Transport phenomena in biological systems. Buy, rent or sell. Latest comments. Category Unclassified Search form. Display RSS link. From Equations Integrating Equation S For steady conduction for a spherical surface of radius R, Equation Integrating equation S T" R S T" S For this problem, assume unsteady conduction in a tissue of thickness 2L. While specific thermal diffusivities for tissue are not provided in Table So, one would expect uniform temperatures in well perfused tissues.
Note: The phase change during freezing is discussed in Section The rate of growth of the ice front is dX dt. X is given by Equation S t S Values of C are tabulated in Table This problem is a modification of the problem presented in Example 6. Thus, Equation 6. The vapor flux is given by Equation The quantity xa can be expressed as xHxs, where xH is the relative humidity.
Using the data for Problem The diffusivity of water in air is provided in the text, p. The error can be computed from the ratio of Equations Thus, Equation Since the enthalpy of vaporization is a function of temperature, application of Equation That is, the enthalpy of vaporization is updated, once the temperature at the air-sweat interface is calculated.
The flux for the 8. When R k equals to 20, the result given by Brinkman equation is only 9. Assume the flow is unidirectional. The solution of Equation S8.
Therefore, the velocity is unidirectional along the radial direction. In this case, the spherical coordinate system is used, in which Equations 8. The infusion rate can be obtained by integrating the velocity at the surface of the fluid cavity. Substituting Equations S8. The dependence of h on t is still the same, i.
Using Equations 8. From Problem 8. Substituting Equation S8. In this case, the decrease in Kchannel is due to both the reduction in h and the consolidation of the extracellular matrix.
If k is fixed at k0, the decrease in Kchannel is caused only by the reduction in h. We also assume that the tissue is infinitely large in the x-direction since its dimension is much larger than the thickness of the membrane. For the spherical implant, it is more convenient to use spherical coordinates.
The diffusion is only in the radial direction. Similar to Problem 8. To simplify, assume that the extracellular matrix is highly compressible compared with the intracellular volume.
Therefore, the normal forces generated by elastic compression of the fibers are negligible compared to the pressure generated within the porous layer. Without this assumption, the problem can still be solved, but it is too difficult for most undergraduate students. The total force on the cell membrane F is in the z direction. The result is Equation 8. From Equation 9. The thickness of a membrane is very small.
As a result, the transport of the solute can reach steady state rapidly. The boundary conditions for Equation S9. In each pore, the diffusion flux of the solute is S9. For fiber matrix materials, G is determined by Equation 8.
In this case, the flow in the cleft is semiunidirectional, i. The press gradient should also be calculated along the route of the cleft. Therefore, S9. In a spherical system, Equation 8. Solve Equation S9. The fluorescence intensity is a linear function of the amount of the solute.
Thus, the flow rate of the solute across the vessel wall is approximately, S9. For a fixed concentration of B, tripling the concentration of A causes a nine-fold increase in rate. For a fixed concentration of A, doubling the concentration of B causes a four-fold increase in rate. Therefore, the rate is proportional to the square of the NO concentration. When the oxygen concentration is reduced by a factor of 4. Thus the rate is first order in O2.
Equation Substituting this expression into Equation S Transport Phenomena in Biological Systems. Read more. Transport Phenomena, 2nd Edition. Modern Physics Instructors Solutions Manual. Instructors Solutions Manual to Abstract Algebra. Transport Phenomena in Metallurgy. Modelling in Transport Phenomena. Transport Phenomena. Advances in Transport Phenomena: Special Topics in Transport Phenomena.
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