Series solutions for a nonlinear model of combined convective and radiative cooling of a spherical body

The homotopy analysis method and the Liénard equation

“…Liao [15,16] has developed this purely analytic technique to solve nonlinear problems in science and engineering. The HAM has been applied successfully to many nonlinear problems such as free oscillations of self-excited systems [17], the generalized Hirota-Satsuma coupled KdV equation [18], heat radiation [19], finding the root of nonlinear equations [20], finding solitary-wave solutions for the fifth-order KdV equation [21], finding solitary wave solutions for the Kuramoto-Sivashinsky equation [22], finding the solitary solutions for the Fitzhugh-Nagumo equation [23], boundary-layer flows over an impermeable stretched plate [24], unsteady boundarylayer flows over a stretching flat plate [25], exponentially decaying boundary layers [26], a nonlinear model of combined convective and radiative cooling of a spherical body [27], and many other problems (see [28,29,30,31,32,33,34,35,36], for example).…”

Finding the one‐loop soliton solution of the short‐pulse equation by means of the homotopy analysis method

“…Setting H[φ(τ ; p), A(p)] = 0, we have the zero-order deformation equation 12) subject to the boundary conditions…”

“…Recently, a powerful analytic method for nonlinear problems, the so-called homotopy analysis method (HAM), has been developed by Liao [1]. The HAM has been applied successfully to many nonlinear problems in engineering and science, such as applications in heat transfer [2], solving the generalized Hirota-Satsuma coupled KdV equation [3], in heat radiation [4], finding solitary-wave solutions for the fifthorder KdV equation [5], finding the solutions of generalized Benjamin-Bona-Mahony equation [6], finding the root of nonlinear equations [7], finding the solitary-wave solutions for the Fitzhugh-Nagumo equation [8], boundary-layer flows over an impermeable stretched plate [9], unsteady boundary-layer flows over a stretching flat plate [10], exponentially decaying boundary layers [11], a nonlinear model of combined convective and radiative cooling of a spherical body [12], and many other problems (see [13][14][15][16][17][18][19][20][21][22][23][24][25][26], for example).…”

Numerical investigation of CO2 emission and thermal stability of a convective and radiative stockpile of reactive material in a cylindrical pipe

“…16 The process involves highly nonlinear interaction of reacting species with products' diffusion and heat conduction which ultimately bring about reactants, products, and temperature gradients that are steep in nature. 17 Detailed reviews of models that involve chemical kinetics for reactions of hydrocarbons with oxygen are outlined in Simmie.…”