat transfer coefficient.

Taking *dA *and *dB *as the thicknesses of the static field of fluid in contact with a wall on one side A and another side B, through which conduction will be by conduction, then heat flow through unit surface area would be

*q = (t*_{A}−t_{B})/[(1/h_{A})+(x/k)+(1/h_{B})]

Equation I is based on the assumption that heat flow through a wall of unit surface area is given by *q = k/x(t _{1 }− t_{2}).*

With *k/x′ = h*, then *Q = hA (t _{w}−t)*

Where, *t _{w }*is the temperatute of the wall and t the temperature of the surrounding fluid.

## Conclusion

The above described equations and laws are instrumental in the calculation of heat transfer rates and the subsequent design of structures that that are thermally sound, including dwellings and special structures.

## Works cited

Incropera,Frank. *Fundamentals of Heat and Mass Transfer 6th Edition*. New York: Hemisphere Publishing, 2006.