Combined Radiation Convection Research Articles

Using the decomposition method to solve the fractional order temperature distribution equation: A new approach

Due to its importance in science, finding both exact and approximate solutions to fractional partial differential equations with boundary conditions is important for the research community. The natural decomposition method (NDM), which is based on the natural transformation method (NTM) and the Adomian decomposition method, is modified in this study to produce exact and approximate solutions for boundary value problems (BVPs) of partial differential equations (PDEs) with fractional coefficients. In addition, we present an exact solution to the temperature distribution in a slab constructed of materials with variable thermal conductivity's combined convection–radiation lumped system. We present these findings as numerical tables and graphs that show the convergence and stability rates. The study demonstrates that this approach is effective since it is simple to apply and produces reliable findings. We are the first to use this approach for such applications, as far as we are aware. Additionally, this method is applicable to a sizable class of BVPs for ordinary differential equations (ODEs) and PDEs.

Transient Heat Conduction in a Planar Slab With Convection and Radiation Effects

Abstract This article presents new semi-analytical solutions for transient heat conduction in a slab, which exchanges heat at the surface with its surroundings via convection, radiation, or simultaneous convection–radiation mechanisms. The concept of thermal penetration depth together with the integral method of heat balances form the basis of the formulation. Explicit expressions are derived that eliminate the need for numerical integration of the ordinary differential equations (ODEs) obtained from space integration of the heat equation. Verification of the temperature relations with a convection boundary condition is performed using an exact solution. In the case of radiation and combined convection–radiation boundary conditions, the accuracy of the explicit solutions is assessed against a numerical model. In all three cases, the new relations predict the surface temperature with high precision. For the radiation boundary condition, the computed midpoint temperature is also in excellent agreement with the numerical solution. In the case of convection heat exchange at the surface, the temperature at internal locations has close agreement with the exact solution for Biot numbers up to Bi = 1. The model prediction deviates from the exact solution in the interior positions for higher values of Bi with the highest deviation occurring at the center. For example, at Bi = 3, the highest relative error is 7.5%. Likewise, for the case of combined convection–radiation boundary conditions, the predicted midpoint temperature is found to closely follow the numerical solution at early stages of the process only. The predictability of the explicit solution of the convection-only boundary condition is more accurate than other approximate solutions at a Fourier number less than 0.2. Additional relations are presented for determination of the total heat transfer as a function of the Fourier and Biot numbers.

Impact of inhomogeneous unsteady participating media in a coupled convection–radiation system using finite element based methods

Combined convection–radiation is a common phenomenon in many engineering problems. A differentially–heated rectangular enclosure is a widely–used benchmark for testing numerical techniques developed for solving the coupled momentum and energy equations related to combined convection–radiation. Previous studies have tended to describe the phenomenon in cases using simplified characteristics for the participating media including the assumptions of: (i) uniform distribution, (ii) homogeneous cross section, (iii) grey gas radiation and (iv) under steady state conditions. The effects of an inhomogeneous unsteady participating media, e.g. composed of a mixture of gases, are arguably understudied. In this work the effect of an inhomogeneous unsteady participating media on combined convection–radiation inside a rectangular enclosure is considered, under both grey and non-grey gas modelling approaches involving a mixture of gases. A key novelty in this work is the inclusion of the ability to handle inhomogeneous participating media which change in space, time and absorption cross section values as a result of the convection–radiation coupling, allowing us to assess different gas modelling approaches. A global gas radiation model is used and a new non–uniform discretisation method for the absorption distribution function is introduced; this method allows a better handling of those energy groups in which the Planck absorption coefficient is low, improving the performance of the spherical harmonics method and mitigating ray–effects on finite elements in angle discretisation. The momentum and energy equations are solved numerically using finite element based discretisation methods. The radiative transfer equation is solved numerically using both spherical harmonics and finite elements for the angular discretisation, with their relative performance compared. The results highlight the importance that the characteristics of the participating media can have on the convection phenomenon and therefore on the resulting temperature field.

