Question

3. A steady state mathematical model for the transport of a solute can be developed using the Krogh tissue model (See figure below). Each wall tissue is 0.007 mm thick having kuss=0.006 Btu hr1.1.051. The capillary is within the tissue walls, which has 0.001 mm thick layer and kop= 0.004 Btu hrl.f1.0F The surface temperature is 158°F. Calculate the steady heat transfer rate per one square millimeter between capillary and tissue. Assume steady conditions in human beings. (25 pts) Venule Arteriole Idealized capillary bed Capillary T= 158°F tissue Tissue T= 98.5 F (capillary 1.007mm 8.ool mathick 7.007mm T=158 F kp 2.000 thee ook Q = 158-98.5 IT po mm 1 304.8 mm KA KcA a. 59.5 59.5 00x300 1. 1377 Bte hrom² 73.

This is a Fluid Mechanic course. Please note that these results are possibly wrong. I would like to know how to solve the problem. Please, be clear to allow me to understand where the values came from, and if you use any value from a table or constant, make a small note beside.

Answer 1

Consider it as Hallow cylinder, inner wall temperature is given as 98.5 F and outer wall temperature i.e., tissue temperature is given as 158 F

The temperature of capillary is given so Heat transfer is taking place from outer wall to inner wall and in between we have only one thermal resistance that is tissue wall resistance.

The solution for the problem is calculated by me with hand calculations and explained clearly there. I hope you will understand my explanation.

Given data, R-10.05 mm Ktissue & Thermal conductivity of tissue = 0.006 Btu/ hr. FERF 0.01 1 0 Cepillery Conductivity of kcapillary mm & Thermal 0.01 = 0.005 = 0.004 Btu/hr Ft. F equation in care of cylinder General Heat transfer is, AT Q = Rth= lanco) 2TX RTKL (06-7; ) multiplying and dividire with Rana an ( 2 ) x 56-si) sonix In (2 ) 27 K L XC70-:) 215 KL TO - 27 K L ni 70-91 x in (A) K(Ao-Ai) This is similar Aequivalent But they have alked to find fleet transfer per in Aequident & Imm² Convert it into (feet? 1 mm = 0.003281 ft. = 0.00001076496 ft2 158 °F 1 0.035 mm = 0.000114835 ft Q = 98.5 °F

158 - 98.5 0.000114828 & Laroon; 0.006 0.00001076496 in ft" Immt equivalent erea K tissue = 0.000 0.0334662 Btu/hr Since we calculated for Imm2 area, we got the above value . a = 0.0334662 Btu/hr. mnt 0.0334662 MM Almm)