W. J. Minkowycz

Handbook of numerical heat transfer

A comprehensive presentation is given of virtually all numerical methods that are suitable for the analysis of the various heat transverse and fluid flow problems that occur in research, practice, and university instruction. After reviewing basic methodologies, the following topics are covered: finite difference and finite element methods for parabolic, elliptic, and hyperbolic systems; a comparative appraisal of finite difference versus finite element methods; integral and integrodifferential systems; perturbation methods; Monte Carlo methods; finite analytic methods; moving boundary problems; inverse problems; graphical display methods; grid generation methods; and programing methods for supercomputers.

Forced convection condensation in the presence of noncondensables and interfacial resistance

Abstract The effect of a noncondensable gas on condensation in a forced convection laminar boundary-layer flow is explored analytically. The analysis is first carried out in general for any arbitrary flow consisting of a vapor and a noncondensable gas, and certain universal results are obtained. Solutions of the similarity differential equations are found both numerically and by an integral method. The general formulation is applied to the steam-air system, and the heat transfer with and without the noncondensable is compared for a wide range of operating conditions. The reductions in heat transfer due to the non-condensable are accentuated at low operating pressures. In general, condensation in the forced convection flow is much less sensitive than that in a gravity flow. The effect of an interfacial resistance (i.e. a temperature jump at the liquid-vapor interface) is also examined. The computed results reveal a negligible effect on the heat transfer.

Free convection about a vertical cylinder embedded in a porous medium

Abstract An analysis is made for free convective flow about a vertical cylinder embedded in a saturated porous medium, where surface temperature of the cylinder varies as x λ , a power function of distance from the leading edge. Within the framework of boundary-layer approximations, exact solution is obtained for the special case where surface temperature varies linearly with x, i.e. λ = 1. For other values of λ, approximate solutions based on local similarity and local non-similarity models are obtained. It is found that the local similarity solutions are sufficiently accurate for all practical purposes. Analytical expressions for local surface heat flux and overall surface heat flux are obtained.

A modified form of the κ-ε model for turbulent flows of an incompressible fluid in porous media

Abstract This work extends the recently published work of Antohe and Lage on the development of a macroscopic two-equation turbulence model for an incompressible flow in porous media. The difference occurs in approximating the Forchheimer term in the time-averaged momentum equation. Unlike the Antohe and Lage’s work, where only the linear terms of the expansion are kept, in the presently proposed model we include the second-order correlation term. This inclusion gives rise to an extra term in the transport momentum equation which, in turn, gives rise to additional terms in the transport equations for the turbulent kinetic energy and the dissipation rate. The additional higher order terms produce correlation coefficients that are used to absorb any departure from the clear flow when expressing the two-equation turbulence model for incompressible flow in a porous medium.

MIXED CONVECTION ABOUT A NONISOTHERMAL CYLINDER AND SPHERE IN A POROUS MEDIUM

The problems of mixed convection about a nonisothermai horizontal cytiner and sphere embedded in a porous medium are analyzed based on a curvilinear orthogonal coordinate system together with boundary-layer simplifications. Different transformations were performed for the horizontal cylinder and the sphere, and the resulting equations are identical for the two geometries. Approximate solutions for the problems are obtained based on the nonlocal similarity method. Numerical computations for the temperature distribution and heat flux were carried out up to the third level of truncation. The effects of buoyancy and wall temperature variations on heat transfer characteristics about a heated horizontal cylinder and sphere in a porous medium are examined.

Numerical solution scheme for local nonsimilarity boundary-layer analysis

Abstract In the analysis of boundary layers by the local nonsimilarity solution method, the central task is the numerical solution of a set of simultaneous ordinary differential equations. The current method of solving these equations is forward integration in conjunction with a shooting method for determining certain of the starting values for the integration. This approach has been found to be less and less effective as the number of simultaneous equations increases. The numerical solution scheme described here is able to deal effectively with the multiequation systems encountered in local nonsimilarity boundary-layer analysis. It employs integrated forms of the governing differential equations. The key feature of the integrated forms is that they already satisfy the boundary conditions. With these equations, initial, almost arbitrary guesses of the profiles are refined automatically until convergence is attained. For concreteness, the description of the scheme is illustrated by a nonsimilar natural con...

The effect of surface mass transfer on buoyancy-induced darcian flow adjacent to a horizontal heated surface

Abstract The effect of uniform surface mass transfer on the buoyancy-induced flow in a porous medium adjacent to a horizontal heated surface with a power law variation of wall temperature, Twαxλ, is considered in this paper. It is found that a similarity solution exists for the problem when λ = 2 . Approximate solutions based on the local nonsimilarity method are obtained for other values of λ. Numerical solutions were carried out up to the third-level of truncation and results are presented for a wide range of massflux parameter and wall temperature distributions.

Certain Anomalies in the Analysis of Hyperbolic Heat Conduction

The hyperbolic diffusion equation is often used to analyze laser heating of dielectric materials and in thermal processing of nonhomogeneous materials. Anomalies in existing solutions of the hyperbolic heat equation are identified. In particular, the singularities associated with the interaction of a wave front and a boundary may cause a violation of the imposed boundary condition. This violation may give rise to physically unacceptable results such as a temperature drop due to heating or a temperature rise due to cooling. The development of appropriate remedies for these happenings is a major focus of this paper. In addition, the unique mathematical features of the hyperbolic heat equation are studied and set forth. Greens function solutions for semi-infinite and infinite bodies are presented. For finite bodies, it is demonstrated that the relevant series solutions need special attention to accelerate their convergence and to deal with certain anomalies

The effect of superheating on condensation heat transfer in a forced convection boundary layer flow

Abstract An analysis of forced convection film condensation on a flat plate is performed for the case in which the free stream vapor flow is superheated. The solution method is applicable to free stream flows that are either binary mixtures of a condensable vapor and a noncondensable gas or pure condensable vapors. Specific numerical results are obtained for the condensation of steam with air as noncondensable. The effect of superheating on condensation heat transfer is found to be significant only in the range of relaively small differences between the free stream saturation temperature and the wall temperature. Furthermore, the influence of superheating is markedly augmented by the presence of noncondensable gases. Comparison of the present results for forced convection condensation with those for gravity-flow condensation indicates that the latter is much more sensitive to superheating.

Non-similar boundary layer analysis of mixed convection about a horizontal heated surface in a fluid-saturated porous medium

Abstract An analysis has been performed for the study of the buoyancy effects in the parallel and stagnation forced flows in a porous medium adjacent to a heated surface with wall temperature being a power function of distance, i.e., T W ≈ x λ . Local non-similarity methods were used to obtain approximate solutions for the problem. Numerical solutions were carried out to the third level of truncation for parallel aiding flow over a heated horizontal surface with 0 ≤ λ ≤ 2 for a wide range of buoyancy parameters. For wall temperature with λ 0.5, and it accentuates as the value of the buoyancy parameter or λ is increased.