Particletransport in hydraulically and thermally developing laminar fluid flowin a smooth pipe/poreis of fundamental and practical interest. To address this problem,as astarting point, an improved approximation of the Siegel’s cubic axial velocity profile for developing, isothermal, incompressible, steady laminar flow of a Newtonian fluid is derived. The computed velocity profiles at different radial and axial positions are compared with the experimentallyand numerically obtaineddata. These clearly demonstrate the envisaged asymptotic improvement. This velocity distribution is used for solving the energy equation by the integral method. For this purpose,aconstant heat flux boundary condition is adopted onthesurface ofthe considered smooth pipeor pore. Based on the obtained developing temperature profile the expressions forlocal Nusselt number are obtained for different Prandlt numbers (≥ 1 or <1) and the results are compared with numerical and correlations based datafor simultaneously developing laminarfluidflow.Subsequently, the obtained velocity and temperature profiles are employed for computing the particle trajectory. In these investigations the effect of applied heating on the circumference of a pore wherein an isolatedparticle is transported with a fluid is analyzed. The results demonstrate that the applied heating will help in mitigating the deposition under the action of an external thermophoretic force.Key-words: Laminar pipe flow, Integral method, Heat transfer in developing laminar pipe flow.