Combined convection–radiation heat transfer from n-octane combusted gas passing through different geometrical ducts

The combined radiation–convection heat transfer occurs in many industrial devices; in many occasions, the significant role of radiation is neglected in engineering modeling. The current study is an attempt to address the importance of radiation heat transfer involvement in numerical computations. The investigation takes place in two heat transfer modes of with radiation (case_rad) and without radiation consideration (case_norad) for different duct geometries of base cylinder, small cylinder, divergent frustum cone, and convergent frustum cone. To account the radiation effect in the ducts, discrete transfer radiation method is applied, while a weighted sum of gray gases model for absorption coefficient modeling in non-homogenous participating media is appropriate for combustion of n-octane gas in ducts. The convergent duct structure shows the most radiative flux of − 1514.4 W m−2, whereas small cylinder demonstrates the lowest radiative flux of − 1033.14 W m−2. The overall heat flux of convergent configuration outperforms due to homogenous distribution of O2 and high oxygen mass fraction for combustion, while increasing the surface area in the flow direction aids the heat transfer improvement. The small cylinder is characterized with better flow dynamics (Vmax = 25.72 m s−1, TKEmax = 9.45 m2 s−2); however, its deficiency in heat transfer leads to high temperature along the duct (Tmax = 710 K).

Analytical and numerical investigation of combined convection-radiation heat transfer from conical spine extended surface

The steady-state, one-dimensional, Cartesian coordinate, non-linear ordinary differential energy equation of heat conduction through a conical spine extended surface of a thermal conductivity temperature dependent property that is proposed by an available quadratic function of a computer fitted model of a published experimental data is solved analytically using Kirchhoff's transformation and numerically using the finite volume method. It is assumed that this extended surface is subjected with a Dirichlet and Neumann's boundary conditions of temperature at its base and tip respectively. The combined convection-radiation mode of heat transfer is imposed along the surface of the conical spine. Three case studies are investigated. The thermal conductivity is assumed constant in the first case and it is variable with temperature in the second and third cases, while the radiation heat transfer is neglected in the first and second cases and it is taken into account in the third case. In addition, the effect of the conical spine aspect ratio on its performance is investigated. Aluminum Alloy (A319) material of extended surface is selected. Excellent agreement between the predicted results of the numerical and analytical solution of the present work (case study 1) when compared with the experimental measurement of previously published paper. In addition, excellent agreement between the analytical and numerical results of the present work for all case studies. It shows a maximum error of temperature difference of less than (0.022%). It is found that the dissipated heat due to combined convection-radiation mode from the surface of the conical spine extended surface to the environment is greater than that due to convection mode only. In addition, increasing the value of aspect ratio of the conical spine extended surface will decrease its efficiency.

Combined radiation-convection in an air filled enclosure with in-line heaters

The effect of two fundamental arrangements of discrete heaters on the combined thermal radiation and natural convection in a square enclosure is investigated numerically. The heaters are placed either side by side or one above the other within the air filled enclosure. The nonlinear conservation equations for the resulting flow were solved by a finite volume based computational method. The steady state results which provide qualitative information on the nature of fluid flow are discussed. The present results are of use in some geometrical considerations for the optimal design of air cooled electronics.

Analysis of the heat transfer for processes of the cylinder heating in the heat-treating furnace on the basis of solving the inverse problem

This paper presents results of experimental test concerning heating of a cylinder in the furnace for heat and thermochemical treatment. Tests were conducted for heating up to temperature of 550 °C, what corresponds to nitriding processes. Calculation model including Chebyshev polynomials enabling determination of temperature distribution in the cylinder is presented.Two variants of calculation model were examined; they differ in terms of the assumed boundary condition. Analysis of regularization of the solution to the inverse problem done by the change of time step (self-regularization) was made. Based on the solution of the non-linear inverse problem for the heat equation and on the gas temperature measurement read from the furnace retort, temperature distributions on the boundary of the cylinder, combined radiation convection heat transfer coefficients (CHTC) and heat flux on the surface of the cylinder were calculated. Due to a great variability of temperature for the processes under consideration, the calculation model includes the variation of the heat conduction coefficient and of the specific heat of the material the cylinder is made of depending on temperature change. Five heating processes differing in parameters of heating rate were analysed. Impact of measurement errors on distributions of temperature on the edge of the cylinder and of the CHTC was determined. Obtained temperature distributions in the element were verified by a check measurement. Maximal error of the obtained results did not exceed 0.5%. Data presented herein give practical knowledge enabling supervising the temperature distribution in the cylindrical element being processed. These problems are of crucial meaning for processes of heat and thermochemical treatment due to formation of proper surface and subsurface layers.

