TRANSIENT MIXED CONVECTION ALONG A VERTICAL PLATE EMBEDDED IN POROUS MEDIA WITH INTERNAL HEAT GENERATION AND OSCILLATING TEMPERATURE

The effects of oscillating plate temperature on transient mixed convection heat transfer from a porous vertical surface embedded in a saturated porous medium with internal heat generation or absorption are studied. The governing equations are transformed into dimenionless form by a set of variables and solved using the Galerkine finite element method. As the energy generation increases, the temperature near the wall will be higher than the wall temperature, thus increasing buoyancy forces inside the boundary layer and consequently increasing the velocity. The increase of energy absorption term for either space or temperature dependence will decrease the velocity inside the boundary layer and increase heat transfer rates. Different temperature and velocity profiles are drawn for different dimensionless groups. Numerical values for Nusselt numbers as well as local skin friction coefficient are also tabulated.     

TRANSIENT MIXED CONVECTION ALONG A VERTICAL PLATE EMBEDDED IN POROUS MEDIA WITH INTERNAL HEAT GENERATION AND OSCILLATING TEMPERATURE

The effects of oscillating plate temperature on transient mixed convection heat transfer from a porous vertical surface embedded in a saturated porous medium with internal heat generation or absorption are studied. The governing equations are transformed into dimenionless form by a set of variables and solved using the Galerkine finite element method. As the energy generation increases, the temperature near the wall will be higher than the wall temperature, thus increasing buoyancy forces inside the boundary layer and consequently increasing the velocity. The increase of energy absorption term for either space or temperature dependence will decrease the velocity inside the boundary layer and increase heat transfer rates. Different temperature and velocity profiles are drawn for different dimensionless groups. Numerical values for Nusselt numbers as well as local skin friction coefficient are also tabulated.     

MIXED CONVECTION BOUNDARY LAYER FLOW OF A MICROPOLAR FLUID ON A HORIZONTAL PLATE

An analysis is performed to study the heat transfer characteristics of laminar mixed convection boundary layer flow of a micropolar fluid past a semi-infinite horizontal fiat plate with variable surface heat flux. A nonsimilar mixed convection parameter £ and a pseudosimilarity variable v are introduced to cast the governing boundary layer equations into a system of dimensionless equations, which are solved numerically using the finite difference method. A single mixed convection parameter is used to cover the entire regime of mixed convection from the pure forced convection limit to the pure free convection limit. The effect of material parameters, the power-law variation of surface heat flux, nonsimilar mixed convection parameter and Prandtl number are considered. The micropolar fluids are observed to display drag reduction and reduced surface heat transfer rate when compared to Newtonian fluids. The effect of the buoyancy force results in the enhancements of friction factor, heat transfer rate and wall couple stress.     

MHD MIXED-CONVECTION INTERACTION WITH THERMAL RADIATION AND nTH ORDER CHEMICAL REACTION PAST A VERTICAL POROUS PLATE EMBEDDED IN A POROUS MEDIUM

This article investigates the hydromagnetic mixed convection heat and mass transfer flow of an incompressible Boussinesq fluid past a vertical porous plate with constant heat flux in the presence of radiative heat transfer in an optically thin environment, viscous dissipation, and an nth order homogeneous chemical reaction between the fluid and the diffusing species. The dimensionless governing equations for this investigation are solved numerically by the fourth-order Runge-Kutta integration scheme along with shooting technique. Numerical data for the local skin-friction coefficient, the plate surface temperature, and the local Sherwood number have been tabulated for various values of parametric conditions. Graphical results for velocity, temperature, and concentration profiles based on the numerical solutions are presented and discussed.     

Analysis of Thermal Stress Resistance of Partially Absorbing Ceramic Plate Subjected to Asymmetric Radiation, II: Convective Cooling at Front Surface

Thermal stresses in a partially absorbing brittle ceramic plate asymmetrically heated by radiation and cooled by convection on the same surface with finite and infinite heat transfer coefficients are analyzed. Comparison of the results from this study with those obtained in Part I, where the plate is subjected to radiation heating in the front surface and cooled by convection at the rear surface, indicates that the magnitudes of the maximum steady-state tensile thermal stresses are nearly identical. Significant differences are found in the transient thermal stresses and the temperature distribution. The relative temperature levels in the present case are found to be significantly lower than those obtained in Part I. Implications of these results to the design and operation of engineering structures such as concentrated solar receivers are discussed.     

