J.N.N. Quaresma

Thermal entry region analysis through the finite integral transform technique in laminar flow of Bingham fluids within concentric annular ducts

Abstract The heat transfer characteristics of Bingham plastics fluids within concentric annular ducts are analytically studied through the classical finite integral transform technique. In the analysis of the thermal entry region, four types of boundary conditions are adopted and prescribed either at the inner or outer duct wall, and the flow is considered to be laminar and fully developed. Local Nusselt numbers are computed along the channel length with high accuracy for different values of aspect ratios and yield numbers, which are systematically tabulated and graphically presented. Comparisons with previous works in the literature are also performed for typical situations, in order to validate the numerical codes developed in this work, as well as to demonstrate that consistent results were produced.

Natural convection in three-dimensional porous cavities: integral transform method

Abstract A transient three-dimensional Darcy model of natural convection in porous medium filled cavities is studied, using a vorticity-vector potential formulation and the generalized integral transform technique (GITT). A general formulation and solution methodology for vertical cavities (insulated vertical walls with differential horizontal wall temperatures) is developed. Results for cubic cavities are presented while evaluating the Rayleigh number effects for stable situations, observing the transient evolution of the heat transfer process. The convergence behavior of the proposed eigenfunction expansion solution is investigated and comparisons with previously reported steady-state solutions are critically performed.

Unified Integral Transforms Algorithm for Solving Multidimensional Nonlinear Convection-Diffusion Problems

The present work summarizes the theory and describes the algorithm related to an open-source mixed symbolic-numerical computational code named unified integral transforms (UNIT) that provides a computational environment for finding hybrid numerical-analytical solutions of linear and nonlinear partial differential systems via integral transforms. The reported research was performed by employing the well-established methodology known as the generalized integral transform technique (GITT), together with the symbolic and numerical computation tools provided by the Mathematica system. The main purpose of this study is to illustrate the robust precision-controlled simulation of multidimensional nonlinear transient convection-diffusion problems, while providing a brief introduction of this open source implementation. Test cases are selected based on nonlinear multidimensional formulations of Burgers’ equation, with the establishment of reference results for specific numerical values of the governing parameters. Special aspects in the computational behavior of the algorithm are then discussed, demonstrating the implemented possibilities within the present version of the UNIT code, including the proposition of a progressive filtering strategy and a combined criteria reordering scheme, not previously discussed in related works, both aimed at convergence acceleration of the eigenfunction expansions.

An Analysis of Heat Conduction Models for Nanofluids

The mechanism of heat transfer intensification recently brought about by nanofluids is analyzed in this article, in the light of the non-Fourier dual-phase-lagging heat conduction model. The physical problem involves an annular geometry filled with a nanofluid, such as typically used for measurements of the thermal conductivity with Blackwells line heat source probe. The mathematical formulation for this problem is analytically solved with the classical integral transform technique, thus providing benchmark results for the temperature predicted with the dual-phase-lagging model. Different test cases are examined in this work, involving nanofluids and probe sizes of practical interest. The effects of the relaxation times on the temperature at the surface of the probe are also examined. The results obtained with the dual-phase-lagging model are critically compared to those obtained with the classical parabolic model, showing that the increase in the thermal conductivity of nanofluids measured with the line heat source probe cannot be attributed to hyperbolic effects.

Eigenfunction Expansion Solution for Boundary-Layer Equations in Cylindrical Coordinates: Simultaneously Developing Flow in Circular Tubes

The Generalized Integral Transform Technique (GITT) is employed, via a novel eigenfunction expansion, in the solution of the steady-state continuity, momentum, and energy equations under the boundary-layer formulation and cylindrical coordinates, and applied to the solution of simultaneously developing laminar flow inside circular ducts. The streamfunction formulation is adopted to automatically satisfy the continuity equation and to eliminate the pressure field. A fourth-order eigenvalue problem is thus considered for the velocity field, eliminating the difficulties associated with the singularity at the channel centerline through this recently introduced expansion basis. A thorough analysis of convergence behavior is undertaken for both the velocity and temperature proposed eigenfunction representations, and here illustrated for representative values of governing parameters and positions along the channel. Results for quantities associated with applications, such as the product of the friction factor–Reynolds number and Nusselt numbers, are also computed along the entrance region for different values of the governing parameters, and tabulated for reference purposes. Critical comparisons with previous results in the literature are also performed, in order to validate the numerical code developed and to inspect the adequacy of previously proposed approximate solutions.

