Unified Hybrid Theoretical Analysis of Nonlinear Convective Heat Transfer

Abstract

The Generalized Integral Transform Technique (GITT) is extended and unified to handle a wide class of nonlinear convective heat and mass transfer formulations that involve nonlinearities in every each equation and boundary condition coefficients and source terms. The proposed hybrid numerical-analytical approach is applicable to both steady and transient situations, and the integral transformation process is promoted so as to yield an explicit transformed system, which can be more efficiently handled by the well-known numerical algorithms for initial value problems. An application of laminar forced convection in duct flow with temperature dependent thermophysical properties is considered more closely to illustrate the formal solution.

Modeling and hybrid simulation of slow discharge process of adsorbed methane tanks

“…(1) so as to incorporate all of the nonlinear terms in the right-hand side of the energy equation, thus leaving the transient operator available for exact integral transformation, which avoids an implicit transformed system that would require matrix inversion for each step of the numerical integration of the transformed ODE system [26]. Since the adsorbed phase concentration, q, can be rewritten as a function of temperature and pressure, its derivative can be rewritten as:…”

“…An implicit filtering procedure is devised to completely eliminate the transient operator from the boundary condition with thermal capacitance, relaxing the need for employing other more cumbersome convergence acceleration techniques. Also, in order to avoid a coupled coefficients matrix in the transient operator of the transformed energy equation, all the nonlinearities of the problem are moved into the general source term [26,27], which also includes the heat of adsorption and compressibility effects. The solution procedure was entirely developed in the Mathematica v. 5.2 system [28], including all of the symbolic computation steps required by the hybrid solution implemented.…”

Experiments and Simulations of Laminar Forced Convection With Water–Alumina Nanofluids in Circular Tubes

“…This problem has a strong practical motivation [26], with a renewed interest due to more recent applications in forced convection with nanofluids. The related energy equation and inlet and boundary conditions are written as [19,25]:…”

“…All the theoretical work was performed by making use of mixed symbolic-numerical computation via the Mathematica 7.0 platform [21], and a hybrid numerical-analytical methodology with automatic error control, the generalized integral transform technique (GITT) [22][23][24][25], in handling the governing nonlinear partial differential equations. Experimental work was also undertaken through a built and tested thermohydraulic circuit, and sample results are briefly discussed and presented to verify the proposed model and available correlations for heat transfer coefficients in laminar tube flow.…”

Nonlinear eigenvalue problem in the integral transforms solution of convection-diffusion with nonlinear boundary conditions

“…In this context, the hybrid numerical-analytical solution of nonlinear diffusion problems through integral transforms has been proposed back in 1990 (Cotta, 1990), by extending the ideas in the so called generalized integral transform technique (GITT), as reviewed and compiled in different sources since then (Cotta, 1990(Cotta, , 1993(Cotta, , 1994(Cotta, , 1998Mikhailov, 1997, 2006). The main idea behind the application of the GITT to nonlinear problems (Cotta, 1990), afterwards progressively extended to various classes of problems with nonlinear coefficients including the boundary layer and 768 HFF 26,3/4 Navier-Stokes equations Cotta, 1990, 1992;Cotta and Serfaty, 1991;Leiroz and Cotta, 1993;Ribeiro and Cotta, 1995;Cotta and Ramos, 1998;Machado and Cotta, 1999;Leal et al, 2000;Macedo et al, 2000;Alves et al, 2001;Cotta et al, 2007;Pontedeiro et al, 2007), is to first of all rewrite the problem formulation, grouping all of the nonlinear information on the equation and boundary conditions operators, into the corresponding source terms within the domain or at the boundary surfaces. Then, the problem is reinterpreted as one of linear differential operators but with nonlinear sources, which naturally leads to a choice of basis for the eigenfunction expansions through the characteristic linear coefficients that were adopted to reformulate the problem.…”