Question

Establish a heat transfer model for a swimmer in the ocean to estimate the limiting
time-duration the swimmer may survive (heart temperature > 30ºC). Assume that
(1) swimming in a turbulent ocean flow, (2) heat generation by food and body-
movement as a given function of time and (3) heat conductivity inside body is a
given function of location and time. Note that, for a human body, Bi >>1. Ocean
temperature is a constant but much lower than body temperature of survival.

Answer 1

The assumptions for the model are, Heat generation is uniform throughout the body due to metabolism and body movement, but it is a function of time. Flow of water in ocean is turbulent. Heat conductivity inside the body is a function of location and time. Since the Biot number for the human body is greater than 1, lumped system analysis cannot be ncorporated. Consider the human body as a cylindrical shape as shown in the figure below, and the heat transfer for a cylindrical body is constant along the length and varies in radial direction. 94 Figure (I) Write the expression for the balance of energy in r direction

4. +@darHa + {ρ(ddyjepr) or ot a dT Here, q is the heat generation per unit volume, q, is the heat transfer at r, qrdr is the heat transfer at (r+dr), k is the thermal conductivity, ρ is the density of the body, cp Is the specific heat of the body Further solve the above equation. ot OT ot OT ot Hence, the heat transfer model for the swimmer is +