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This study aims to investigate thermo-bioconvection of oxytactic microorganisms occurring in a nanofluid-saturated porous lid-driven cavity in the presence of the magnetic field. The heating is provided through a bell-shaped curved bottom wall heated isothermally. The effects of the peak height of the curved bottom wall, bioconvection Rayleigh number (Rb), Darcy number (Da), Hartmann number (Ha), Peclet number (Pe), Lewis number (Le) and Grashof number (Gr) on the flow structure, temperature and the iso-concentrations of oxygen and microorganisms are examined and explained systematically. The local and global, characteristics of heat transfer and oxygen concentration, are estimated through the Nusselt number (Nu) and Sherwood number (Sh), respectively.

The governing equations of continuity, momentum, energy and additionally consisting of species transport equations for oxygen concentration and population density of microorganisms, are discretized by the finite volume method. The evolved linearized algebraic equations are solved iteratively through the alternate direction implicit scheme and the tri-diagonal matrix algorithm. The computation domain has meshed in non-uniform staggered grids. The entire computations are carried out through an in-house developed code written in FORTRAN following the SIMPLE algorithm. The third-order upwind and second-order central difference schemes are used for handling the advection and diffusion terms, respectively. The convergence criterion for the iterative process of achieving the final solution is set as 10–8 and 10–10, respectively, for the maximum residuals and the mass defect.

The results show that the flow and temperature distribution along with the iso-concentrations of oxygen and microorganisms are markedly affected by the curvature of the bottom wall. A secondary circulation is developed in the cavity that changes the flow physics significantly. The Nu increases with the peak height of the curved bottom wall and Da; however, it decreases with Ha and Rb. The Sh increases with Da but decreases with Ha and the peak height of the curved wall.

A similar study of bioconvection could be extended further considering thermal radiation, chemical attraction, gravity, light, etc.

The outcomes of this investigation could be used in diverse fields of multi-physical applications such as in food industries, chemical processing equipment, fuel cell technology and enhanced oil recovery.

The insights of bioconvection of oxytactic microorganisms using a curved bottom surface along with other physical issues such as nanofluid, porous substance and magnetic field are addressed systematically and thoroughly.

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).

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 (S_ψ and S_θ). Average Nusselt number ( Nub¯) and average dimensionless spatial temperature ( θ^) are also evaluated via the finite element basis sets.

Based on larger Nub¯, larger θ^ and optimal S_total 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 S_total) and concave (larger Nub¯). Containers with curved walls lead to enhance the thermal performance or efficiency of convection processes.

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.

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 S_ψ (S_ψ,max), S_θ (S_θ,max) and magnitude of S_total 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.

Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.

This study aims to elucidate the role of curved walls in the presence of identical mass of porous bed with identical heating at a wall for two heating objectives: enhancement of heat transfer to fluid saturated porous beds and reduction of entropy production for thermal and flow irreversibilities.

Two heating configurations have been proposed: Case 1: isothermal heating at bottom straight wall with cold side curved walls and Case 2: isothermal heating at left straight wall with cold horizontal curved walls. Galerkin finite element method is used to obtain the streamfunctions and heatfunctions associated with local entropy generation terms.

The flow and thermal maps show significant variation from Case 1 to Case 2 arrangements. Case 1 configuration may be the optimal strategy as it offers larger heat transfer rates at larger values of Darcy number, Da_m. However, Case 2 may be the optimal strategy as it provides moderate heat transfer rates involving savings on entropy production at larger values of Da_m. On the other hand, at lower values of Da_m (Da_m ≤ 10⁻³), Case 1 or 2 exhibits almost similar heat transfer rates, while Case 1 is preferred for savings of entropy production.

The concave wall is found to be effective to enhance heat transfer rates to promote convection, while convex wall exhibits reduction of entropy production rate. Comparison between Case 1 and Case 2 heating strategies enlightens efficient heating strategies involving concave or convex walls for various values of Da_m.

This study aims to carry out the analysis of Rayleigh-Bénard convection within enclosures with curved isothermal walls, with the special implication on the heat flow visualization via the heatline approach.

The Galerkin finite element method has been used to obtain the numerical solutions in terms of the streamlines (ψ ), heatlines (Π), isotherms (θ), local and average Nusselt number ( Nut¯) for various Rayleigh numbers (10³ ≤ Ra ≥ 10⁵), Prandtl numbers (Pr = 0.015 and 7.2) and wall curvatures (concavity/convexity).

