View factor computation and radiation energy analysis in baking oven with obstructions: Analytical and numerical method

Abstract

In a baking oven, radiation heat transfer is the most prevalent mode of heat exchange. In the present investigation, a new baking oven was designed with two hemi cylindrical domes (called reflectors) attached to the heating coils at the top and bottom of the baking oven. Firstly, view factors were computed by finite element and analytical methods with different bread dimensions, as well as with and without the reflectors. The network representative method and S2S method were employed to analyze the radiation energy transfer in the oven at different baking temperatures using the same bread sizes. The results obtained from numerical and analytical methods were fairly similar. The radiative heat energy absorbed by bread surface was higher with the reflector than without the reflector in the oven. As the number of obstructions increased, the radiative heat flux was reduced. The inclusion of reflector shield in oven affect the heat lux on the bread. The radiative heat flux received by bread was found to have increased on increasing the oven temperatures. Moreover, quality parameter such as the color of the bread with and without the reflectors were also examined. The oven reflector had a noticeable effect on the color of the bread (p < 0.05). Practical applicationsIn recent years, reducing energy consumption has become more important in the design of ovens. Although domestic electric ovens are a convenient way to bake quality goods, they have a very significant energy loss. Prior research has focused on CFD modeling for commercial ovens to assess the thermal behavior of the system and overall energy efficiency of baking. Baking ovens operate at higher temperatures, hence, heat transfer by radiation is highly essential. In reality, one or more surfaces in oven are obstructing the surfaces. To calculate view factors and achieve accurate radiative heat transfer in such cases, the shadow effect must be taken into account. To solve them precisely in this situation, numerical techniques are highly beneficial.

Contour integration for the view factor calculation between two rectangular surfaces

“…The contour III-A 1 has an origin and end point a (− , 0), respectively, while x = 0 1 because dx 1 is not displaced from the origin. Substituting these conditions into Equation (11), the integral relation for contour III is…”

“…Subsequently, a new method to obtain the view factor was developed, which is valid only if the projection of the leaving and reaching surfaces intersects in the normal or axial direction, however, this solution also does not offer satisfactory results if both surfaces share a common side 11 . Ehlert and Smith 12 propose an analytical solution for calculating the sight factor between rectangular surfaces, which was later improved by Yi et al 13 and Zhou et al 14 These solutions already guarantee convergence in the sum of series when both surfaces share a common edge, but it is mandatory that the $${x}$$ or $$y$$ axes be one of the sides of the leaving and reaching surfaces.…”

Contour integration for the exchange of radiant energy between rectangular geometries

“…However, this solution fails when both rectangles share a common side, requiring in these cases the use of shape factor algebra, which makes its implementation by computational methods difficult. An improved solution was later given by Krishnaprakas [11]. This new method allows obtaining the view factor between surfaces 1 and 2, provided that the space between planes 1 and 2 intersects in a normal or axial direction; it is also considered that all planes and edges are parallel or perpendicular, however, when common edges are shared the series solution also diverges.…”