Preface. 1 Introduction. 1.1 Importance of Heat Transfer. 1.2 Heat Transfer Modes. 1.3 The Laws of Heat Transfer. 1.4 Formulation of Heat Transfer Problems. 1.4.1 Heat transfer from a plate exposed to solar heat flux. 1.4.2 Incandescent lamp. 1.4.3 Systems with a relative motion and internal heat generation. 1.5 Heat Conduction Equation. 1.6 Boundary and Initial Conditions. 1.7 Solution Methodology. 1.8 Summary. 1.9 Exercise. Bibliography. 2 Some Basic Discrete Systems. 2.1 Introduction. 2.2 Steady State Problems. 2.2.1 Heat flow in a composite slab. 2.2.2 Fluid flow network. 2.2.3 Heat transfer in heat sinks (combined conduction-convection). 2.2.4 Analysis of a heat exchanger. 2.3 Transient Heat Transfer Problem (Propagation Problem). 2.4 Summary. 2.5 Exercise. Bibliography. 3 The Finite Elemen t Method. 3.1 Introduction. 3.2 Elements and Shape Functions. 3.2.1 One-dimensional linear element. 3.2.2 One-dimensional quadratic element. 3.2.3 Two-dimensional linear triangular elements. 3.2.4 Area coordinates. 3.2.5 Quadratic triangular elements. 3.2.6 Two-dimensional quadrilateral elements. 3.2.7 Isoparametric elements. 3.2.8 Three-dimensional elements. 3.3 Formulation (Element Characteristics). 3.3.1 Ritz method (Heat balance integral method-Goodman's method). 3.3.2 Rayleigh-Ritz method (Variational method). 3.3.3 The method of weighted residuals. 3.3.4 Galerkin finite element method. 3.4 Formulation for the Heat Conduction Equation. 3.4.1 Variational approach. 3.4.2 The Galerkin method. 3.5 Requirements for Interpolation Functions. 3.6 Summary. 3.7 Exercise. Bibliography. 4 Steady State Heat Conduction in One Dimension. 4.1 Introduction. 4.2 Plane Walls. 4.2.1 Homogeneous wall. 4.2.2 Composite wall. 4.2.3 Finite element discretization. 4.2.4 Wall with varying cross-sectional area. 4.2.5 Plane wall with a heat source: solution by linear elements. 4.2.6 Plane wall with a heat source: solution by quadratic elements. 4.2.7 Plane wall with a heat source: solution by modified quadratic equations (static condensation). 4.3 Radial Heat Flow in a Cylinder. 4.3.1 Cylinder with heat source. 4.4 Conduction-Convection Systems. 4.5 Summary. 4.6 Exercise. Bibliography. 5 Steady State Heat Conduction in Multi-dimensions. 5.1 Introduction. 5.2 Two-dimensional Plane Problems. 5.2.1 Triangular elements. 5.3 Rectangular Elements. 5.4 Plate with Variable Thickness. 5.5 Three-dimensional Problems. 5.6 Axisymmetric Problems. 5.6.1 Galerkin's method for linear triangular axisymmetric elements. 5.7 Summary. 5.8 Exercise. Bibliography. 6 Transient Heat Conduction Analysis. 6.1 Introduction. 6.2 Lumped Heat Capacity System. 6.3 Numerical Solution. 6.3.1 Transient governing equations and boundary and initial conditions. 6.3.2 The Galerkin method. 6.4 One-dimensional Transient State Problem. 6.4.1 Time discretization using the Finite Difference Method (FDM). 6.4.2 Time discretization using the Finite Element Method (FEM). 6.5 Stability. 6.6 Multi-dimensional Transient Heat Conduction. 6.7 Phase Change Problems-Solidification and Melting. 6.7.1 The governing equations. 6.7.2 Enthalpy formulation. 6.8 Inverse Heat Conduction Problems. 6.8.1 One-dimensional heat conduction. 6.9 Summary. 6.10 Exercise. Bibliography. 7 Convection Heat Transfer 173 7.1 Introduction. 7.1.1 Types of fluid-motion-assisted heat transport. 7.2 Navier-Stokes Equations. 7.2.1 Conservation of mass or continuity equation. 7.2.2 Conservation of momentum. 7.2.3 Energy equation. 7.3 Non-dimensional Form of the Governing Equations. 7.3.1 Forced convection. 7.3.2 Natural convection (Buoyancy-driven convection). 7.3.3 Mixed convection. 7.4 The Transient Convection-diffusion Problem. 7.4.1 Finite element solution to convection-diffusion equation. 7.4.2 Extension to multi-dimensions. 7.5 Stability Conditions. 7.6 Characteristic-based Split (CBS) Scheme. 7.6.1 Spatial discretization. 7.6.2 Time-step calculation. 7.6.3 Boundary and initial conditions. 7.6.4 Steady and transient solution methods. 7.7 Artificial Compressibility Scheme. 7.8 Nusselt Number, Drag and Stream Function. 7.8.1 Nusselt number. 7.8.2 Drag calculation. 7.8.3 Stream function. 7.9 Mesh Convergence. 7.10 Laminar Isothermal Flow. 7.10.1 Geometry, boundary and initial conditions. 7.10.2 Solution. 7.11 Laminar Non-isothermal Flow. 7.11.1 Forced convection heat transfer. 7.11.2 Buoyancy-driven convection heat transfer. 7.11.3 Mixed convection heat transfer. 7.12 Introduction to Turbulent Flow. 7.12.1 Solution procedure and result. 7.13 Extension to Axisymmetric Problems. 7.14 Summary. 7.15 Exercise. Bibliography. 8 Convection in Porous Media. 8.1 Introduction. 8.2 Generalized Porous Medium Flow Approach. 8.2.1 Non-dimensional scales. 8.2.2 Limiting cases. 8.3 Discretization Procedure. 8.3.1 Temporal discretization. 8.3.2 Spatial discretization. 8.3.3 Semi- and quasi-implicit forms. 8.4 Non-isothermal Flows. 8.5 Forced Convection. 8.6 Natural Convection. 8.6.1 Constant porosity medium. 8.7 Summary. 8.8 Exercise. Bibliography. 9 Some Examples of Fluid Flow and Heat Transfer Problems. 9.1 Introduction. 9.2 Isothermal Flow Problems. 9.2.1 Steady state problems. 9.2.2 Transient flow. 9.3 Non-isothermal Benchmark Flow Problem. 9.3.1 Backward-facing step. 9.4 Thermal Conduction in an Electronic Package. 9.5 Forced Convection Heat Transfer From Heat Sources. 9.6 Summary. 9.7 Exercise. Bibliography. 10 Implementation of Computer Code. 10.1 Introduction. 10.2 Preprocessing. 10.2.1 Mesh generation. 10.2.2 Linear triangular element data. 10.2.3 Element size calculation. 10.2.4 Shape functions and their derivatives. 10.2.5 Boundary normal calculation. 10.2.6 Mass matrix and mass lumping. 10.2.7 Implicit pressure or heat conduction matrix. 10.3 Main Unit. 10.3.1 Time-step calculation. 10.3.2 Element loop and assembly. 10.3.3 Updating solution. 10.3.4 Boundary conditions. 10.3.5 Monitoring steady state. 10.4 Postprocessing. 10.4.1 Interpolation of data. 10.5 Summary. Bibliography. A Green's Lemma. B Integration Formulae. B.1 Linear Triangles. B.2 Linear Tetrahedron. C Finite Element Assembly Procedure. D Simplified Form of the Navier-Stokes Equations. Index.

