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 Introduction to Heat Transfer


Heat transfer is the exchange of thermal energy between physical systems. The rate of heat transfer is dependent on the temperatures of the systems and the properties of the intervening medium through which the heat is transferred. The three fundamental modes of heat transfer are conduction, convection and radiation.


Fourier Law of Heat Conduction


When there exists a temperature gradient within a body, heat energy will flow from the region of high temperature to the region of low temperature. This phenomenon is known as conduction heat transfer, and is described by Fourier's Law (named after the French physicist Joseph Fourier),


This equation determines the heat flux vector q for a given temperature profile T and thermal conductivity k. The minus sign ensures that heat flows down the temperature gradient.


Heat Equation (Temperature Determination)


The temperature profile within a body depends upon the rate of its internally-generated heat, its capacity to store some of this heat, and its rate of thermal conduction to its boundaries (where the heat is transfered to the surrounding environment). Mathematically this is stated by the Heat Equation,


along with its boundary conditions, equations that prescribe either the temperature T on, or the heat flux q through, all of the body boundaries W,




In the Heat Equation, the power generated per unit volume is expressed by qgen. The thermal diffusivity a is related to the thermal conductivity k, the specific heat c, and the density r by,


For Steady State problems, the Heat Equation simplifies to,



Derivation of the Heat Equation


The heat equation follows from the conservation of energy for a small element within the body,

heat conducted in        +      heat generated within  =      heat conducted out      +        change in energy stored within

We can combine the heats conducted in and out into one "net heat conducted out" term to give,

net heat conducted out=      heat generated within  -       change in energy stored within

Mathematically, this equation is expressed as,


The change in internal energy e is related to the body's ability to store heat by raising its temperature, given by,



One can substitute for q using Fourier's Law of heat conduction from above to arrive at the Heat Equation,


Temperature limits of some common insulation materials are indicated in the table below:

Insulation Material

Temperature Range







Calcium Silicate





Cellular Glass





Elastomeric foam










Mineral Wool, Ceramic fiber




Mineral Wool, Glass





Mineral Wool, Stone





Phenolic foam
















Calcium Silicate Insulation

Non-asbestos Calcium Silicate insulation board and pipe insulation feature with light weight, low thermal conductivity, high temperature and chemical resistance.

Cellular Glass Insulation

Cellular glass insulation is composed of crushed glass combined with a cellulating agent.

These components are mixed, placed in a mold, and then heated to a temperature of approximately 950 oF. During the heating process, the crushed glass turns to a liquid. Decomposition of the cellulating agent will cause the mixture to expand and fill the mold. The mixture creates millions of connected, uniform, closed-cells and form at the end a rigid insulating material.

Cellulose Insulation

Cellulose is made from shredded recycled paper, such as newsprint or cardboard. It's treated with chemicals to make it fire- and insect-resistant, and is applied as loose-fill or wet-sprayed through a machine.

Fiberglass Insulation

Fiberglass is the most common type of insulation. It's made from molten glass spun into microfibers.

Mineral Wool Insulation

mineral wool insulation

Mineral wool is made from molten glass, stone, ceramic fibre or slag that is spun into a fiber-like structure. Inorganic rock or slag are the main components (typically 98%) of stone wool. The remaining 2% organic content is generally a thermosetting resin binder (an adhesive) and a little oil.

Polyurethane insulation

Polyurethane is an organic polymer formed by reacting a polyol (an alcohol with more than two reactive hydroxyl groups per molecule) with a diisocyanate or a polymeric isocyanate in the presence of suitable catalysts and additives.

Polyurethanes are flexible foams used in mattresses, chemical-resistant coatings, adhesives and sealants, insulation for buildings and technical applications like heat exchangers, cooling pipes and much more.

Polystyrene Insulation

Polystyrene is an excellent insulator. It is manufactured in two ways:

  • Extrusion - which results in fine, closed cells, containing a mixture of air and refrigerant gas
  • Molded or expanded - which produces coarse, closed cells containing air

Extruded polystyrene, or XPS, is a closed-cell, thermal plastic material manufactured by a variety of extrusion processes. The main applications of extruded polystyrene insulation are in building insulation and construction in general.

Molded or expanded polystyrene is commonly called beadboard and has a lower R-value than extruded polystyrene.

Polyisocyanurate Insulation

Polyisocyanurate or polyiso is a thermosetting type of plastic, closed-cell foam that contains a low-conductivity gas (usually hydrochlorofluorocarbons or HCFC) in its cells.