The presence of the larger fluid velocity within the curved cavities resulted in the larger heat transfer rates and thermal mixing compared to the square cavity. Case 3 (high concavity) exhibits the largest Nut¯ at the low Ra for all Pr. At the high Ra, Nut¯ is the largest for Case 3 (high concavity) at Pr = 0.015, whereas at Pr = 7.2, Nut¯ is the largest for Case 1 (high concavity and convexity).

The results may be useful for the material processing applications.

The study of Rayleigh-Bénard convection in cavities with the curved isothermal walls is not carried out till date. The heatline approach is used for the heat flow visualization during Rayleigh-Benard convection within the curved walled enclosures for the first time. Also, the existence of the enhanced fluid and heat circulation cells within the curved walled cavities during Rayleigh-Benard heating is illustrated for the first time.

The study aims to assess the heater and cooler positional impacts systematically using four different quadrantal cavities filled with hybrid nanofluid, keeping the curved surface adiabatic under the orientated magnetic fields. Both heat transfer and entropy generation analyses are performed for a hybrid nanofluid flow in a quarter circular cavity considering different orientations of magnetic fields. The investigation is focused to assess the heater and cooler positional impacts systematically using four different quadrantal cavities (first to fourth quadrantal cavities), keeping the curved surface always adiabatic. The impacts of pertinent variables like Rayleigh number, Hartmann number and volumetric concentration of hybrid nanofluid on heat transfer characteristics are in consideration with the second law of thermodynamics. The analysis includes the thermal, viscous and magnetic aspects of entropy generation.

After validating against the experimental results, the present work explores numerically following the Galerkin weighted finite element technique. The solution is obtained through an iterative process satisfying the convergence limit of 10⁻⁸ and 10⁻¹⁰ for the maximum residuals and the mass defect, respectively.

It revealed that the mutual exchange of heater-cooler positions on the adjacent straight edges of the quadrant cavity does not have any impact on the flow direction. Although the magnitude of flow velocity enhances, the sidewall plays a decision-making role in the formation of a single circulation vortex. It also shows that thermal entropy production is the main cause behind thermodynamic irreversibility. The second or third quadrantal arrangement could have been opted as the best configuration of the heater-cooler position for achieving superior heat transfer. The Lorentz force plays a great role to moderate the heat transfer process. The maximum entropy generation is located, as expected, at the heating-cooling junction point.

There are plenty of prospects for extension of the present research concept numerically or experimentally, adopting three-dimensional analysis, working fluids, boundary conditions, etc. In fact, the study could be carried out for unsteady or turbulent fluid flow.

As the position of the heated source and cold sink on the enclosure geometry can significantly alter the thermo-fluid phenomena, this kind of analysis is of utmost relevance for the further development of efficient heating/cooling arrangements and proper management of the devices subjected to magnetic field applications. This original contribution could be a potentially valuable source for future research and exploration pertaining to a thermal system or device, like heat exchangers, solar collectors, thermal storage, electronic cooling, food and drying technologies and others.

In the literature, an inadequate number of works have focused on a quadrantal cavity, mostly considering the first quadrant of the circle. However, during practical applications, it is possible that the cavity can take the shape of the other three quadrants too, and the corresponding knowledge on relative performance is still missing. Furthermore, the present investigation includes the existence of magnetic fields at various orientations. The impact analysis of this field-induced Lorentz force on the nanofluid thermal performance is another major contribution from the present work that would enrich the domain knowledge and could be useful for thermal system engineers.

Marketing persuasive materials are often displayed on a curved surface (e.g. a curved hallway). This study aims to investigate how the curvature (concave vs convex) of a display surface influences the persuasion of the marketing appeals presented on it.

The conceptual framework was tested in a field experiment, a lab experiment and two online experiments on Amazon Mechanical Turk. Analyses of variance and mediation analysis were used to test the hypotheses.

This research demonstrates that a concave (vs convex) display surface may increase persuasion for marketing materials with social appeals. This occurs because a concave surface enhances consumers’ perception of self–other overlap, which is matched with the content of the social appeal presented on it, thereby enhancing the appeal’s persuasiveness. It further identifies the appeal content as an important moderator of the effect; a convex (vs concave) display would enhance persuasion when the marketing materials contain personal appeals.

Future research could investigate how a time delay (e.g. hours, days) and the curvature of a display board or wall would play a role in the effect of display curvature.

The findings offer a novel, simple and cost-effective approach to enhance persuasion for both nonprofit and for-profit marketing materials.

This research contributes to the persuasion literature by investigating the impact of one ubiquitous but overlooked aspect of the message setting (i.e. the curvature of the message’s display surface) on persuasion while holding the message source and content constant. It also advances knowledge on consumer shape perception by examining an underexplored shape (i.e. the curved shape of a display surface) that is nondiagnostic in message persuasion.

