Acta Physica Hungarica 73. (1993)
1993 / 1. szám - Fluids, Plasmas and Electric Discharges - A. Ogulu - A. R. Bestman: Deep heat muscle treatment: a mathematical model I.
Acta Physica Hungarica 73 (l), yy. 3-16 (1993) DEEP HEAT MUSCLE TREATMENT A MATHEMATICAL MODEL - I A. Ogulu* International Centre for Theoretical Physics Trieste, Italy and A. R. Bestman** Mathematics Department, University of Port Harcourt Port Harcourt, Nigeria (Received 10 September 1992) The flow of blood during deep heat muscle treatment is studied. We model the blood vessel as a long tube of circular section whose radius varied slowly. Under the Boussinesq approximation, we seek asymptotic series expansions for the velocity components, temperature and pressure about a small parameter, e, characterizing the radius variation. The study reveals mathematically why physicians recommend a hot bath for cuts and physiotherapists use ice packs for bruises. 1. Introduction The principle question around which the study of physiological fluid dynamics is centered concerns the range of validity of the assumptions of the Newtonian nature of blood in large blood vessels. In a previous analysis, Bestman [1] studied the unsteady low Reynolds number flow in a heated tube of slowly varying section. In that analysis the effect of forced and free convection heat transfer on flow in an axisymmetric tube whose radius varied slowly in the axial direction was addressed. The temperature of the body, that is the temperature in the interior, called the core temperature is fairly well regulated, normally varying from the mean by not more that 1 °C. Hence the walls of the blood vessels which travel deep inside the body will not show much variation in temperature. On the other hand, the surface temperature of the body rises and falls with the temperature of the surroundings, within a certain limit. In such a case, the wall temperature of the blood vessels which start from the core and travel to the surface will exhibit variation with axial distance. Examples of such blood vessels abound ’Permanent address: Department of Physics. R/S University of Science and Technology, Port Harcourt, Nigeria. ^^Regretfully, Professor A. R. Bestman passed away before the publication of this report. Acta Physica Hungarica 73, 1993 Akadémiai Kiadó, Budapest