Inverse boundary design problem of combined radiation convection heat transfer in a duct with diffuse-spectral design surface

In the present work, an optimization technique is applied for inverse boundary design problem of radiative convective heat transfer of laminar duct flow by numerical method. The main goal is to verify how the solution of inverse problem is affected by the spectral behavior of the boundary surfaces. The conjugate gradient method is used to find the unknown temperature distribution over the heater surface to satisfy the prescribed temperature and heat flux distributions over the design surface. The bottom boundary surface (including design surface) is diffuse-spectral, while the top wall (heater surface) behaves as gray one. The variation of emissivity with respect to the wavelength is approximated by considering a set of spectral bands with constant emissivity and then the radiative transfer equation is solved by the discrete ordinates method for each band. The performance of the present method is evaluated by comparing the results with those obtained by considering a diffuse-gray design surface. Finally an attempt is made to investigate the spectral behavior of the design surface on the calculated temperature distribution over the heater surface.

Modeling Radiative–Convective Panels for Nighttime Passive Cooling Applications

Passive cooling by combined radiation–convection from black panels at night is a potential source of significant energy-efficient cooling for both homes and industry. Assessing the technology requires system models that connect cooling load, passive cooling technology performance, and changing weather conditions in annual simulations. In this paper, the performance of an existing analytical model for a passive cooling panel is validated using a full two-dimensional finite differences model. The analytical model is based on a solar hot water collector model but uses the concept of adiabatic surface temperature to create an intuitive, physically meaningful sink temperature for combined convection and radiation cooling. Simulation results are reported for cooling panels of different sizes and operating in both low temperature (comfort cooling) and high temperature (power plant) applications. The analytical model using adiabatic minimum temperature agrees with the high-fidelity finite differences model but is more practical to implement. This model and the validations are useful for the continued study of passive cooling technology, in particular, as it is integrated into system-level models of higher complexity.

Heat transfer enhancement and pressure drop penalty in porous solar heaters: Numerical simulations

A comprehensive numerical study is performed on the fluid flow and heat transfer within a porous solar heater. The effects of porous material on the heat transfer enhancement and pressure drop are presented in details. Also, the attention is focused on the effects of several parameters on the combined convection–radiation heat transfer and flow structures. Volume averaged equations are applied to simulate the transport phenomena within the porous substrate. Furthermore, the regular continuity, momentum, and energy equations are used in the clear fluid region. These equations are discretized using the control volume technique. It is found that the Nusselt number increases by inserting the porous substrate to the heater. These augmentations are up to 3, 4.4 and 5.9 times for δ=1/3, 2/3 and 1, respectively at Da=10-2. Also, the pressure drop increases with an increase in the porous layer thickness and decrease in the Darcy number.

Influence of nozzle design on the performance of a partial combustion lance: A CFD study

This paper presents a computational fluid dynamics (CFD) simulation of a partial combustion lance (PCL) aiming to evaluate the effect of nozzle design on its performance. Four turbulence models, namely, standard k–ɛ (SKE), realisable k–ɛ (RKE), renormalised (RNG) k–ɛ and Reynolds stress model (RSM) were used. The combustion process was modelled using the species transport model, whereas the heat transfer was calculated by considering a combined convection–radiation boundary condition. The best CFD prediction was obtained using the second-order discretisation, standard pressure, unsteady solver and RSM with a 6% deviation from the experimental data. The modified nozzle design shows increases in excess of 45% of the peak combustion temperature in the PCL. The findings from this work may be useful for design retrofits of a PCL.

