Abstract
In this paper, we study the mathematical physics model, which is an Abel-type Volterra integral equation that describes the distribution Temperature of heat along the surface when the heat transfer to it is balanced by radiation from it. We applied the adomian decomposition method (ADM) to the heat transfer Lighthill Singular integral equation and by converting it to the nonlinear singular Volterra equation of the second kind using the Maple program. The nonlinear term can easily be handled with the help of adomian polynomials. The solution takes the form of a convergent series with easily computable terms. The method is based on the application of Heat Transfer to a nonlinear Integral equation. The Pad e approximants are used effectively in the study to capture the solution's critical behavior. The method's efficiency and reliability are demonstrated by numerical examples. For a broad range of linear and nonlinear singular Integral equations, the approach is very effective and useful in finding analytical and numerical solutions. It gives you more concrete series solutions that converge quickly.