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Deep heat muscle treatment a mathematical model — II

  • Fluids, Plasmas and Electric Discharges
  • Published:
Acta Physica Hungarica

Abstract

The effect of viscosity variation on the flow of blood during deep heat muscle treatment is studied. Two methods: an asymptotic series expansion technique and a perturbation technique are employed to obtain the temperature distribution. The results are compared with the problem of Part I. A novel development in this part of the study is the combined asymptotic patching and matching technique.

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Abbreviations

ε:

a small parameter

s :

an arbitrary function

r :

radial coordinate

z :

axial coordinate

ϕ:

azimuthal coordinate

u, v, w :

velocity components

R a :

radiation parameter

P r :

Prandtl number

R :

Reynolds number

G r :

Grashof number

p :

pressure

a 0 :

characteristic radius

u(0),v(0),w(0):

leading component of the velocity vector

p (0) :

leading component of the pressure

p (1) z :

perturbed pressure gradient

K :

applied pressure gradient

I n :

Bessel function of the 1st kind of ordern

k n :

Bessel function of the 2nd kind of ordern

ϕ:

small correction

θ w :

wall temperature

GI,GII:

Green’s function

C1,C2,C3,C4:

constants

δ:

Dirac delta function

References

  1. J. T. Pedley, Fluid Dynamics of Large Blood Vessels, Cambridge University Press, Cambridge, 1980.

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  2. J. O. Rowan, Physics and Circulation. Medical Physics Handbook 9. Adam Hilger Ltd, Bristol, 1981.

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  3. A. Ogulu and A. R. Bestman, Acta Phys. Hung.,73, 3, 1993.

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  4. B. R. Byron, W. E. Stewart and E. N. Lightfoot, Transport Phenomenon. Wiley International Edition, New York, 1960.

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  5. A. Ogulu, Ph. D. Thesis. Rivers State University of Science and Technology, Port-Harcourt, Nigeria, 1991.

  6. M. Abramowitz and I. A. Stegun, A Handbook of Mathematical Functions. Dover Publications Inc., New York.

  7. A. R. Bestman, Il Nuovo Cimento,11c No 3, 1988.

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Author notes

  1. A. Ogulu

    Present address: Department of Physics, R/S University of Science and Technology, Port Harcourt, Nigeria

Authors and Affiliations

  1. International Centre for Theoretical Physics, Trieste, Italy

    A. Ogulu

  2. Mathematics Department, University of Port Harcourt, Port Harcourt, Nigeria

    A. R. Bestman

Authors
  1. A. Ogulu
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  2. A. R. Bestman
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Additional information

Regretfully, Professor A. R. Bestman passed away before the publication of this report.

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Ogulu, A., Bestman, A.R. Deep heat muscle treatment a mathematical model — II. Acta Physica Hungarica 73, 17–27 (1993). https://doi.org/10.1007/BF03054178

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  • DOI: https://doi.org/10.1007/BF03054178

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