Modeling Edge Heat Loss in a Flat-Plate Absorber Employed in an Indirect Solar Dryer—A 2D Galerkin Finite Element Analysis

An absorber plate is an essential component of some solar energy devices. As a primary energy conversion component, useful energy loss is not desired. The interactions and interrelationship between the parameters for use, insulation thermophysical properties, and ambient parameters are pertinent in the design of solar air heaters. A 2D finite element analysis was used to quantify the influence of edge convection heat loss on a simple absorber plate model. Results showed that the performance of the air heater can be significantly affected by edge heat loss from the absorber. The average temperature of the absorber, computed from the nodal temperature profile of the absorber, rose with superior edge insulation for low values of the heat transfer coefficient of the working fluid. However, when the ambient temperature was high, the average temperature of the absorber increased with poor edge insulation, although this condition is irregular due to fluctuations in the ambient condition. For low values of the heat transfer coefficient of the working fluid and low ambient temperature, the nondimensional edge loss flux was negligible for the absorber with superior edge insulation, and for high values of the heat transfer coefficient of the working fluid and low ambient temperature, the nondimensional edge loss flux was high for a poorly insulated absorber.     

THERMAL DISPERSION EFFECTS ON NON-DARCY NATURAL CONVECTION WITH INTERNAL HEAT GENERATION

A similarity solution is presented to study the influence of lateral mass flux and thermal dispersion on non-Darcy natural convection over a vertical fiat plate with an exponential type of internal heat generation in a fluid saturated porous medium. The coefficient of thermal diffusivity has been assumed to be the sum of molecular diffusivity and the dispersion thermal diffusivity due to mechanical dispersion. The suction/injection velocity distribution has been assumed to have power function form Ax^λ, where x is the distance from the leading edge and the wall temperature distribution is assumed to be uniform.     

Model of oxygen cutting of a metal plate with chemical heat release

A model for the process of oxygen cutting of a metal plate is proposed which takes into account heating by external and internal heat sources, heat release from the cutting zone and reducing the thickness of the cutting geometry. The model was implemented numerically. It is shown that the model can describe different cutting modes: surface cutting, severing, and cutting in the kinetic and diffusion regimes. From the calculations results, the temperature field was constructed and the effect of the parameters on the thickness of the workpiece and the shape of the cutting edge was studied. The results are qualitatively consistent with experimental data.     

Wall effect on mixed convection from horizontal surfaces with a variable surface heat flux

This work investigates analytically the wall effect on the mixed convection from a horizontal plate embedded in porous media. Variable surface heat flux is assumed at the plate. The wall effect due to no-slip boundary condition at the wall is introduced using the Brinkman model. Two sets of transformations are used, one for the forced convection dominating regime (FCDR) and the other one for the natural convection dominating regime (NCDR). The wall effect is found to be characterized by the boundary parameters L = Da_xPe_x /? in FCDR and by M = Da_x Ra:/? in NCDR. Velocity as well as temperature profiles are calculated at different values of governing parameters. Local Nusselt number variation for the entire mixed convection regime is also calculated and presented. Accurate correlations for local and average Nusselt number valid for the entire regime of mixed convection and for the range of boundary-parameter from 0 to 100 are obtained.     

Measuring incident heat flux and adiabatic surface temperature with plate thermometers in ambient and high temperatures

A new more insulated and faster responding plate thermometer (PT) is introduced, which has been developed for measurements particularly in air at ambient temperature. It is a cheaper and more practical alternative to water‐cooled heat flux meters (HFMs). The theory and use of PTs measuring incident radiation heat flux and adiabatic surface temperature are presented. Comparisons of measurements with PTs and HFMs are made. Finally, it is concluded that incident radiation in ambient air can be measured with HFMs as well as with the new insulated type of PT. In hot gases and flames, however, only PTs can be recommended. At elevated gas temperatures, convection makes measurements with HFMs difficult to interpret and use for calculations. However, they can be used in standard or well‐defined configurations for comparisons.     

