Combined Conductive and Radiative Heat Transfer in an Absorbing and Scattering Infinite Slab

1978 ◽  
Vol 100 (1) ◽  
pp. 98-104 ◽  
Author(s):  
J. A. Roux ◽  
A. M. Smith
Keyword(s):  
Heat Transfer ◽  
Energy Equation ◽  
Radiative Heat ◽  
Convective Boundary Condition ◽  
Dimensionless Temperature ◽  
Temperature Profiles ◽  
Scattering Medium ◽  
Convective Boundary ◽  
One Dimensional ◽  
Infinite Slab

Simultaneous radiation and conduction heat transfer results are presented for an absorbing and isotropically scattering medium having negligible emission. The radiatively participating medium is assumed to be one-dimensional and bounded by an opaque substrate and by a semi-transparent top interface. The boundary interfaces are assumed to reflect and transmit radiation in accordance with Fresnel’s equations and Snell’s law, respectively. A diffuse radiative flux, along with a conductive flux, is assumed incident upon the participating medium at the top interface. The Chandrasekhar solution to the transport equation is employed, then the solution of the governing energy equation is formulated for the radiatively participating medium. Heat transfer to the substrate is presented as a function of the governing parameters: albedo, optical thickness, and substrate and medium refractive indices. Finally, dimensionless temperature profiles are shown. Solutions for a convective boundary condition are also derived.

Impact of Angular Magnetic Field and Convective Boundary Condition on Heat Transfer of Newtonian Fluid Flow in a Channel

2021 ◽  
pp. 095440622110064
Author(s):  
Mostafa Hossein Saeidi ◽  
Ali Bagheri ◽  
Mehdi Ghamati ◽  
Mohsen Javanmard ◽  
Mohammad Hasan Taheri
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Fluid Flow ◽  
Heat Transfer Rate ◽  
Newtonian Fluid ◽  
Transfer Rate ◽  
Energy Equation ◽  
Dimensionless Temperature ◽  
Governing Equations ◽  
Convective Boundary

In this study, the heat transfer of a laminar, steady, fully developed, and Newtonian fluid flow in a channel is investigated. The main goal of the present study is solving the hydromagnetic Newtonian fluid flow and heat transfer inside a channel with the angular magnetic field and convective boundary conditions on the walls. As a novelty, the effect of thermal diffusion and advection term the walls and Joule heating in the energy equation has been considered. The governing equations include the continuity, momentum, and energy are presented, and considering the assumptions are simplified. Afterward, employing the dimensionless parameters, the governing equations are transformed into dimensionless forms. The exact solution is provided for the momentum equation. For solving the full energy equation, the analytical collocation method (CM) is conducted. The results are validated using the 4th order Runge-Kutta method. The results demonstrated that the dimensionless velocity, the bulk temperature inside the channel, and the channel wall's heat transfer rate decline when the Hartmann number and the magnetic field angle increase. Since the Prandtl and Eckert numbers reduce, the dimensionless temperature becomes more uniform, and the heat transfer rate on the channel wall decreases. Since the Biot number augments, the dimensionless temperature inside the channel reduces, but the channel wall's heat transfer rate first increases and then reduces.

Line-by-Line Random-Number Database for Monte Carlo Simulations of Radiation in Combustion System

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Tao Ren ◽  
Michael F. Modest
Keyword(s):  
Heat Transfer ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Radiative Heat ◽  
Random Number ◽  
Test Cases ◽  
Combustion System ◽  
Absorption Coefficients ◽  
One Dimensional ◽  
The Monte Carlo Method

With today's computational capabilities, it has become possible to conduct line-by-line (LBL) accurate radiative heat transfer calculations in spectrally highly nongray combustion systems using the Monte Carlo method. In these calculations, wavenumbers carried by photon bundles must be determined in a statistically meaningful way. The wavenumbers for the emitting photons are found from a database, which tabulates wavenumber–random number relations for each species. In order to cover most conditions found in industrial practices, a database tabulating these relations for CO2, H2O, CO, CH4, C2H4, and soot is constructed to determine emission wavenumbers and absorption coefficients for mixtures at temperatures up to 3000 K and total pressures up to 80 bar. The accuracy of the database is tested by reconstructing absorption coefficient spectra from the tabulated database. One-dimensional test cases are used to validate the database against analytical LBL solutions. Sample calculations are also conducted for a luminous flame and a gas turbine combustion burner. The database is available from the author's website upon request.

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