Analysis of the conduction–radiation problem in absorbing, emitting, non-gray planar media using an exact method

Moore, Travis J.; Jones, Matthew R.

doi:10.1016/j.ijheatmasstransfer.2014.02.029

Cited by 20 publications

(20 citation statements)

References 21 publications

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“…Examples of the application of such coatings include thermal barrier coatings (TBCs) which are used in power generation and aerospace turbines to protect super alloy components from large and extended heat loads, and glass coatings that are used as sacrificial ablating coatings to protect the interior of a body from high external temperatures. The method of variation of parameters has been used to analyze the conduction-radiation problem in a non-scattering, non-gray medium with non-gray opaque boundaries [29]. For simplicity in demonstrating this method here, the simplest case of a gray medium with black boundaries, as shown in Fig.…”

Section: Example 2 Combined Conduction-radiation Problemmentioning

confidence: 99%

“…The method of variation of parameters is used to find the particular solution to Equation (15). The details of this solution are omitted here for brevity, but are provided in [29]. An expression for the temperature profile is found by summing the complementary and particular solutions and applying the boundary conditions and is shown in Equation (20).…”

Section: Example 2 Combined Conduction-radiation Problemmentioning

confidence: 99%

“…Fig. 3 shows these comparisons for different values of N. A discussion of the comparison of the computational expense for these different methods is available in [29].…”

Section: Example 2 Combined Conduction-radiation Problemmentioning

confidence: 99%

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Solving nonlinear heat transfer problems using variation of parameters

Moore

Jones

2015

International Journal of Thermal Sciences

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a b s t r a c tNonlinear problems arise in many heat transfer applications, and several analytical and numerical methods for solving these problems are described in the literature. Here, the method of variation of parameters is shown to be a relatively simple method for obtaining solutions to four specific heat transfer problems: 1. a radiating annular fin, 2. conduction-radiation in a plane-parallel medium, 3. convective and radiative exchange between the surface of a continuously moving strip and its surroundings, and 4. convection from a fin with temperature-dependent thermal conductivity and variable cross-sectional area. The results for each of these examples are compared to those obtained using other analytical and numerical methods. The accuracy of the method is limited only by the accuracy with which the numerical integration is performed. The method of variation of parameters is less complex and relatively easy to implement compared to other analytical methods and some numerical methods. It is slightly more computationally expensive than traditional numerical approaches. The method presented may be used to verify numerical solutions to nonlinear heat transfer problems.

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Section: Example 2 Combined Conduction-radiation Problemmentioning

confidence: 99%

Section: Example 2 Combined Conduction-radiation Problemmentioning

confidence: 99%

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Solving nonlinear heat transfer problems using variation of parameters

Moore

Jones

2015

International Journal of Thermal Sciences

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“…Recently, Moore [20] used this method in the solution of nonlinear direct and inverse heat transfer problems. Moore and Jones [21] analyzed a conduction-radiation problem in absorbing, and emitting non-gray planar media using this method. In order to test the accuracy and efficiency of the method, Moore compared the solution in the literature and the results obtained from this method proved that it gives accurate and precise results [20].…”

Section: Introductionmentioning

confidence: 99%

“…In order to test the accuracy and efficiency of the method, Moore compared the solution in the literature and the results obtained from this method proved that it gives accurate and precise results [20]. References [20] and [21] are the first studies in which VPM has been used in the solution of nonlinear heat transfer problems.…”

Section: Introductionmentioning

confidence: 99%

Variation of parameters method for optimizing annular fins with variable thermal properties

Arslantürk¹

2018

Pamukkale J Eng Sci

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Radiant energy exchange through participating media composed of arbitrary concentrations of H₂O, CO₂, and CO

Camaraza‐Medina,

Hernandez‐Guerrero,

Luviano‐Ortiz

2024

Heat Trans

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In this work, an approximate analytical solution (AS) is presented to evaluate the radiative thermal exchange through a gaseous participating medium composed of H2O, CO2, and CO, which is valid for the product values of pressure path‐length (PL) from 0.06 to 20 atm m and temperatures (T) from 300 K to 2100 K. The Spence root weighting method is used to approximate the exact solutions. For each set of , the value of exact spectral emissivity and absorptivity and for the gas mixture is calculated using the AS, the Hottel graphical method (HGM) and the proposed approximate solution. The weaker adjustment was achieved in the modeling of the HGM, with a mean deviation obtained of ±15% and ±20% for 43.8% and 56.3% of the data evaluated, respectively, while the best indices were obtained in the estimation of the proposed method, with a mean deviation obtained of ±10% and ±15% for 81.3% and 98.1% of the available data, respectively. In all cases, the agreement of the proposed model with the available experimental data is good enough to be considered satisfactory for practical design.

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Analysis of the conduction–radiation problem in absorbing, emitting, non-gray planar media using an exact method

Cited by 20 publications

References 21 publications

Solving nonlinear heat transfer problems using variation of parameters

Solving nonlinear heat transfer problems using variation of parameters

Variation of parameters method for optimizing annular fins with variable thermal properties

Radiant energy exchange through participating media composed of arbitrary concentrations of H₂O, CO₂, and CO

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Analysis of the conduction–radiation problem in absorbing, emitting, non-gray planar media using an exact method

Cited by 20 publications

References 21 publications

Solving nonlinear heat transfer problems using variation of parameters

Solving nonlinear heat transfer problems using variation of parameters

Variation of parameters method for optimizing annular fins with variable thermal properties

Radiant energy exchange through participating media composed of arbitrary concentrations of H2O, CO2, and CO

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Product

Resources

About

Radiant energy exchange through participating media composed of arbitrary concentrations of H₂O, CO₂, and CO