TWO DIMENSIONAL ANALYTICAL SOLUTION FOR TEMPRATURE, STRESS AND DISPLACEMENT FIELDS FOR A HOLLOW CYLINDER SUBJECT TO ASYMMETRIC AND TIME DEPENDENT HEAT FLUX

In the present paper, a two dimensional analytical solution for temperature, stress and displacement fields in a hollow cylinder is presented. An asymmetric and time dependent heat flux is exposed on the outer surface of the hollow cylinder. Moreover, the cylinder carries a fluid that transfers heat through convection on its inner surface. The separation of variable method to obtain temperature field is used. Also, stress distribution is taken by means of thermal stress function method. Afterwards, displacement components is obtained by means of stress-strain and strain-displacement relations. The cylinder is regarded as a model for the absorber tube of parabolic trough collector. Using the analytical solution together with the actual properties of the model in solar power plant in shiraz city, results are presented for a period of twelve hours from 06:00 AM until 06:00 PM. The analytical solution is employed to extract numerical results using MATLAB software package. The results are also validated with those given by FEM, conducted via ANSYS computer code. Finally, we are concluded that differences between the results of analytical solution and output of ANSYS computer code are in reason of infirmity of MATLAB software package to calculating the kelvin functions in high accuracy.