Showing papers in "Numerical Heat Transfer Part B-fundamentals in 1993"
TL;DR: The finite volume method has been shown to effectively predict radiant exchange in geometrically simple enclosures where the medium is gray, absorbing, emitting, and scattering as mentioned in this paper, and it has been used to predict radiant heat transfer on the same mesh employed to solve the equations of fluid motion.
Abstract: The finite-volume method has been shown to effectively predict radiant exchange in geometrically simple enclosures where the medium is gray, absorbing, emitting, and scattering. Cartesian and circular cylindrical meshes have always been used. The present article shows that the method applies equally well to geometrically complex enclosures where nonorthogonal, boundary-fitted meshes are used. This development permits radiant heat transfer to be computed on the same mesh employed to solve the equations of fluid motion.
594 citations
TL;DR: In this article, a discussion on the ray effect and false scattering occurring in discrete ordinates solution of the radiative transfer equation is presented, and four sample problems are used to explain these two effects.
Abstract: A discussion on the ray effect and false scattering occurring in discrete ordinates solution of the radiative transfer equation is presented in this article. Ray effect arises from the approximation of a continuously varying angular nature of radiation by a specified set of discrete angular directions. It is independent of the spatial discretization practice. False scattering, on the other hand, is a consequence of the spatial discretization practice and is independent of the angular discretization practice. In multidimensional computations, when a beam is not aligned with the grid line, false scattering smears the radiative intensity field. It reduces the appearance of unwanted bumps, but does not eliminate ray effect. An inappropriate view of false scattering is also presented. Four sample problems are used to explain these two effects.
286 citations
TL;DR: In this article, a comparison of two frequently used computational techniques for solving phase-change problems is presented, where the governing equations for the conservation of mass, momentum, and energy are solved using a control-volume-based discretization scheme.
Abstract: A comparison of two frequently used computational techniques for solving phase-change problems is presented. The governing equations for the conservation of mass, momentum, and energy are solved using a control-volume-based discretization scheme. In Ike first approach, the physical space is mapped onto a simpler domain and the moving boundary is immobilized using Landau transformation. The computations are carried out on a uniform orthogonal grid in the transformed space using the stream function-vorticity formulation. The need to retain all the terms in the governing equations arising from the transformation, for an accurate simulation, is investigated. Simplifications in the governing equations have been used in the literature and are discussed. Both implicit and explicit methods are used to track the phase front. In the second approach, the computations are carried out on a uniform fixed grid in the physical space with primitive variables. The enthalpy-porosity formulation, with appropriate so...
130 citations
TL;DR: In this article, a high-resolution discretization scheme is proposed for the calculation of incompressible steady-state convective flow with finite-volume methods, which combines a second-and third-order interpolation profile applied in the context of the normalized variable formulation (NVF).
Abstract: A high-resolution (HR) discretization scheme is proposed for the calculation of incompressible steady-state convective flow with finite-volume methods. The basic algorithm combines a second- and third-order interpolation profile applied in the context of the normalized variable formulation (NVF). The new scheme is tested by solving three problems: (1) a two-dimensional pure convection of a scalar involving a step profile in an oblique velocity field; (2) a two-dimensional pure convection of a scalar involving an elliptic profile in an oblique velocity field; (3) the Smith-Hutton [1] problem involving pure convection of a step profile in a rotational velocity field. The computational results obtained are compared with the results of six HR schemes: Leonard's EVLER scheme, Gaskell and Lau's SMART scheme, Van Leer's CLAM and MUSCL schemes, Chakravarthy and Osher's OSHLR scheme, Roe's M1NMOD scheme, and the exact solution. The results for the new scheme, STOIC demonstrate its capability in capturing ...
116 citations
TL;DR: In this article, a finite element model capable of simulating solidification of binary alloys and the formation of freckles is presented, which uses a single system of equations to deal with the all liquid region, the dendritic region, and the all solid region.
Abstract: A finite element model capable of simulating solidification of binary alloys and the formation of freckles is presented. It uses a single system of equations to deal with the all-liquid region, the dendritic region, and the all-solid region. The dendritic region is treated as an anisotropic porous medium. The algorithm uses the bilinear isoparametric element, with a penalty function approximation and a Petrov-Galerkin formulation. Numerical simulations are shown in which an NH4Cl-H2O mixture and a Pb-Sn alloy melt are cooled. The solidification process is followed in time. Instabilities in the process can be clearly observed and the final compositions obtained.