Fundamentals of the Finite Element Method for Heat and Fluid Flow

Variable-density flow and transport in porous media: approaches and challenges

With the ever increasing demand for energy to meet the needs of growth in population and improvement in the living standards in particular in developing countries, the abundant unconventional oil reserves (about 70% of total world oil), such as heavy oil, oil/tar sands and shale oil, are playing an increasingly important role in securing global energy supply. Compared with the conventional reserves unconventional oil reserves are characterized by extremely high viscosity and density, combined with complex chemistry. As a result, petroleum production from unconventional oil reserves is much more difficult and costly with more serious environmental impacts. As a key underpinning science, understanding the interfacial phenomena involved in unconventional petroleum production, such as oil liberation from host rocks, oil–water emulsions and demulsification, is critical for developing novel processes to improve oil production while reducing GHG emission and other environmental impacts at a lower operating cost. In the past decade, significant efforts and advances have been made in applying the principles of interfacial sciences to better understand complex unconventional oil-systems, while many environmental and production challenges remain. In this critical review, the recent research findings and progress in the interfacial sciences related to unconventional petroleum production are critically reviewed. In particular, the chemistry of unconventional oils, liberation mechanisms of oil from host rocks and mechanisms of emulsion stability and destabilization in unconventional oil production systems are discussed in detail. This review also seeks to summarize the current state-of-the-art characterization techniques and brings forward the challenges and opportunities for future research in this important field of physical chemistry and petroleum.