Heat transfer enhancement and pressure drop penalty in porous solar heat exchangers: A sensitivity analysis

Porous materials have a positive effect upon the heat transfer enhancement and a negative impact on pressure drop. Combined convection–radiation heat transfer inside a porous solar heat exchanger with a sensitivity analysis is performed to calculate the effects of porous material on the heat transfer rate and the pressure drop. Reynolds and Darcy numbers and porous substrate thicknesses are selected as the influence parameters. The analysis is carried out by using Response Surface Methodology (RSM). Also, the input parameters for optimization process are obtained by numerical methods. The computational simulations are done for different Reynolds numbers (1⩽Re⩽100), Darcy number (10−6⩽Da⩽10−2) and dimensionless porous substrate thickness (1/3⩽δ⩽1). It is found that the reductions in pressure drop ratio with increasing Darcy number are in the vicinity of 58% and 23% for δ=1/3 and 1, respectively and Da=10−6–10−2. Note that above values are obtained at Re=100. However, the augmentation in Nusselt number with increasing the porous substrate thicknesses is in the vicinity of 96% for δ=1/3–1 and Da=10−2. Also, the maximum errors between the RSM and CFD results are in the vicinity of 3% and 1.37% for the Nusselt number and pressure drop ratio, respectively.

Non-Boussinesq convection in a square cavity with surface thermal radiation

The interaction of natural convection with surface radiation in a differentially heated square cavity filled with air is considered under large temperature differences. The study has been investigated by direct numerical simulations with a two-dimensional finite volume numerical code solving the time-dependent Navier–Stokes equations under the Low Mach Number (LMN) approximation. Calculations were performed for cases with strong non-Boussinesq effects. The results reveal that the fluid flow and heat transfer are influenced significantly by the surface radiation. At steady state, the top wall is cooled and the bottom wall is heated compared to the case without radiation. The air flow is reinforced near the horizontal walls and the thermal stratification at the core is reduced. The surface radiation reduces the convection heat transfer at the hot wall and increases it on the cold wall.Transition from steady to unsteady flow has also been investigated. By comparing the solutions in pure convection, the results in combined convection–radiation show that the radiation promotes the occurrence of instabilities leading to an early transition to the unsteadiness and contributes to the modification of the physical mechanism responsible for their onset.

Natural Convection-Radiation from a Vertical Base-Fin Array with Emissivity Determination

Experiments have been conducted to determine the emissivity for black chrome coated and uncoated aluminum surfaces. The emissivity of the surfaces is estimated considering combined convection radiation heat transfer and observed to be a constant in the range of 60 to 110 o C. The combined heat transfer coefficients from black chrome coated vertical base vertical fin array of size 70 x 70 mm consisting of 22 aluminum fins with a fin spacing of 10 mm by natural convection and radiation has been determined at different heat inputs. Theoretical analysis of single fin geometry of constant thickness considering both convection and radiation has been used to predict the temperature distribution and heat flow. The theoretical values of heat flow estimated for a fin array is in good agreement with the experimental observations validating the emissivity of the surface. The experimental data is further validated with the equations of Nusselt presented by Churchill and Chu.

Assessment of Haar Wavelet-Quasilinearization Technique in Heat Convection-Radiation Equations

We showed that solutions by the Haar wavelet-quasilinearization technique for the two problems, namely, (i) temperature distribution equation in lumped system of combined convection-radiation in a slab made of materials with variable thermal conductivity and (ii) cooling of a lumped system by combined convection and radiation are strongly reliable and also more accurate than the other numerical methods and are in good agreement with exact solution. According to the Haar wavelet-quasilinearization technique, we convert the nonlinear heat transfer equation to linear discretized equation with the help of quasilinearization technique and apply the Haar wavelet method at each iteration of quasilinearization technique to get the solution. The main aim of present work is to show the reliability of the Haar wavelet-quasilinearization technique for heat transfer equations.