56 citations
TL;DR: In this paper, two higher-order up-wind schemes, secondorder upwind and QUICK, are examined in terms of their interpretation, implementations, as well as performance for a recirculating flow in a lid-driven cavity, in the context of a control-volume formulation using the SIMPLE algorithm.
Abstract: Two higher-order upwind schemes - second-order upwind and QUICK - are examined in terms of their interpretation, implementations, as well as performance for a recirculating flow in a lid-driven cavity, in the context of a control-volume formulation using the SIMPLE algorithm. The present formulation of these schemes is based on a unified framework wherein the first-order upwind scheme is chosen as the basis, with the remaining terms being assigned to the source term. The performance of these schemes is contrasted with the first-order upwind and second-order central difference schemes. Also addressed in this study is the issue of boundary treatment associated with these higher-order upwind schemes. Two different boundary treatments - one that uses a two-point scheme consistently within a given control volume at the boundary, and the other that maintains consistency of flux across the interior face between the adjacent control volumes - are formulated and evaluated.
53 citations
TL;DR: In this paper, the authors proposed an alternative time discretization for the apparent heat capacity method (AHCM) for heat transfer problems with phase change, which can better approximate the time derivative of enthalpy while maintaining the same form as the conventional AHCM.
Abstract: In the apparent heat capacity method (AHCM) for heat transfer problems with phase change, the conventional time discretization is subject to severe restrictions on time steps in spite of the various approximation techniques that have been developed so far. To improve the conventional AHCM we propose an alternative formulation. By introducing a nominal heat capacity, the new time discretization can better approximate the time derivative of enthalpy while maintaining the same form as the conventional AHCM. The new formulation also establishes an equivalent relation between the full enthalpy formulation and the AHCM. A one-dimensional (I-D) Stefan problem is used as a test problem, and comparison is made between the solutions of the conventional and the new AHCM formulations. It is found that for implicit schemes with large time steps, the new formulation performs much better than the conventional AHCM
53 citations
TL;DR: In this article, an approximation for the interface conductivity is developed using the Kirchhoff transformation, tested on a range of one-and two-dimensional, steady and transient phase-change problems.
Abstract: Phase-change problems often involve discontinuities in the thermal properties at the phase-change boundary. This feature needs to be handled carefully when seeking a numerical solution based on a fixed space grid. Of particular concern are discontinuities in the thermal conductivity. In the context of a control-volume finite-difference solution, the requirement is an appropriate approximation of the conductivity values at the control-volume interfaces. In this article, using the Kirchhoff transformation, an approximation for the interface conductivity is developed. The approach is tested on a range of one- and two-dimensional, steady and transient phase-change problems. In addition, a discussion on the extension of the approach to finite-element schemes is included.
52 citations
TL;DR: In this paper, the authors investigated the well-posedness of the pressure-correction equation and the proper prescription of flow variables at open boundaries, particularly if inflow occurs. And they showed that the global continuity constraint is often sufficient for the numerical problem for a flow with an open boundary to be well posed, regardless of whether or not inflow occurred at that boundary.
Abstract: Two numerical issues important to proper problem specification for pressure-based algorithms are investigated, including (1) well posedness of the pressure-correction equation, and (2) proper prescription of flow variables at open boundaries, particularly if inflow occurs. Lid-driven cavity flow and flow past a backward-facing step are used to help discuss the issues. It is shown that during each iteration, the explicit enforcement of global mass conservation is important even for the intermediate, nonconvergent flow field in order to maintain good convergence rates. This requirement stems from the fact that the pressure distribution is an outcome of the continuity equation. Furthermore, it seems that the global continuity constraint is often sufficient for the numerical problem for a flow with an open boundary to be well posed, regardless of whether or not inflow occurs at that boundary. Thus, in the pressure-based algorithm with a staggered grid the downstream boundary can, if necessary, pass through a recirculation region without adverse effects on solution accuracy.
50 citations
TL;DR: In this article, an explicit corrector step is proposed that is imposed on the first corrected velocities, which are obtained from the existing algorithms, which is tested by three flow problems, driven cavity flow, backward-facing step flow, and rectangular tank flow, with different Reynolds numbers.