Integral transforms solution for flow development in wavy wall ducts

Purpose – The purpose of this paper is to provide an analysis of two‐dimensional laminar flow in the entrance region of wavy wall ducts as obtained from the solution of the steady Navier‐Stokes equations for incompressible flow.Design/methodology/approach – The study is undertaken by application of the generalized integral transform technique in the solution of the steady Navier‐Stokes equations for incompressible flow. The streamfunction‐only formulation is adopted, and a general filtering solution that adapts to the irregular contour is proposed to enhance the convergence behavior of the eigenfunction expansion.Findings – A few representative cases are considered more closely in order to report some numerical results illustrating the eigenfunction expansions convergence behavior. The product friction factor‐Reynolds number is also computed and compared against results from discrete methods available in the literature for different Reynolds numbers and amplitudes of the wavy channel.Research limitations/...

Solutions for the internal boundary layer equations in simultaneously developing flow of power-law fluids within parallel plates channels

Abstract The generalized integral transform technique (GITT) is employed in the solution of the boundary layer equations in simultaneously developing laminar flow of power-law non-Newtonian fluids within a parallel plates channel. In the modeling of the related momentum and energy equations within the range of validity of the boundary layer equations, a streamfunction formulation is employed which offers a better computational performance than the primitive-variables formulation. Numerical results for the bulk temperature and Nusselt numbers are established at different axial positions along the channel and for various power-law indices, and critical comparisons with previously reported works in the literature are also performed.

Forced Convection Heat Transfer to Power-Law Non-Newtonian Fluids Inside Triangular Ducts

A hybrid analytical-numerical approach based on the Generalized Integral Transform Technique is employed to simulate the laminar forced convection (hydrodynamically fully developed and thermally developing laminar flow) of power-law non-Newtonian fluids inside ducts with arbitrary shaped cross-sections. The analysis is illustrated through consideration of both right angularly and isosceles triangular ducts subjected to constant wall temperature as thermal boundary condition. Reference results for quantities of practical interest such as dimensionless average temperature and Nusselt numbers within the thermal entry region were produced for different values of power-law index and apex angles. Finally, critical comparisons are performed with results available in the literature for direct numerical and approximate approaches.

INTEGRAL TRANSFORM METHOD FOR LAMINAR HEAT TRANSFER CONVECTION OF HERSCHEL-BULKLEY FLUIDS WITHIN CONCENTRIC ANNULAR DUCTS

Related momentum and energy equations describing the heat and fluid flow of Herschel-Bulkley fluids within concentric annular ducts are analytically solved using the classical integral transform technique, which permits accurate determination of parameters of practical interest in engineering such as friction factors and Nusselt numbers for the duct length. In analyzing the problem, thermally developing flow is assumed and the duct walls are subjected to boundary conditions of first kind. Results are computed for the velocity and temperature fields as well as for the parameters cited above with different power-law indices, yield numbers and aspect ratios. Comparisons are also made with previous work available in the literature, providing direct validation of the results and showing that they are consistent.

Improved lumped-differential formulations in hyperbolic heat conduction

Abstract The present work aims at applying the ideas in the so-called Coupled Integral Equations Approach (CIEA) to the one-dimensional thermal wave propagation problem in a finite solid medium, leading to improved lumped-differential formulations through Hermite-type approximations for integrals. The application of CIEA methodology makes it possible to reduce the partial differential equation governing the hyperbolic heat conduction problem to a simple system consisting of two or three ordinary differential equations for the average and surface temperatures, depending on the choice of the Hermite-type approximation. The Runge-Kuta method, enclosed in the IVPRK routine from IMSL Library [1], is used to solve the system of ordinary differential equations. Results for the average and surface temperatures are computed for different thermal relaxation times.