Question

Consider a section of muscle tissue of a cylindrical shape with a radius of 1.5 cm. During highly rigorous exercise, metabolic processes generate 15 kW/m3 of bulk tissue. The outer surface of the tissue is maintained at 37oC. The thermal conductivity of the muscle tissue is k =0.419 W/m*KDevelop a mathematical model to predict the steady-state temperature distribution, T(r), in the tissue along the radial position r. What is the temperature of the tissue at a distance of 0.75 cm from the surface?

Answer 1

Complete Question

The complete question is shown on the first uploaded image

Answer:

a)The mathematical model to predict the steady temperature distribution is

       =  $T + \frac{q^{*}r^{2}}{4k} = 312.014$

b)The mathematical model to predict the maximum temperature inside the muscle tissue is

      = $\frac{\delta T}{\delta r} = 0 \implies r = 0$

c) The heat flux leaving the muscle is

      = 1.06 W

d) The new maximum temperature within the muscle is

     = 38.59°C

Explanation:

The explanation is shown on the second, third , fourth and fifth image