Abstract: Due to an assumption made on the pressure-velocity coupling for the SIMPLE algorithm and its variants, the corrected velocity can be obtained from the corrected pressure. However, substituting these quantities into the momentum equations may result in failure to satisfy the momentum equations. Therefore, the equations should be solved iterativety to obtain better velocities, thus giving a more satisfactory solution to the equations. In this article an explicit corrector step is proposed that is imposed on the first corrected velocities, which are obtained from the existing algorithms. This new corrector step has been tested by three flow problems, driven cavity flow, backward-facing step flow, and rectangular tank flow, with different Reynolds numbers. With this additional corrector step imposed on the SIMPLEC and PISO algorithms, the results show that the number of iterations can be reduced drastically due to the much better satisfaction of the momentum equations. Considerable savings in computi...
50 citations
TL;DR: In this article, boundary integral concepts over subintervals or elements in the radial direction are used to eliminate the radial heat conduction operator, which leads to a new discretization scheme whereby the problem is reduced to a set of ordinary differential equations for the nodal temperatures and their radial gradients as a function of the axial distance.
Abstract: This article describes a new method for the numerical solution of the generalized Graetz problem. The method involves the use of boundary integral concepts over subintervals or elements in the radial direction to eliminate the radial heat conduction operator. This leads to a new discretization scheme whereby the problem is reduced to a set of ordinary differential equations for the nodal temperatures and their radial gradients as a function of the axial distance. This set of equations is then solved by axial marching using the implicit Euler method. The method yields accurate solutions both in the entry region as well as for the fully developed regions of the pipe, and an example problem of heat transfer with a constant wall temperature is used for numerical testing of the computational scheme.
TL;DR: In this paper, the numerical accuracy of the finite-volume discretization for the natural-convection flow of air in a square cavity with differentially heated vertical walls and adiabatic horizontal walls was investigated.
Abstract: This study investigates the numerical accuracy of the finite-volume discretization for the natural-convection flow of air in a square cavity with differentially heated vertical walls and adiabatic horizontal walls. The regime of high Rayleigh numbers is considered, in which the steady flow bifurcates to a periodic unsteady flow. Investigated is how the accuracy depends on (1) the numerical discretization scheme for the convective fluxes and (2) the number of grid points. The fourth-order central interpolation scheme for the convective derivative turns out to be the most accurate scheme. At least 240[sup 2] grid points are required to obtain good accuracy for the amplitude of the oscillations.
TL;DR: In this article, necessary and sufficient conditions for satisfaction of the discrete maximum principle are discussed, and special elements that satisfy a discrete maximal principle for a wider range of parameters, thereby improving the accuracy of the solution, are introduced into standard finite-element formulations for the heat conduction equation.
Abstract: Under certain conditions, usually intense surface heat transfer associated with radiation, finite-element solutions display anomalous behaviors. These behaviors have been traced to the violation of a discrete maximum principle. Here, necessary and sufficient conditions for satisfaction of the discrete maximum principle are discussed. Special elements that satisfy a discrete maximum principle for a wider range of parameters, thereby improving the accuracy of the solution, are introduced into standard finite-element formulations for the heat conduction equation. The improved performance of these elements is then demonstrated by means of a few examples.
TL;DR: In this paper, a finite-element method based on finite element discretizations was developed for calculating radiant heat transfer among diffuse-gray surfaces in an enclosure, and the method of Gebhart is compared with solutions of the rigorous integral equations using these formulations.
Abstract: Accurate formulations based on finite-element methods are developed for calculating radiant heat transfer among diffuse-gray surfaces in an enclosure. The method of Gebhart is compared with solutions of the rigorous integral equations using these formulations. A Swartz-Wendroff approximation applied to the finite-element discretizations yields higher-order-accurate analogs of view factors that depend on geometry only and can be readily employed for more accurate solution of general radiant heat transfer problems. The accuracy and efficiency of these approaches are presented in the context of a model problem representative of a high-temperature crystal growth system.
TL;DR: In this article, a finite-element formulation for coupled conduction and convection problems is obtained by a direct approach based on energy balances, at both element and node levels, for both convection and conduction problems.
Abstract: Finite-element formulations for coupled conduction and convection problems are obtained by a direct approach based on energy balances, at both element and node levels. This way, clear physical interpretations are provided for all the essential steps of conventional finite-element procedures of the Galerkin type. In the examples, the finite-element formulation is validated first by comparison with the analytical solution of a typical benchmark problem. Then the capabilities of the finite-element method are demonstrated by the analysis of coupled conduction and convection problems of practical interest
TL;DR: In this article, a numerical method for calculating two-dimensional turbulent incompressible flow on unstructured triangular meshes is developed, where a primitive variable formulation is used to enforce the velocity continuity relation.
