A generous amount of gel is applied to the surface of the windowof an ultrasound probe prior to its use. The window is made of apolycarbonate material of density Ï = 1200 kg/m3, thermalconductivity k = 0.2 W/m · K, and specific heat cp = 1200 J/kg · K.The probe is initially at a temperature of Ti = 20°C. To ensurethat the gel remains adhered to the probe until the probe isbrought into contact with the patient's skin, itstemperature-dependent viscosity must not fall below a criticalvalue. This corresponds to a requirement that the maximum geltemperature remain below 12°C prior to making contact with thepatient. Determine the required initial gel temperature. Thethermal conductivity, density, and specific heat of the gel may beassumed to be those of liquid water.
The correct method is to use the Surface Convection of TransientConduction (Case 3 in Theodore Bergman, Adrienne Lavine 8th edition- Page 289, Equation 5.66)
