Can the shape influence entropy generation for thermal convection of identical fluid mass with identical heating? A finite element introspection

Abstract

Purpose This paper aims to investigate the role of shapes of containers (nine different containers) on entropy generation minimization involving identical cross-sectional area (1 sq. unit) in the presence of identical heating (isothermal). The nine containers are categorized into three classes based on their geometric similarities (Class 1: square, tilted square and parallelogram; Class 2: trapezoidal type 1, trapezoidal type 2 and triangular; Class 3: convex, concave and curved triangular). Design/methodology/approach Galerkin finite element method is used to solve the governing equations for a representative fluid (engine oil: Pr = 155) at Ra = 103–105. In addition, finite element method is used to solve the streamfunction equation and evaluate the entropy generation terms (Sψ and Sθ). Average Nusselt number ( Nub¯) and average dimensionless spatial temperature ( θ^) are also evaluated via the finite element basis sets. Findings Based on larger Nub¯, larger θ^ and optimal Stotal values, containers from each class are preferred as follows: Class 1: parallelogrammic and square, Class 2: trapezoidal type 1 and Class 3: convex (larger θ^, optimum Stotal) and concave (larger Nub¯). Containers with curved walls lead to enhance the thermal performance or efficiency of convection processes. Practical implications Comparison of entropy generation, intensity of thermal mixing ( θ^) and average heat transfer rate give a clear picture for choosing the appropriate containers for processing of fluids at various ranges of Ra. The results based on this study may be useful to select a container (belonging to a specific class or containers with curved or plane walls), which can give optimal thermal performance from the given heat input, thereby leading to energy savings. Originality/value This study depicts that entropy generation associated with the convection process can be reduced via altering the shapes of containers to improve the thermal performance or efficiency for processing of identical mass with identical heat input. The comparative study of nine containers elucidates that the values of local maxima of Sψ (Sψ,max), Sθ (Sθ,max) and magnitude of Stotal vary with change in shapes of the containers (Classes 1–3) at fixed Pr and Ra. Such a comparative study based on entropy generation minimization on optimal heating during convection of fluid is yet to appear in the literature. The outcome of this study depicts that containers with curved walls are instrumental to optimize entropy generation with reasonable thermal processing rates.

Thermal irreversibility demystified

“…Authors non-dimensionalised the entropy generation term with a characteristic entropy generation rate. Lukose and Basak (2021) used the heat transfer and fluid friction contributions of the entropy generation term to study the effect of container curved and straight walled shapes on thermal performance or efficiency of convection process. At low Reynolds number ($1,000), the effect of thermal irreversibility was dominant in comparison to fluid friction irreversibility.…”

Natural convection with water-copper nanofluid around a finned vertical cylindrical electronic component

“…Among the most important are the temperature levels, the thermophysical characteristics of the object and the used fluid, the generated heat flux, the dimensions of the object and the cavity and the distance between the active walls. Arrangement of the object with respect to the gravity field and its geometry and the shape of the cavity which contains them also play a major role in the free convective heat transfer phenomena (Lukose and Basak, 2021). Design of assemblies in all engineering areas must therefore take into account these geometry and architectural parameters to ensure their correct operation in the worst conditions.…”