Abstract: A numerical method for calculating two-dimensional turbulent incompressible flow on unstructured triangular meshes is developed. A primitive variable formulation is used. The Helmholtz pressure equation algorithm is used to enforce the velocity continuity relation for incompressible flow. A careful treatment of the pressure dissipation model is presented. A standard k-ϵ turbulence model with wall functions is used to provide closure for the governing equations. A backward-facing step turbulent flow is calculated using an unstructured triangular mesh and the results are compared to experimental and computational data.
TL;DR: In this article, a finite element thermal transport code is modified to include the effects of chemistry with thermally controlled kinetics, and two types of pathways for a chemical reaction in energy-temperature space: one resembles a phase change and the other resembles a burn.
Abstract: A finite-element thermal transport code is modified to include the effects of chemistry with thermally controlled kinetics There are two types of pathways for a chemical reaction in energy-temperature space: one resembles a phase change and the other resembles a burn Effective heat capacity methods are robust and stable for phase-change calculations, while heat source methods give the best results for a burn We propose an energy-conserving method that adapts to the heat release (or absorption) mechanism using either effective heat capacity or heat source ideas The method is applied to two examples: a burn and a phase change
TL;DR: The purpose of this work is to evaluate the performance and accuracy of flow calculations under different discretization schemes in the light of experimental results.
Abstract: A finite-volume calculation procedure for steady, incompressible, elliptic flows in complex geometries is presented. The methodology uses generalized body-fitted coordinates to model the shape of the boundary accurately. All variables are stored at the centroids of the elements, thus achieving simplicity and low cost of computations. Turbulence is modeled by using the standard two-equation k-e model. The purpose of this work is to evaluate the performance and accuracy of flow calculations under different discretization schemes in the light of experimental results. The discretization schemes that are incorporated in the code include the classical hybrid scheme, the third-order QUICK scheme, and a fifth-order upwind scheme. Benchmark tests are performed for laminar and turbulent flows in 90° curved ducts of square and circular cross sections. Flow solutions obtained using the classical hybrid scheme are compared with solutions obtained with the higher-order schemes. The results show that accurate s...
TL;DR: In this paper, an error and stability analysis of sequential methods for solving the linear inverse heat conduction problem is presented, where the well-known method of J.V. Beck is studied as well as modifications thereof.
Abstract: The emphasis of this article is on an error and stability analysis of sequential methods solving the linear inverse heat conduction problem. The well-known method of J.V. Beck is studied as well as modifications thereof. At the end, the authors results are discussed by means of numerical examples. The following aspects are most important in the article. A fundamental relation is established that shows how the heat fluxes determined by Beck`s method depend explicitly on the previous heat fluxes on the data. On the one hand, this presents a new way of computing the Beck method and, on the other hand, leads to various modifications of the method for which analogous relations and computational procedures are available. Moreover, for all sequential methods under consideration, and error analysis can be established.
TL;DR: It is demonstrated that by extending these high resolution shock capturing schemes to a sequential solver, the speed of signal propagation in the solution has to be coordinated by assigning the local convection speed as the characteristic speed for the whole system.
Abstract: An exploration is conducted of the applicability of such high resolution schemes as TVD to the resolving of sharp flow gradients using a sequential solution approach borrowed from pressure-based algorithms. It is shown that by extending these high-resolution shock-capturing schemes to a sequential solver that treats the equations as a collection of scalar conservation equations, the speed of signal propagation in the solution has to be coordinated by assigning the local convection speed as the characteristic speed for the entire system. A higher amount of dissipation is therefore needed to eliminate oscillations near discontinuities.
TL;DR: In this article, a heat transfer analysis for solidification problems has been conducted to evaluate the temperature field and the location of the phase change interface, and an arbitrary Lagrangian-Eulerian kinematic description has been utilized in the finite-element formulation to impart flexibility to the motion of the nodes.
Abstract: A heat transfer analysis for solidification problems has been conducted to evaluate the temperature field and the location of the phase-change interface. An arbitrary Lagrangian-Eulerian kinematic description has been utilized in the finite-element formulation to impart flexibility to the motion of the nodes. By detaching the nodal points from the underlying material, nodes can be monitored to follow the evolving front, while maintaining shapes of the elements. Special numerical techniques to smoothen the deforming front and to avoid continuous remeshing have been introduced. Numerical examples have been solved to establish the validity of the present model and its strength.
