The heat transport at microscale is vital important in the field of micro-technology. In this paper heat transport in a two-dimensional thin plate based on single-phase-lagging (SPL) heat conduction model is investigated. The solution was obtained with the help of superposition techniques and solution structure theorem. The effect of internal heat source on temperature profile is studied by utilizing the solution structure theorem. The whole analysis is presented in dimensionless form. A

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... al example of particular interest has been studied and discussed in details. KEYWORDS-SPL heat conduction model, superposition technique, solution structure theorem, internal heat source 1. INTRODUCTION Cattaneo [1] and Vernotte [2] removed the deficiency [3]-[6] occurs in the classical heat conduction equation based on Fourier's law and independently proposed a modified version of heat conduction equation by adding a relaxation term to represent the lagging behavior of energy transport within the solid, which takes the form q kT t        q q   1 where k is the thermal conductivity of medium and q  is a material property called the relaxation time. This model characterizes the combined diffusion and wave like behavior of heat conduction and predicts a finite speed 1 2 b q k c c         2 for heat propagation [7], where  is the density and b c is the specific heat capacity. This model addresses short time scale effects over a spatial macroscale. Detailed reviews of thermal relaxation in wave theory of heat propagation were performed by Joseph and Preziosi [8], and Ozisik and Tzou [9]. The natural extension of CV model is (,) (,) q t k T t      q r r   3 which is called the single-phase-lagging (SPL) heat conduction model [10]-[14]. According to SPL heat conduction model, there is a finite built-up time q  for onset of heat flux at r , after a temperature gradient is imposed there i.e. q  represents the time lag needed to establish the heat flux (the result) when a temperature gradient (the cause) is suddenly imposed. Due to the complexity of the SPL model, the exact solution can be obtained only for specific initial and boundary conditions. The most popular solution methodology has resorted to either finite-difference or finite-element methods. Only a few simple cases can be solved analytically. In the literature most popular analytical solutions are the method of Laplace transformation [15], Fourier solution technique [16], Green's function solution [17], and the integral equation method by Wu [18] for the solution of the hyperbolic heat conduction equation. Recently, Lam and Fong [19] and Lam [20] conducted studies by employing the superposition technique along with solution structure theorems for the analysis of the CV hyperbolic heat conduction equation and one dimensional generalized heat conduction model. The temperature profile inside a one-dimensional