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Research Papers: Conduction

# Steady-Periodic Heating of a Cylinder

[+] Author and Article Information
Kevin D. Cole

Department of Mechanical Engineering, University of Nebraska, Lincoln, NE 68588-0656kcole1@unl.edu

Paul E. Crittenden

Department of Mathematics, Jacksonville University, Jacksonville, FL 32211pcritte@ju.edu

J. Heat Transfer 131(9), 091301 (Jun 22, 2009) (7 pages) doi:10.1115/1.3139107 History: Received May 28, 2008; Revised March 26, 2009; Published June 22, 2009

## Abstract

Steady periodic heating is an important experimental technique for measurement of thermal properties. In these methods the thermal properties are deduced from a systematic comparison between the data (such as temperature) and a detailed thermal model. This paper addresses steady-periodic heat transfer on cylindrical geometries with application to thermal-property measurements. The method of Green's functions is used to provide a comprehensive collection of exact analytical expressions for temperature in cylinders. Five kinds of boundary conditions are treated for one-, two-, and three-dimensional geometries. For some geometries an alternate form of the Green's function is given, which can be used for improvement of series convergence and for checking purposes to produce highly accurate numerical values. Numerical examples are given.

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## Figures

Figure 1

Effect of varying convection on the amplitude and phase of the temperature in a cylinder of aspect ratio b/L=0.5. The cylinder is heated at z=0 and cooled by convection at r/b=1 and z/L=1. The heating frequency is fixed at ωb2/α=1.0 and the boundary convection is given by hb/k=0.2, 1.0, and 5.0 for the top, middle, and bottom of the figure, respectively.

Figure 2

Fin effectiveness in the pin fin heated at the base (z=0) as a function of Biot number and dimensionless frequency ωb2/α for aspect ratios b/L=0.1, 0.5, and 1.0

Figure 3

Amplitude and phase of the temperature around the circumference of a cylinder (r=b, z=L/2) for several values of the (dimensionless) heating frequency. The cylinder surface is heated steady periodically over a small strip 0<ϕ<0.2 and the convection on the curved surface is characterized by B2=1.

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