THERMAL DISPERSION EFFECTS ON NON-DARCY NATURAL CONVECTION WITH INTERNAL HEAT GENERATION

A similarity solution is presented to study the influence of lateral mass flux and thermal dispersion on non-Darcy natural convection over a vertical fiat plate with an exponential type of internal heat generation in a fluid saturated porous medium. The coefficient of thermal diffusivity has been assumed to be the sum of molecular diffusivity and the dispersion thermal diffusivity due to mechanical dispersion. The suction/injection velocity distribution has been assumed to have power function form Ax^λ , where x is the distance from the leading edge and the wall temperature distribution is assumed to be uniform.     

MATHEMATICAL MODELING OF THERMAL RADIATION EFFECTS ON TRANSIENT GRAVITY-DRIVEN OPTICALLY THICK GRAY CONVECTION FLOW ALONG AN INCLINED PLANE WITH PRESSURE GRADIENT

We study theoretically the unsteady gravity-driven thermal convection flow of a viscous incompressible absorbing-emitting gray gas along an inclined plane in the presence of a pressure gradient and significant thermal radiation effects. The Rosseland diffusion flux model is employed to simulate thermal radiation effects. The momentum and energy conservation equations are nondimensionalized and solved exactly using the Laplace transform technique. Expressions are derived for the frictional shearing stress at the inclined plane surface and also the critical Grashof number. The effects of time (T), Grashof number (Gr), Boltzmann-Rosseland radiation parameter (K₁), and plate inclination (α) on velocity (u) and temperature (θ) distributions are studied. The flow is found to be accelerated with increasing inclination of the plane, increasing free convection effects, and for greater thermal radiation contribution but decelerated with progression of time. Temperature is found to be enhanced with progression of time and with greater thermal radiation contribution. Applications of the model arise in solar energy collector analysis and industrial materials processing.     

NATURAL CONVECTION HEAT AND MASS TRANSFER FROM A VERTICAL FLAT PLATE WITH VARIABLE WALL TEMPERATURE AND CONCENTRATION TO POWER-LAW FLUIDS WITH YIELD STRESS IN A POROUS MEDIUM

The problem of natural convection coupled heat and mass transfer of non-Newtonian power law fluids with yield stress from a vertical flat plate in a fluid-saturated porous medium is analyzed under boundary layer approximations. Similarity solutions are obtained for the general case of power law variations of the wall temperature and concentration. Velocity, temperature, and concentration profiles as well as local heat and mass transfer rates are presented and discussed for different values of the rheological parameters of a power-law fluid, the Lewis number, and the thermal and concentration buoyancy ratio.     

HEAT TRANSFER DURING GLASS FORMING

An important step in the optimization of a glass container production cycle is the determination of the glass temperature distribution during heat treatment. The ideal approach to this problem is to formulate a theoretical model for comparison against experimental data measured in a well-determined system. Discrepancies between theory and experiment may then give further direction for model improvement. This approach, however, is limited because of the difficulties in measuring glass temperature distribution during forming.

Another approach is to use the model to predict glass surface heat fluxes during the forming cycle and test the computed results against published values of glass to metal heat fluxes measured during glass container production on an individual section (I.S.) Blow-and-Blow bottle machine.

A computer model has been developed to calculate the temperature distribution in a glass plate. The model includes the three modes of heat transfer: conduction, convection and radiation. The process is complicated by simultaneous internal emission and reabsorption of radiant energy within the glass in the non-opaque region of the spectrum. With the problem being simplified to a one-dimensional case, the glass plate is divided into several slices. An energy balance on each slice yields a system of integro-partial differential equations which are solved to obtain the temperature distribution.

Results in the form of temperature-time, temperature-distance and surface heat flux-time plots arc presented and compared with published models and with experimental data.     