Fanwing airfoil is a new lift‐generating section invented in 1997 by Patrick Peebles. The early shape of the airfoil has not changed until now. So far, no research has been done to change or modify the airfoil shape in order to improve its aerodynamic performance. In this paper, possibility of changing the airfoil shape to improve its aerodynamic performance is studied. For this purpose, six different geometric shapes of the airfoil are investigated numerically to determine the best airfoil on the basis of lift and drag coefficients. Flow over the airfoil is solved by developing a computational fluid dynamics (CFD) code. The purpose of this paper is to find a more efficient configuration for the Fanwing airfoil with lower power consumption and better performance.

Flow over the airfoil is investigated by CFD. At the airfoil solid walls, the no slip condition is applied. Re‐Normalization Group k‐ε model is used for turbulence modeling. The pressure‐velocity coupling is calculated by the SIMPLEC algorithm. Second‐order upwind discretization is considered for the convection terms. Finite volume method with rectangular computational cells is used for the entire solution domain.

It is observed that the airfoil with curved bottom wall and a slot in upper wall has the maximum lift coefficient. Also, the airfoil with curved bottom wall and no slot has the minimum drag or maximum thrust (negative drag) coefficient. Therefore, instead of increasing the airfoil lift or decreasing its drag by enhancing driving motor speed with larger energy consumption, this can be done only by changing the airfoil shape. It is perceived that the airfoil lift coefficient can be augmented at least 10 percent and its drag can be reduced more than 2.8 percent only by changing its shape and no excessive power consumption. Since the airfoil shape is modified, these advantages are permanent and its benefits are cumulative through time. Eccentric vortex inside the cross flow fan that is reported earlier in the research paper is found in this airfoil, too. In addition, velocity vectors, contours of static pressure and distribution of the static pressure over the airfoils surfaces are illustrated for better understanding of the flow details.

Since the airfoil shape is very complicated for numerical study, two‐dimensional simulation has been carried out. Also, flow over the airfoil is considered steady‐state and incompressible.

In this paper, some modifications for the Fanwing airfoil are suggested in order to improve its aerodynamic performance. This is the first research for changing the configuration of the Fanwing airfoil and can be very helpful for the researchers involved in this topic as well as aerospace industries.

This paper is valuable for researchers in the new and up to date concept of the Fanwing airfoil. This work is original.

The particle distribution in a fluid is mostly not homogeneous. The inhomogeneous dispersion of solid particles affects the velocity profile as well as the heat transfer of fluid. This study aims to highlight the effects of varying density of particles in a fluid. The fluid flows through a wavy curved passage under an applied magnetic field. Heat transfer is discussed with variable thermal conductivity.

The mathematical model of the problem consists of coupled differential equations, simplified using stream functions. The results of the time flow rate for fluid and solid granules have been derived numerically.

The fluid and dust particle velocity profiles are being presented graphically to analyze the effects of density of solid particles, magnetohydrodynamics, curvature and slip parameters. Heat transfer analysis is also performed for magnetic parameter, density of dust particles, variable thermal conductivity, slip parameter and curvature. As the number of particles in the fluid increases, heat conduction becomes slow through the fluid. Increase in temperature distribution is noticed as variable thermal conductivity parameter grows. The discussion of variable thermal conductivity is of great concern as many biological treatments and optimization of thermal energy storage system’s performance require precise measurement of a heat transfer fluid’s thermal conductivity.

This study of heat transfer with inhomogeneous distribution of the particles in a fluid has not yet been reported.

A few earlier studies presented infeasible heatline trajectories for natural convection within annular domains involving an inner circular cylinder and outer square/circular enclosure. The purpose of this paper is to revisit and illustrate the correct heatline trajectories for various test cases.

Galerkin finite element based methodology and space adaptive grid have been used to simulate natural convective flows within the annular domains. The prediction of heatlines involves derivatives at the nodes, which are evaluated based on finite element basis functions and contributions from neighboring elements.

The heatlines in the earlier work indicate infeasible heat flow paths such as heat flow from one portion to the other of isothermal hot walls and heat flow across the adiabatic walls. Current results illustrate physically consistent heat flow paths involving perpendicularly emerging heatlines from hot to cold walls for conductive transport, long heat flow paths around the closed-loop heatline cells for convective transport and parallel layout of heatlines to the adiabatic walls. Results also demonstrate complex heatlines involving multiple flow vortices and complex flow structures.

Current work translates heatfunctions from energy flux vectors, which are determined by using basis sets. This work demonstrates the expected heatline trajectories for various scenarios involving conductive and convective heat transport within enclosures with an inner hot object as a first attempt, and the results are precursors for the understanding of energy flow estimates.