A FINITE DIFFERENCE MODEL TO DETERMINE CONDUCTION HEAT LOSS TO A WATER–FILLED MATTRESS FOR DAIRY COWS

Abstract

A finite difference mathematical model was developed utilizing measured data to predict the temperature profilethrough a waterbed used in cow stalls. The model also predicts conduction heat flux from a cow lying down on the waterbed.Convection and radiation heat losses were determined from measured data. Conduction heat flux comprised 2.0 and 1.8 timesthat of convection and radiation, respectively. Because of limited contact area with the waterbed, conduction heat flowconstitutes 19% of the total heat flow and is a small fraction of convection and radiation.<br><br>Sensitivity analyses were conducted to determine effects of thermal conductivity of the surface material and fluid in thewaterbed on conduction heat loss. Increasing the surface thermal conductivity by 100% increased conduction heat loss by55%, while increasing the fluid thermal conductivity by 100% increased conduction heat loss by only 11%. Decreasing thewater temperature from 27.1.C to 10.C by cooling the water in the waterbed at rates of 10, 15, and 20 kW/m3 increasedconduction heat flux by 174%, 200%, and 226%, respectively. It may be concluded that lying on waterbeds filled with chilledwater may alleviate thermal heat stress of cows.