Bio-Fluid Mechanics and Bio-Heat Transfer

Course Description

EGM 4853 Bio-Fluid Mechanics and Bio-Heat Transfer is an upper-division engineering elective that applies fluid mechanics and heat transfer to the human body. The statewide description is two sentences: a "study of biothermal fluid sciences" with "emphasis on physiological processes occurring in human blood circulation and underlying physical mechanisms from an engineering perspective." Students take the mechanics they learned for pipes and machines and use it on blood, blood vessels and living tissue.

The course sits under the EGM (Engineering Science) prefix, in the state's Mechanical Engineering discipline. ⚠ The University of Florida is the only Florida public institution that carries it, at 3 credits. So this guide describes UF's course. The outcomes and topics below are built from the statewide description, UF's catalog entry and what courses on this subject normally cover. UF's own syllabus is the authority for any given term.

It is taken mainly by mechanical, aerospace and biomedical engineering students in their third or fourth year, after fluid mechanics. It is an elective, not a degree requirement, so expect it to run in some terms and not others. Check UF's schedule of courses before planning around it.

UF also carries a graduate version, EGM 6855, with the same title and the same description. Its prerequisite is simply "undergraduate fluid mechanics." See Special Information before taking both.

Learning Outcomes

Required Outcomes

• Describe the structure of the human circulatory system — heart, arteries, capillaries, veins — in the quantities an engineer works with: pressures, flow rates, vessel sizes and velocities.
• Describe the composition of blood and explain why it behaves as a non-Newtonian fluid, including shear-thinning and the effect of hematocrit on viscosity.
• Apply the conservation equations of fluid mechanics (mass, momentum, energy) to flow in blood vessels, and state the assumptions each simplified model makes.
• Analyze steady flow in vessels with the Poiseuille relationship, compute vascular resistance, and judge when that model is and is not valid.
• Explain pulsatile flow in arteries and use the Womersley number to judge whether a flow is quasi-steady or dominated by unsteadiness.
• Apply heat-transfer principles to living tissue, including the role of blood perfusion and metabolic heat, using the Pennes bioheat equation.
• Connect a physiological process to the physical mechanism behind it, from an engineering perspective, as the statewide description requires.

Optional Outcomes

• Fit blood viscosity data to a constitutive model such as the Casson or power-law model.
• Explain the Fåhræus and Fåhræus–Lindqvist effects in small vessels.
• Model arterial wall compliance and estimate pulse-wave speed (Moens–Korteweg).
• Analyze flow through a stenosis or an aneurysm and relate wall shear stress to disease.
• Describe exchange in the microcirculation using Starling filtration.
• Model temperature in tissue during a thermal therapy (hyperthermia, ablation or cryotherapy) and estimate thermal damage.
• Set up a simple computational model of vessel flow or tissue heating.

Major Topics

Required Topics

• The cardiovascular system for engineers: the cardiac cycle, pressure–volume behaviour, and pressures and flows through the systemic circulation.
• Blood as a fluid: plasma, red cells, hematocrit, and non-Newtonian viscosity.
• Governing equations: continuity, Navier–Stokes and the energy equation, with the simplifications used for vessels.
• Steady laminar flow in tubes: Poiseuille flow, resistance in series and parallel, and entrance effects.
• Unsteady and pulsatile flow in arteries; the Womersley solution and number.
• Heat transfer in living tissue: conduction, perfusion and metabolic heat generation; the Pennes bioheat equation; thermal properties of tissue.
• Body temperature regulation as a heat-transfer problem.

Optional Topics

• Constitutive models for blood: power-law, Casson, Carreau.
• Flow in small vessels and the microcirculation: Fåhræus–Lindqvist effect, capillary exchange, Starling forces.
• Elastic arteries and wave propagation; the windkessel model.
• Flow in diseased vessels: stenosis, aneurysm, wall shear stress and atherosclerosis.
• Heart valves and flow through medical devices such as stents and blood pumps.
• Thermal therapies and injury: hyperthermia, radiofrequency and laser ablation, cryosurgery, and Arrhenius damage models.
• Computational hemodynamics and image-based modelling.

