ANALYSIS OF TRANSIENT HEAT CONDUCTION OF MULTIDIMENSIONAL IN CYLINDRICAL SHAPE
Keywords:
lumped model, method of separation of variables, polynomial approximation method, transient, conduction and modified biot number.Abstract
Present work deals with the analytical solution of unsteady state 1D, 2D & 3D dimensional heat conduction and temperature variation problems. The method of separation variable has been adopted to predict the variation of temperature in long cylindrical shape bar. The method of separation of variables to solve the transient conduction equations for the cylindrical geometry. A variety of models including a number of guess temperature profiles have been assumed to obtain a generalized solution. Based on the analysis, a modified Biot number and Fourier number has been proposed that predicts the temperature variation irrespective the geometry of the problem. In all the cases, a closed form solution is obtained between temperature, Biot number, heat source parameter and time. The result of the present analysis by analytical solution (method of separation variable) has been compared by using Matlab software. A good agreement has been obtained between the present analysis and the available data.