THERMAL CONVECTIVE INSTABILITY IN TRANSLUCENT POROUS MEDIA WITH RADIATIVE HEAT TRANSFER

The onset of thermal convection in a translucent porous layer is considered. Attention is focused on the effect of radiative heat transfer on the critical Rayleigh-Darcy number and the convection cell shape. If we consider the contribution of radiative heat transfer, the basic temperature profile is non-linear and the thermal convective instability is influenced by the ratio of conduction to radiation heat flux, the temperatures at the boundary surfaces, and radiative parameters such as wall emissivity, scattering albedo and extinction coefficient as well as the usual Rayleigh-Darcy number. Effects of these parameters on the onset of convective instability are investigated with the help of linear stability theory employing the Darcy's law and the radiative transport equation simplified by the P₁ approximation. The increased effective thermal conductivity due lo the radiation inhibits the onset of convection and causes increased critical Rayleigh-Darcy number and decreased convection cell size. The results of the present work may be exploited to find out the optimal diameter of aerogel pellets and the air pressure in the double pane window filled with the translucent silica aerogel granules to suppress natural convection.     

COMBINED LAMINAR FREE AND FORCED CONVECTION FROM A VERTICAL PLATE TO POWER LAW FLUIDS

The boundary layer heat transfer for the steady two-dimensional incompressible combined laminar free and forced convection from a vertically static or moving plate to a power-law non-Newtonian fluid is analyzed by local similarity method. The effects of the flow index, buoyancy parameter, modified Prandtl number and streamwise distance on the heat transfer rate are discussed for the prescribed surface temperature and prescribed wall heat flux cases.     

COMBINED LAMINAR FREE AND FORCED CONVECTION FROM A VERTICAL PLATE TO POWER LAW FLUIDS

The boundary layer heat transfer for the steady two-dimensional incompressible combined laminar free and forced convection from a vertically static or moving plate to a power-law non-Newtonian fluid is analyzed by local similarity method. The effects of the flow index, buoyancy parameter, modified Prandtl number and streamwise distance on the heat transfer rate are discussed for the prescribed surface temperature and prescribed wall heat flux cases.     

FORCED CONVECTION BOUNDARY LAYER FLOW AT A FORWARD STAGNATION POINT WITH NEWTONIAN HEATING

The steady forced convection boundary layer flow near the forward stagnation point of an infinite plane wall generated by Newtonian heating in which the heat transfer from the surface is proportional to the local surface temperature is investigated in this study. The governing partial differential equations are first transformed into a system of ordinary differential equations before they are solved numerically by a finite-difference scheme, namely the Keller box method. Numerical solutions are obtained for a large range of values of the Prandtl number.     

Mixed convection in a doubly stratified micropolar fluid saturated non‐Darcy porous medium

The effects of thermal and solutal stratification on mixed convection along a vertical plate embedded in a micropolar fluid saturated non‐Darcy porous medium are analysed. The nonlinear governing equations and their associated boundary conditions are initially cast into dimensionless forms by pseudo‐similarity variables. The resulting system of equations is then solved numerically using the Keller‐box method. The numerical results are compared and found to be in good agreement with previously published results as special cases of the present investigation. The velocity, microrotation, temperature and concentration profiles are shown for different values of the coupling number, non‐Darcy parameter, mixed convection parameter, thermal and solutal stratification parameters. The numerical values of the skin friction, wall couple stress, heat and mass transfer rates for different values of governing parameters are also tabulated. © 2011 Canadian Society for Chemical Engineering     

GENERALIZED FINITE DIFFERENCE SOLUTION FOR HEAT AND MASS TRANSFER FROM A FINITE CYLINDER DURING QUENCH

A generalized nondimensional solution is presented that describes heat or mass transfer from a finite cylinder during quench. The solution is applicable to three important cases:

Conduction with convection heat transfer at the surface during any single step hot or cold quench.

Conduction with radiation heat transfer at the surface during a single step cold quench with negligible background radiation.

Diffusion with surface desorption of a diatomic gas from a metal specimen during a single step quench in a high vacuum with negligible background pressure.

Application of the generalized solution, which utilizes the numerical method of finite differences with forward stepping, is illustrated by determining a cylinder's transient temperature distribution and surface transfer rate (both instantaneous and cumulative) for an example L/D ratio of 2.0. Selected results are graphed and tabulated for the three cases. The results for the conduction/convection case are verified using the familiar analytical product solution as well as the lumped solution. For the conduction/radiation and diffusion/desorption cases, no analytical solutions are available other than the lumped limit which is in agreement.