Numerical investigations on coupled heat transfer and synthetical performance of a pressurized volumetric receiver with MCRT–FVM method

This paper presents an axisymmetric steady-state computational fluid dynamics model and further studies on the complex coupled heat transfer combined radiation–convection–conduction in the pressurized volumetric receiver (PVR), by combining the Finite Volume Method (FVM) and the Monte Carlo Ray-Trace (MCRT) method. Based on this, effects of geometric parameters of the compound parabolic concentrator (CPC) and properties of the porous absorber on synthetical characteristics and performance of the photo-thermal conversion process in the PVR are further analyzed and discussed detailedly. It is found that the solar flux density distributions are always very heterogeneous with large nonuniformities, and the variation trends of the corresponding temperature distributions are very similar to these but with much lower order of magnitude. The CPC shape determined by the CPC exit aperture has much larger effects on synthetical characteristics and performance of the PVR than that of the CPC entry aperture with a constant acceptance angle. And a suitable or optimal thickness of the porous absorber could be determined by examining where the drastic decreasing trends occur at the curves of variations of synthetical characteristics and performance with the porosity.

Numerical analysis of laminar forced convection recess flow with two inclined steps considering gas radiation effect

In this work, a numerical analysis of combined convection–radiation heat transfer over a recess including two inclined backward and forward facing steps in a horizontal duct is presented. The fluid is treated as a gray, absorbing, emitting and scattering medium. Discretized forms of the continuity, momentum and energy equations are obtained by the finite volume method and solved using the SIMPLE algorithm, while the blocked off method is employed in simulation of the inclined surfaces. The radiative transfer equation (RTE) is solved numerically by the discrete ordinates method (DOM). Numerical results reveal that the radiation–conduction parameter, optical thickness, step inclination angle and recess length have considerable effects on heat transfer behavior of the recess flow. Comparison of numerical results with the available data published in open literature shows a good consistency.

Modeling of laser transmission contour welding process using FEA and DoE

In this research, a systematic investigation on laser transmission contour welding process is carried out using finite element analysis (FEA) and design of experiments (DoE) techniques. First of all, a three-dimensional thermal model is developed to simulate the laser transmission contour welding process with a moving heat source. The commercial finite element code ANSYS® multi-physics is used to obtain the numerical results by implementing a volumetric Gaussian heat source, and combined convection–radiation boundary conditions. Design of experiments together with regression analysis is then employed to plan the experiments and to develop mathematical models based on simulation results. Four key process parameters, namely power, welding speed, beam diameter, and carbon black content in absorbing polymer, are considered as independent variables, while maximum temperature at weld interface, weld width, and weld depths in transparent and absorbing polymers are considered as dependent variables. Sensitivity analysis is performed to determine how different values of an independent variable affect a particular dependent variable.

Extension of the Discrete Ordinates Interpolation Method to Combined Convection-Radiation Problems with Fluid Flow in Three-Dimensional Geometries Filled with Gray Participating Media

Combined convection-radiation problems in gray absorbing/emitting/scattering media are investigated numerically. The discrete ordinates interpolation method (DOIM) is incorporated into commercial software (FLUENT) using userdefined functions (UDFs). As preliminary tests, combined conduction/natural convection-radiation problems in a rectangular geometry are solved to validate the accuracy. The original DOIM is modified to solve the radiative heat transfer in an irregular geometry with internal obstacles. Then the combined turbulent forced convection-radiation problem is solved, and the radiation effects are discussed through the profiles of velocity and temperature. Fine agreement with other reference solutions is found. The DOIM promises reliable accuracy and excellent versatility for incorporation into fluid flow codes. Further computational issues are also discussed.

Comparison of symmetry and homotopy solutions for nonlinear heat transfer systems

This study deals with the analytic solutions for the two nonlinear problems arising in heat transfer. These problems are due to (i) temperature distribution in lumped system of combined convection–radiation and (ii) temperature distribution in a uniformly thick rectangular fin radiation to free space. Large symmetry algebras are obtained for the nonlinear ordinary differential equations (ODEs) describing the heat transfer. We use method of canonical variables to either linearize or transform the governing equations to integrable forms. Exact solutions are constructed. Finally, a comparison is given between the homotopy and symmetry solutions.