Natural convection from a vertical surface covered with hair

Heat transfer through a vertical skin surface covered with perpendicular hair strands of uniform density is investigated numerically. The heat transfer rate is the result of (1) direct heat transfer to the air that makes contact with the skin and (2) the heat conducted by each strand away from the skin. The hair strand and its surrounding air are not in local thermal equilibrium. Hair strands have the desirable effect of slowing the air that sweeps the vertical surface and the undesirable effect of acting as fins, thereby augmenting the overall heat transfer rate. Two distinct air flow models are considered: the Darcy model and the Forchheimer-Brinkman extended Darcy model. The overall heat transfer charts reported in this paper show that heat transfer rate can greatly exceed the estimate based on the traditional homogeneous porous medium model. By means of numerical examples, the Darcy model is shown to be adequate for modeling air flow through mammal hair.