Publication Cover
Numerical Heat Transfer, Part A: Applications
An International Journal of Computation and Methodology
Volume 71, 2017 - Issue 11
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Original Articles

A numerical simulation of heat transfer in an enclosure with a nonlinear heat source

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Pages 1081-1093 | Received 15 Oct 2016, Accepted 27 May 2017, Published online: 28 Jun 2017
 

ABSTRACT

Two-dimensional simulations of natural convection driven by the absorption of nonuniform concentrated solar radiation in a molten binary salt-filled enclosure inclined at 0 ≤ ϕ ≤ 60 are presented. The enclosure is volumetrically heated from the top boundary and accommodates a black rigid, heat-conducting plate of finite thickness at the lower boundary, which aids in the generation of natural convective mixing at the lower boundary. The governing equations that account for the depth-dependent absorption of radiation are solved using the finite-element method. Numerical results reveal that increasing the inclination angles decreases the natural convection and higher Rayleigh promotes natural convection.

Nomenclature

C=

concentration ratio

Cp=

heat capacity, J(kgK)−1

D=

diameter m

G=

acceleration due to gravity, ms−2

H=

height, m

h=

mesh element size, m

I=

solar irradiation, Wm−2

k=

thermal conductivity, W(mK)−1

Nu=

Nusselt number

P=

pressure, Pa

Pr=

Prandtl number

S=

volumetric heat generation, Wm−3

q=

heat flux, Wm−2

Ra=

Rayleigh number

T=

temperature, K

t=

time, s

α=

absorption coefficient, m−1

η=

optical efficiency

κ=

thermal diffusivity, m2s−1

λ=

wavelength, m

µ=

dynamic viscosity, Nsm−2

ϑ=

kinematic viscosity, m2s−1

ρ=

density, kgm−3

θ=

inclination angle

V=

velocity, ms−1

u x=

velocity component, ms−1

v y=

velocity component, ms−1

w z=

velocity component, ms−1

Nomenclature

C=

concentration ratio

Cp=

heat capacity, J(kgK)−1

D=

diameter m

G=

acceleration due to gravity, ms−2

H=

height, m

h=

mesh element size, m

I=

solar irradiation, Wm−2

k=

thermal conductivity, W(mK)−1

Nu=

Nusselt number

P=

pressure, Pa

Pr=

Prandtl number

S=

volumetric heat generation, Wm−3

q=

heat flux, Wm−2

Ra=

Rayleigh number

T=

temperature, K

t=

time, s

α=

absorption coefficient, m−1

η=

optical efficiency

κ=

thermal diffusivity, m2s−1

λ=

wavelength, m

µ=

dynamic viscosity, Nsm−2

ϑ=

kinematic viscosity, m2s−1

ρ=

density, kgm−3

θ=

inclination angle

V=

velocity, ms−1

u x=

velocity component, ms−1

v y=

velocity component, ms−1

w z=

velocity component, ms−1

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