From Biomechanics: Concepts and Computation

15.1 Introduction

This chapter extends the formulation of the previous chapter for the onedimensional diffusion equation to the time-dependent convection-diffusion equation. Although a good functioning of the human body relies on maintaining a homeostasis or equilibrium in the physiological state of the tissues and organs, it is a dynamic equilibrium. This means that all processes have to respond to changing inputs, which are caused by changes of the environment. The diffusion processes taking place in the body are not constant, but instationary, so time has to be included as an independent variable in the diffusion equation. Thus, the instationary diffusion equation becomes a partial differential equation.

Convection is the process whereby heat or particles are transported by air or fluid moving from one point to another point. Diffusion could be seen as a process of transport through immobilized fluid or air. When the fluid itself moves, particles in that fluid are dragged along. This is called convection and also plays a major role in biomechanics. An example is the loss of heat because moving air is passing the body. The air next to the body is heated by conduction, moves away and carries off the heat just taken from the body. Another example is a drug that is released at some spot in the circulation and is transported away from that spot by means of the blood flow. In larger blood vessels the prime mechanism of transportation is convection.

15.2 The Convection-Diffusion Equation

Assuming that the source term f

Products & Services
Air Heaters
Air heaters are devices used to heat air.  They include forced air products as well as all types of radiant and space heaters.
High Vacuum Pumps
High and ultrahigh vacuum pumps operate efficiently in the high vacuum region and develop molecular flow for highly evacuated systems.
Heat Pipes
Heat pipes are self-contained heat pumps that can transport heat at high rates over fairly substantial distances with no external pumping power.
Industrial Heaters
This is a general search form for all types of industrial heaters, devices which are available in a variety of sizes, shapes, and heating configurations.
Vacuum Greases and Vacuum Pump Oils
Vacuum greases and vacuum pump oils are suitable for vacuum sealing, diffusion pumps and other vacuum fluid applications.

Topics of Interest

16.1 Introduction The two- and three-dimensional convection-diffusion equation plays an important role in many applications in biomedical engineering. One typical example from recent research is the...

1.1 Mass Transfer by Diffusion or Convection: Basic Equations The matter transfers taking place between polymer packaging and a liquid are controlled either by convection at the liquid-solid...

3.0 Introduction Engineering thermal science includes thermodynamics and heat transfer. Thermodynamic analyses consider only systems in equilibrium. The role of heat transfer is to supplement...

4.1 Mass Transfer When a mixture of gases or liquids is contained such that a concentration gradient of one or more of the components exists across the system, there will be mass transfer on a...

3.1 Introduction In Chapters 1 and 2, we have analyzed the motion of a liquid under the form of microflow as well as under the form of microdrop (digital microfluidics). In reality the fluid we have...