Interfacial sciences in unconventional petroleum production: from fundamentals to applications

Numerical study of double-diffusive natural convection in a square cavity

Convective dissolution of CO2 in saline aquifers: Progress in modeling and experiments

Unconventional oils - mainly heavy oils, extra heavy oils and bitumens - represent a significant share of the total oil world reserves. Oil companies have expressed interest in unconventional oil as alternative resources for the energy supply. These resources are composed usually of viscous oils and, for this reason, their use requires additional efforts to guarantee the viability of the oil recovery from the reservoir and its subsequent transportation to production wells and to ports and refineries. This review describes the main properties of high-viscosity crude oils, as well as compares traditional and emergent methods for their recovery and transportation. The main characteristics of viscous oils are discussed to highlight the oil properties that affect their flowability in the processes of recovery and pipeline transportation. Chemical composition is the starting point for the oil characterization and it has major impact on other properties, including key properties for their dynamics, such as density and viscosity. Next, enhanced oil recovery (EOR) methods are presented, followed by a discussion about pipeline and transportation methods. In addition, the main challenges to achieve viable recovery and transportation of unconventional oils are compared for the different alternatives proposed. The work is especially focused on the heavy oils, while other hydrocarbon solid sources, such as oil sands and shale oil, are outside of the scope of this review.

/pdf/an-overview-of-heavy-oil-properties-and-its-recovery-and-3pe6bju9y3.pdf

An overview of heavy oil properties and its recovery and transportation methods

Natural convection with combined heat and mass transfer buoyancy effects in a porous medium

Mass and heat transfer by natural convection in a vertical slot filled with porous medium

The phenomenon of natural convection caused by combined temperature and concentration buoyancy effects is studied analytically and numerically in a rectangular slot with uniform heat and mass fluxes along the vertical sides. The analytical part is devoted to the boundary layer regime where the heat and mass transfer rates are devoted to the boundary layer regime where the heat and mass transfer rates are ruled by convection. An Oseen-linearized solution is reported for tall spaces filled with mixtures characterized by Le = 1 and arbitrary buoyancy ratios. The effect of varying the Lewis number is documented by similarity solution valid for Le > 1 in heat-transfer-driven flows, and for Le < 1 in mass-transfer-driven flows. The analytical results are validated by numerical experiments conducted in the range 1 {le} H/L {le} 4, 3.5 {times} Ra {le} 7 {times} 10{sup 6}, {minus}11 {le} n {le} 9, 1 {le} Le {le} 40, and Pr = 0.7, 7. Massline patterns are used to visualize the convective mass transfer path and the flow reversal observed when the buoyancy ratio n passes through the value {minus}1.

Combined heat and mass transfer by natural convection in a vertical enclosure

Publisher Summary The chapter describes the combined heat and mass-transfer natural convection mechanisms, which are considered an important subfield in contemporary heat and mass-transfer research. This subfield essentially brings together the studies concerned with the combined heat and mass-transfer or double-diffusive processes that are driven by buoyancy through porous media saturated with fluid. The density gradients that provide the driving buoyancy effect are induced by the combined effects of temperature and species concentration nonuniformities present in the porous medium. The chapter considers the phenomena of convection through fluid-saturated porous media generally in terms of volume-averaged quantities. There are four conservation principles considered in the study of convection with more than one buoyancy effect. These include conservation of mass, energy, species, and momentum. Heat and mass transfer in the vertical direction and in horizontal direction are discussed in detail. Another category of studies of combined buoyancy effects in porous media deals with the local fields around buried sources of heat and mass. The recent work in this field focuses on the multilayer structure of flows of the boundary-layer or concentrated-source type.

Osvair Vidal Trevisan

Papers

An overview of heavy oil properties and its recovery and transportation methods

Natural convection with combined heat and mass transfer buoyancy effects in a porous medium

Mass and heat transfer by natural convection in a vertical slot filled with porous medium

Combined heat and mass transfer by natural convection in a vertical enclosure

Combined Heat and Mass Transfer by Natural Convection in a Porous Medium