It is a well-known physiological phenomenon that some materials feel cooler to the touch than others. This is important in the design of instruments for the use of operators, especially in a space station. Experiments conducted at NASA have shown that different materials, e.g., aluminum and plastic, though in identical size and temperature feel very different to the touch. Consider two plates, one made of aluminum and the other of plastic, each at an initial temperature of 25°C. Determine which of the two will feel hotter to the touch of your finger if it is initially at 32°C. Assume that your finger has a density of 1000 kg/m3, specific heat of 4180 J/(kg K), and thermal conductivity of 0.625 W/(m K). Also, properties of aluminum are given in and plastic is considered to have a density

Question

of 1990 kg/m3, specific heat of 1470 J/(kg K), and thermal conductivity of 0.21 W/(m K).



GIVEN



FIND

which of the aluminum or plastic feel hotter to touch to your finger.

ASSUMPTIONS

constant thermal properties

Negligible contact resistance

The finger and plate behave as semi infinite solid.

SKETCH

Answer 1

for change in surface temperature.



For plastic plate heat flux is given by



For finger heat flux is given by



Equilibrium surface temperature is attained when



Solving the above equation for Ts substituting ?=k/?c we get



Substituting the properties for plastic and hand given above we get



Similarly for Aluminum plate when touched by hand the surface temperature is



Thus plastic will feel hotter than Aluminum when touched with finger after a while.