Fundamentals of heat transfer

The following is a brief overview of some fundamental heat transfer concepts.

Introduction to thermodynamics

1st and 2nd laws of thermodynamics

The 1st law of thermodynamics involves the conservation of energy. It states that within a closed system where no other energy material can enter or leave, energy can neither be created nor destroyed. Although energy cannot be created or destroyed, it can be transferred to work as other forms of energy.

Transferring heat energy is subject to the 2nd law of thermodynamics. The 2nd law says within a closed system, there is a net increase in entropy for spontaneous processes. Entropy is defined as a measure of disorder that exists in a system.

Three alternate but equivalent ways to describe the 2nd Law are:

Heat flows spontaneously from a hot body to a cool one. (Example: A hot microprocessor or laser diode is cooled by heat flow into heat sink or cold plate.)

It is impossible to convert heat completely into useful work. (Example: In a combustion engine, a certain heat component must always be exhausted without performing work.)

Every isolated system becomes disordered in time. (Example: When hot and cold bodies first contact each other during conduction, the system is somewhat ordered. Hotter molecules move faster than cooler molecules. But once the entire system attains a uniform temperature, this order is lost.)

Expressed in mathematical terms, any of the above statements imply the other two.

The 1st and 2nd laws of thermodynamics govern the various modes of heat transfer: conduction, convection and radiation.

Modes of heat transfer

Conduction

In conduction, heat flows from a higher temperature region to regions of lower temperature. This occurs within solid, liquid or gaseous mediums or between different mediums that make direct physical contact with each other. The transfer of the energy of motion between adjacent molecules conducts heat. In a gas, the ‘hotter’ molecules, have greater energy and motion which impart energy to adjacent molecules at lower energy levels. This type of transfer occurs in all solids, gases or liquids in which a temperature gradient exists. Energy can also be conducted by "free electrons", especially within metallic solids. Examples of conduction are heat transfer through the surfaces of a cold plate or through the walls of a refrigerator.

Convection

Convection transports energy through the combined action of heat conduction, energy storage and mixing motions. Convection is the essential energy transfer mechanism mechanism between a solid surface and a fluid. Energy transfer from convection can either be classified as natural convection or forced convection. Natural or free convection describes fluid circulation from the pressure differential generated by the warming or cooling of fluid next to a solid surface. In forced convection heat transfer, an active mechanism like a fan or pump circulates fluid past a solid surface. Free convection is the loss of heat into ambient air via the fins of a heat exchanger. If a fan is used to circulate the air over the heat exchanger fins, this becomes an example of forced convection.

Radiation

In radiation, heat flows from a higher temperature body to a lower temperature body when the bodies are separated in space, even across a vacuum. Thermal radiation follows the same physical laws as light. Solids and liquids absorb thermal radiation that travel through it, so radiation is important mainly in heat transfer through space or gases.

An example of radiation includes the transfer of heat from the sun to the earth.

Mathematical representation and calculation of heat transfer

Fourier’s equation

The rate of heat flow by conduction in a material, qk , equals the product of the following three quantities:

• k – Thermal conductivity of the material
• A – Area of the section through which heat flows by conduction as measured perpendicularly to the direction of heat flow
• dT/dx – Temperature gradient at the section, i.e., the rate of change of temperature T with respect to the difference in the direction of the heat flow x.

Writing the heat conduction equation in mathematical form requires a sign convention; i.e., the direction of increasing distance x is the direction of positive heat flow. According to the second law of thermodynamics, heat will automatically flow from points of higher temperature to points of lower temperature. Thus, heat flow will be positive when the temperature gradient is negative. The basic equation for one-dimensional conduction in the steady state is: qk = -kA (dT/dx).

Thermal conductivity

Thermal conductivity is a measurement of the rate at which a given material will transfer heat. The thermal conductivity of a substance is the quantity of heat in cal/sec passing through a body 1 cm thick with a cross section of 1 cm² when the temperature difference between the hot and cold sides of the body is 1 deg. C. This intrinsic property is independent of the materials size, shape or orientation.

Thermal resistance

Thermal resistance is the inverse of thermal conductivity and indicates how a material inhibits the conduction of heat. Materials with a high thermal conductivity have a low thermal resistance and have poor heat insulation qualities , like copper and aluminum. Conversely, materials with a low thermal conductivity have a high thermal resistance and have good heat insulation qualities such as fiberglass insulation and corkboard.