TL;DR: In this paper, a new and effective virtual-pulse (VIP) time integral methodology of computation for linear transient heat transfer analysis is proposed. But, the proposed methodology is strictly restricted to linear models and is not suitable for general heat transfer problems.
Abstract: The present article introduces a new and effective virtual-pulse (VIP) time integral methodology of computation for linear transient heat transfer analysis and serves to lay down the theoretical basis for subsequent applications to general heat transfer problems. For expository purposes, attention is purposely restricted to linear models. For this class of problems, the proposed methodology is explicit, unconditionally stable, and possesses second-order accuracy for a general heat loading situation. Unlike past approaches and ongoing practices, the methodology offers several computationally attractive yet accurate features, and, promises to be an attractive alternative for heat transfer analysts
TL;DR: In this article, a split velocity concept is introduced to eliminate the checkerboard pressure field in the arbitrary Lagrangian-Eulerian (ALE) grid system, which is corrected to account for the true pressure gradients by a simple algebraic arrangement of adjacent velocities.
Abstract: The arbitrary Lagrangian-Eulerian (ALE) grid system possesses some computational merits over the fully staggered and collocated grids in solving the fluid flow problem with primitive variables. However, severe pressure wiggle problems will occur when a standard centered difference scheme is adopted in this grid. In this article, a split velocity concept is introduced to eliminate the checkerboard pressure field in the ALE grid. In this scheme, the cell face velocities are corrected to account for the true pressure gradients by a simple algebraic arrangement of adjacent velocities. The consequence of cell face velocities is analogous to that from momentum interpolation in the collocated grid; however, the split velocities do not produce deterioration of the total mass flux in the original velocity field. Computed results are compared with other numerical predictions and available experimental data for developing channel flow, lip-driven cavity flow, sudden expansion flow, and flow over a backward-facing st...
TL;DR: The boundary element method (BEM) as discussed by the authors was proposed to solve the problem of tracking the phase front, which is a nonlinear function of the temperature distribution, by reducing the problem to a set of integral equations, which can be solved numerically using simple basis functions.
Abstract: Solutions for problems involving phase change have been attempted using a variety of techniques, including finite-difference, finite element, and approximate analytical methods. In all these methods the main difficulty is tracking the phase front, since it evolves as a nonlinear function of the temperature distribution. The objective of this article is to demonstrate the numerical advantages of the boundary element method (BEM)for this class of problems. The proposed BEM reduces the problem to a nonlinear set of integral equations for the location of the phase front. These integral equations can be solved numerically using simple basis functions for the unknown boundary data, with no need to discretize the entire domain. A general solution for multidimensional problems is proposed. The numerical accuracy and characteristics of the method are demonstrated using a one-dimensional freezing problem. It is shown that accurate, computationally efficient, and numerically stable solutions can be obtained...
TL;DR: In this paper, a boundary-dispatch Monte Carlo (Exodus) method is developed, in which the particles are dispatched from the boundaries of a conductive medium or source of heat.
Abstract: A boundary-dispatch Monte Carlo (Exodus) method, in which the particles are dispatched from the boundaries of a conductive medium or source of heat, is developed. A fixed number of particles are dispatched from a boundary node to the nearest internal node. These particles make random walks within the medium similar to that of the conventional Monte Carlo method. Once a particle visits an internal node, a number equal to the temperature of the boundary node from which particles are dispatched is added to a counter. Performing this procedure for all boundary nodes, the temperature of a node can be determined by dividing the flag, or the counter, of this node by the total number of particle visits to this node. Two versions of the boundary-dispatch method (BDM) are presented, multispecies and bispecies BDM. The results of bispecies BDM based on the Exodus dispatching method compare well with the Gauss-Seidel method in both accuracy and computational time. Its computational time is much less than the shrinkin...
TL;DR: A method that combines Anderson's grid method and a grid-point control scheme is developed in order to solve elliptic equations in a manner that simultaneously controls grid spacing and orthogonality on all of the boundaries.
