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This study aims to investigate heat transfer and entropy production in the non-similar flow of an incompressible fluid, with nonlinear convection and viscous dissipation. To obtain precise solutions, the Sparrow-Quack-Boerner local non-similarity method is implemented. The non-similarity arises from the nonlinear convection term present in the momentum equation. The non-similarity arises from the nonlinear convection term present in the momentum equation. Consequently, the inclusion of non-similarity terms into the energy equation is achieved through the interconnection of momentum and energy equations. Entropy generation is explored by employing the second law of thermodynamics. Numerical results from several truncation levels are presented in tabular form, and equations for both first and second-level truncations are generated. The one- and two-equation models are solved by implementing the Generalized Differential Quadrature Method (GDQM). Comparison with a second level of truncation reveals significantly greater inaccuracies in numerical results obtained from the first level. This discrepancy arose due to the omission of non-similar terms in the primary governing equations at the first truncation stage. The validity and accuracy of the derived numerical solutions are further demonstrated by the application of the GDQM and the midpoint method with Richardson extrapolation. Additionally, a plot of the numerical data produced from the second level of truncations is presented together with a discussion of the various physical factors. Increasing the mixed convection parameter accelerates fluid velocity, also when the viscous dissipation parameter increases, temperature and the Bejan number increase. The Prandtl number and the thickness of the thermal boundary layer are observed to be inversely related. Moreover, the quantity of entropy generated at the stretching surface and inside the boundary layer rises in proportion to the increases in the Prandtl and Eckert numbers. [ABSTRACT FROM AUTHOR]

• One-phase cylindrical Stefan problem with size-dependent thermal conductivity and convection is considered. • Time dependent temperature and Newton type temperature boundary conditions are subjected at the outer surface of the body. • Heat Balance Integral Method is applied to obtain the numerical result of the problem. • Convection produced pronounced impact on propagation rate of the melting interface. • It is observed that size-dependent thermal conductivity produced pronounced effect on melting process. The melting of a phase change material is the most applicable process in thermal energy storage system to capture heat transfer phenomena arising in a class of moving boundary problem. Demand of present technology motivates researchers to develop new theories and techniques for thermal management of a material. Experimental work on melting of a material may be difficult and development of robust theoretical formulation in cylindrical geometry with convection is critical. While there is already available study on cylindrical moving boundary problem, but still insufficient modeling of a size-dependent thermal conductivity and convection effect is not addressed properly, which is being considered in this paper and is expected to improve the previous understanding. In this work, a one-dimensional moving boundary problem with size-dependent heat conductivity and convection effect is analyzed in cylindrical geometry. In the mathematical model, we have considered a time-dependent temperature boundary condition which later assumed in periodic form, and a convective boundary condition at the outer surface of the body. The numerical result of the problem is obtained successfully via heat-balance integral method. Our numerical result is compared with a previous work and found in good acceptance. From mathematical framework, it is found that convection delayed melting process. With a size-no independent thermal conductivity, the rate of moving front decreases more in comparison to the fixed thermal conductivity. [ABSTRACT FROM AUTHOR]

The presence of micro-elements inside a complex fluidic medium (e.g., bubbly liquids, some lubricants, synovial fluids, certain man-made liquids, physiological fluids, polymeric suspensions, muddy fluids, blood liquids, and granular fluids) can change completely the rheological behavior of the resulting mixture according to the micropolar constitutive laws by providing a substantial inertial effect with an increase in the effective viscosity of the medium due to the micro-rotational impact of these micro-species. Motivating by the practical uses of the micropolar theory (e.g., blood rheology, ferrofluids, nanofluids, microfluidics, and liquid crystals), the present examination aimed to explore the main consequences arising from the convective motion of a bi-phasic mixture near a linearly stretching sheet for a micropolar nanofluidic medium including 60% of ethylene glycol, 40% of pure water, and a certain volume fraction of alumina nanoparticles. To achieve those main objectives, rigorous physical theories and assumptions are adopted in this respect to state properly the leading conservation equations based on the passive control approach of Buongiorno's model. By applying distinctive amendments, the governing boundary layer equations are transformed into a system of ordinary differential equations, which are solved numerically by a GDQLLM procedure for realistic boundary conditions. Moreover, the flow pattern and heat transfer appearances are revealed accordingly via multiple portrays, whose results are discussed comprehensively for various emerging parameters. Among the main interesting findings, it is found that the mass loading of alumina nanoparticles provides a significant thermal enhancement, speeds up its motion, and increases the coefficients of skin- friction and couple-stress at the stretching sheet. However, a dual behavior is noticed in the micro-rotation velocity profile against the increasing values of the volume fraction of nanoparticles [ABSTRACT FROM AUTHOR]