Resources & Tools

• Biofluid Mechanics: The Human Circulation, Chandran, Rittgers and Yoganathan — the standard engineering text on blood flow.
• Transport Phenomena in Biological Systems, Truskey, Yuan and Katz — covers both the fluid and the heat and mass transfer halves.
• Biomechanics: Circulation, Y. C. Fung — the classic reference on blood rheology and vessel mechanics.
• H. H. Pennes (1948), "Analysis of tissue and arterial blood temperatures in the resting human forearm," Journal of Applied Physiology — the original bioheat equation paper, still assigned.
• Your fluid mechanics and heat transfer texts from earlier courses — the course builds directly on them.
• Software: MATLAB or Python for analytical and numerical solutions; COMSOL Multiphysics (it has a bioheat interface) or ANSYS Fluent where the course includes computational work.

Career Pathways

• Biomedical engineer (SOC 17-2031): cardiovascular devices, thermal therapy systems, diagnostic equipment. See the site's biomedical engineer career path.
• Mechanical engineer (SOC 17-2141) in medical-device design and testing, where flow and thermal analysis of devices is routine.
• Computational modelling and simulation roles in the medical-device and simulation-software industries.
• Graduate study in biomedical or mechanical engineering, especially cardiovascular biomechanics. This elective is a strong signal of interest for that route.
• Florida context: the Gainesville–Alachua medical-device cluster near UF (for example Exactech and AxoGen), and device makers in Jacksonville. Clinical engineering and research roles also exist in Florida's large hospital systems.

Special Information

Offering Notes

One public carrier: the University of Florida, at 3 credits. UF does not publish contact hours. The 45-hour figure is derived by Florida's convention of 15 hours per credit for a lecture course; the statewide record marks the course as having no laboratory.

Prerequisites and preparation

UF's only listed prerequisite is EGN 3353C Fluid Mechanics, which itself requires Calculus III (MAC 2313). ⚠ The title includes heat transfer, but no heat-transfer course is listed as a prerequisite. If you have not taken heat transfer (UF's EML 4140), review steady and transient conduction, the heat equation and convection coefficients before the bioheat half of the course. That is where students without it struggle. Comfort with ordinary and partial differential equations helps throughout.

No physiology background is assumed. The course teaches the circulation it needs, but reading a short introduction to cardiovascular physiology before the term makes the first weeks easier.

The graduate twin: EGM 6855

UF carries EGM 6855 with the same title and description, for graduate students. UF's catalog does not say the two are taught together. ⚠ Many universities do not allow credit for both an undergraduate course and its graduate version. If you plan to continue to a UF master's degree, especially in a combined bachelor's/master's programme, ask the department before registering which one you should take.

Related courses at other Florida universities

No other Florida public institution carries EGM 4853. The same subject is taught elsewhere under biomedical engineering numbers, and these are different course numbers, so they do not transfer as equivalents automatically:

• BME 3261C Biofluid Mechanics — Florida Gulf Coast University.
• Biotransport courses covering momentum, heat and mass transfer: BME 3631 (FAMU and Florida State), BME 3632 (FIU, USF), BME 4632 (UF), BME 4632C (FGCU).
• Graduate biofluids courses: BME 5267 and BME 6268 (UCF), BME 6266 (FIU).

⚠ UF's own BME 4632 Biomedical Transport Phenomena overlaps with this course. It covers momentum, heat and mass transport in biomedical systems and is aimed at biomedical engineering majors; EGM 4853 is the mechanical-engineering route into the same physics. If you are a UF biomedical engineering student, check which one your degree counts before choosing.

Transfer

As an upper-division elective taught only at UF, this course is mostly taken by UF students. A student transferring to UF from a state college will not have met it; the preparation that matters is the calculus, physics and fluid mechanics sequence that leads to EGN 3353C.

FE exam

The FE Mechanical exam tests fluid mechanics and heat transfer, but not biofluids. This course gives extra practice applying both to unfamiliar problems, which is useful, but it is not FE preparation in itself.

AI Integration (Optional)

AI tools are useful here for algebra, checking units, and writing MATLAB or Python code to solve the Womersley or bioheat equations. ⚠ The typical mistakes AI tools make are the mistakes this course exists to correct. A model asked about blood flow will usually treat blood as a Newtonian fluid and apply Poiseuille flow everywhere, including in large arteries, where the flow is pulsatile, and in capillaries, where the red cells are about as wide as the vessel. Asked about tissue temperature, it will often drop the perfusion term or get its units wrong.

So use AI to check working, never to choose the model. Before accepting an answer, ask whether its assumptions hold: steady or pulsatile? Newtonian at this vessel size? Is perfusion included? Check physiological numbers (pressures, flow rates, tissue properties) against a textbook table, since AI tools often state them confidently and wrongly. Follow UF's and your instructor's rules on AI use for graded work.