Abstract—Present work deals with the analytical solution of unsteady state one-dimensional heat conduction problems. An improved lumped parameter model has been adopted to predict the variation of temperature field in a long slab and cylinder. Polynomial approximation method is used to solve the transient conduction equations for both the slab and tube geometry. A variety of models including boundary heat flux for both slabs and tube and, heat generation in both slab and tube has been analyzed. Furthermore, for both slab and cylindrical geometry, a number of guess temperature profiles have been assumed to obtain a generalized solution. Based on the analysis, a modified Biot number has been proposed that predicts the temperature variation irrespective of 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 has been compared with earlier numerical and analytical results. A good agreement has been obtained between the present prediction and the available results.

Index Terms—Lumped model, Polynomial approximation method, Transient, Conduction, Modified biot number.

Cite: Devanshu Prasad, "Analysis of Transient Heat Conduction in Different Geometries by Polynomial Approximation Method," International Journal of Mechanical Engineering and Robotics Research, Vol. 2, No. 2, pp. 69-79, April 2013.