In today's era, energy resources are among the essential objectives for the economic advancement of any developed country. Alternatively, fossil fuels that meet a large percentage of the world's energy needs are becoming increasingly rare and their quantity is dwindling. Solar systems which convert solar radiation into useable heat or electricity now play a vital part in the production of renewable energies. Solar energy, despite its somewhat higher operating costs, is a better alternative energy type when considering environmental safety and substantial uncertainty about future energy provisions. Due to the demand for solar radiation in nowadays era, the features of solar radiation towards the heat transfer of three-dimensional magnetohydrodynamic generalized and sodium alginate-based iron oxide Fe 3 O 4 - SA nanofluid flows past a spinning disk are investigated in this article. Furthermore, the Brownian motion and thermophoresis phenomena, and Arrhenius activation energy are taken into account. The obtained equations are altered from partial differential equations into ordinary differential equations with the help of reasonable similarity transformations. The transformed system is solved thereafter semi-analytically by the homotopy analysis method. The convergence area of the applied technique is displayed with the help of figures and tables. Here, we have found that the variation in sodium alginate-based iron oxide nanofluid due to film width is greater as compared to generalized nanofluid. The greater magnetic parameter has reduced the velocity profiles. Also, the generalized nanofluid has gained extraordinary velocity as compared to Fe 3 O 4 - SA nanofluid. On the other hand, the greater thermophoresis parameter has augmented the temperature profile while the opposing impact is observed for the concentration profile. Additionally, the generalized nanofluid has gained the greater variation in temperature profile as compared to Fe 3 O 4 - SA nanofluid, while no difference is found for concentration profile. The augmented absorption parameter, irradiance parameter, and thermal Biot number have amplified the temperature profile. In addition, the temperature profile of the generalized nanofluid increases significantly as compared to Fe 3 O 4 - SA nanofluid. [ABSTRACT FROM AUTHOR]

Neglet of further analysis of Taylor-Couette flow problem is associated to the difficulty in research methodology for the examination of such transport phenomenon. However, little is known on the efficiency of Gear-Generalized Differential Quadrature Method (GGDQM) and thermal analysis across Taylor-Couette flow of second-grade fluid through Darcy-Forchheimer porous cylindrical medium subject to Lorentz force. The aforementioned research methodology was used to explore oscillatory magnetohydrodynamic (MHD) convective laminar flow of a second-grade fluid. The governing equations for the proposed fluid flow model are derived and simplified with the aid of suitable transformations in order to obtain nonlinear dimensionless set of partial differential equations (PDEs). The numerical solution of the corresponding problem was obtained using Gear-Generalized Differential Quadrature Method to provide appropriate graphical and tabular results in terms of velocity and temperature profiles, as well as the skin friction coefficient and Nusselet number on the surface of the inner cylinder. It is worth concluding that the elasticity of the fluidic medium has an enhancing influence on the dynamical and thermal features of the dynamics. However, the porosity characteristics of the medium together with the strength of the applied magnetic field exhibit a revere trend towards the velocity and temperature distributions. [ABSTRACT FROM AUTHOR]

In this analysis, the collective effect of temperature-reliant viscosity and internal heat generation on the appearance of convective motion in couple-stress fluids saturated a thin porous layer is investigated employing linear stability principle. The significant influences of viscosity deviation parameter Q , internal heat generation parameter H S , couple-stress parameter C s and Darcy number Da on the stability of the arrangement are obtained analytically and presented graphically in term of the critical thermal Darcy-Rayleigh number R t , c. Below the critical values, no convective motion arises in the considered system. It is recognized that the viscosity deviation parameter Q and internal heat generation parameter H S have destabilizing effect, while the couple-stress parameter C s and the Darcy number Da show stabilizing effect on the stability of the fluidic system. By increasing the couple-stress parameter C s from 0.2 to 0.4 and the Darcy number Da from 0.25 to 0.50, the critical thermal Darcy-Rayleigh number R t , c increased approximately 21% and 51%, respectively. [ABSTRACT FROM AUTHOR]