Abstract: A method that combines Anderson's grid method and a grid-point control scheme is developed in order to solve elliptic equations in a manner that simultaneously controls grid spacing and orthogonality on all of the boundaries. Both the finite-difference and finite-volume methods have become increasingly important in the solving of partial differential equations. These numerical methods rely on discretization of the domain of definition, most frequently employing numerical grid generation. In order to accurately solve a problem numerically, the proper location of the nodal points of the computational domain and the orthogonal grid around the boundaries are of prime importance. While the adaptive grid method resolves physical variables by moving grid points from areas of small solution variation to regions of larger variation, it does not address problems associated with the gradient of a physical quantity normal to the boundaries. This latter factor is particularly important for friction factor or heat transfer coefficient evaluation. If orthogonality at the mesh points adjacent to the boundaries can be guaranteed, then the error induced from the treatment of the boundary conditions can be decreased. One of the most popular methods for grid generation involves solving the elliptical partial differential equation; however, the choice ofmore » control functions poses a major problem. The authors combine previous techniques in order to produce a grid generation system that gives the desired grid control over all the boundaries. The present investigation combines the adaptive grid procedure with their previously developed grid and boundary grid methods are first restated. Subsequently, several numerical tests will be employed to demonstrate the applicability of the proposed method.« less
TL;DR: In this paper, a control volume method based on generalized nonorthogonal curvilinear coordinates for the prediction of incompressible flow and related transport processes in complex geometries is presented.
Abstract: Transport processes in most engineering applications occur in complex geometries. A control volume method is presented, based on generalized nonorthogonal curvilinear coordinates for the prediction of incompressible flow and related transport processes in complex geometries, The primitive variable formulation is adopted and a staggered grid, with contravariant velocities used as the primary unknowns in the momentum equations, is utilized. A method for the discretization of the scalar transport equation, which accounts for possible discontinuities in the diffusivities, is described. A local coordinate approach is used to obtain the momentum source terms that arise due to the grid curvature. Subtle details of the discretization of the pressure gradient term in the momentum equations for nonorthogonal grids, in the presence of discontinuities in the flow resistance, are described. The SIMPLER algorithm is used for handling the velocity-pressure coupling. A discussion on the derivation and the solution of the...
TL;DR: In this article, the drying process in a fixed-bed dryer is modeled in terms of balance equations of masses and energies that result in a hyperbolic system of conservation laws with a source term.
Abstract: The drying process in a fixed-bed dryer can be modeled in terms of balance equations of masses and energies that result in a hyperbolic system of conservation laws with a source term. This system is solved numerically by an operator-splitting technique based on Strang's algorithm. A similar approach has been used before in agricultural engineering research, but the system of equations was simplified to a set of ordinary differential equations by dropping certain terms. Comparison of numerical results indicates that this commonly employed simplification has not been fully justified and should be reexamined by further research work (e.g., carefully designed experiments accompanied by appropriate computation may be needed).
TL;DR: In this article, the three-dimensional piecewise parabolic finite analytic method (PPFAM3D) with vector potential and vorticity as dependent variables was used to solve the steady 3D laminar cavity flow.
Abstract: The three-dimensional piecewise parabolic finite analytic method (PPFAM3D), with vector potential and vorticity as dependent variables, was used to solve the steady three-dimensional (3-D) laminar cavity flow. Predictions were obtained for Reynolds numbers between 100 and 2000. Results for Re = 100, 400, and 1000 are compared with those available in the literature. The overall agreement is excellent. Results are also compared with the two-dimensional PPFAM cavity flow, showing the effect of three-dimensionality on the velocity predictions at the symmetry plane. The PPFAM3D is a robust numerical algorithm requiring no relaxation to produce physically meaningful and numerically converged solutions. It is a promising tool for solving a variety of flow phenomena governed by unsteady second-order partial differential convection-diffusion equations
TL;DR: In this article, a modified version of the SIMPLE algorithm, called MAPLE (Modified Algorithm for Pressure-Linked Equations), was proposed for the pressure-velocity coupling.
Abstract: In solving multidimensional transient fluid flow and heat transfer problems, the strongly coupled conservation laws of mass, momentum, and energy require segregated iterative procedures. Derived from the SIMPLE algorithm, the fully explicit iteration scheme MAPLE (Modified Algorithm for Pressure-Linked Equations) for the pressure-velocity coupling is introduced here. A substantial speedup is gained in the iteration by utilizing hybrid relaxation, a combination of under- and overrelaxation, instead of the usual underrelaxation. Moreover, hybrid relaxation is not restricted to pressure-velocity algorithms only, but can be applied in more general iterations.