Chapter 4, Problem 4.83P

To determine which parts of a spider’s brain are triggered into neural activity in response to various optical stimuli, researchers at the University of Massachusetts Amherst desire to examine the brain as it is shown images that might evoke emotions such as fear or hunger. Consider a spider at $T_i=20°C$ that is shown a frightful scene and is then immediately immersed in liquid nitrogen at $T_{\infty }=77K$. The brain is subsequently dissected in its frozen state and analyzed to determine which parts of the brain reacted to the stimulus. Using your knowledge of heat transfer, determine how much time elapses before the spider’s brain begins to freeze. Assume the brain is a sphere of diameter $D_b=1mm$, centrally located in the spider’s cephalothorax, which may be approximated as a spherical shell of diameter $D_c=3mm$. The brain and cephalothorax properties correspond to those of liquid water. Neglect the effects of the latent heat of fusion and assume the heat transfer coefficient is $h=100W/m^2\cdot K$.