Heat transfer processes are prominent in engineering due to several applications in industry and environment. Heat transfer is central to the performance of propulsion systems, design of conventional space and water heating systems, cooling of electronic equipment, and many manufacturing processes (Campos 3).

Unsteady state conduction is the class of heat transfer in which the temperature of the conducting medium varies with time and position. This occurs frequently in industrial processes, especially food preservation and sterilization, where the temperature of the food or of the heating or cooling medium constantly changes (Farid2).

The work reported here involves the investigation of unsteady state heat transfer in two cylindrical rods and the conformity of experimental results to different methods of theoretical analysis. Aluminum and Plexiglas cylinders were used. Thermocouples were placed at different radial and axial positions, and the cylinders, which were in thermal equilibrium with an ice bath, were placed in a warm water bath at 370C. Temperature profiles were obtained using a data acquisition system on a computer.

Theory

The applicable form of the heat transfer equation for conduction in solids is given by (Welty1):

ρcp∂T∂t=∇∙k∇T+q (1)

If the thermal conductivity is constant and the conducting medium contains no heat sources, Equation 1 reduces to Fourier’s second law of heat conduction (Welty1):

∂T∂t=α∇2T (2)

Where α = (k/ρcp). Equation 2 can be written in cylindrical coordinates as (Welty1):

∂T∂t=α∂2T∂r2+1r∂T∂r+1r2∂2T∂θ2+∂2T∂z2 (3)

Assuming that no heat transfer occurs in the axial position, and temperature varies with radial position and time only,

∂2T∂θ2=∂2T∂z2=0 (4)

References: 1. Welty, James R., Charles E. Wicks, Robert Wilson, and Gregory L. Rorrer. Fundamentals of Momentum, Heat, and Mass Transfer. New York: Wiley, 2001. Print.