Thermal slip in oblique radiative nano-polymer gel transport with temperature-dependent viscosity : solar collector nanomaterial coating manufacturing simulation

Nano-polymeric solar paints and sol-gels have emerged as a major new development in solar cell/collector coatings offering significant improvements in durability, anti-corrosion and thermal efficiency. They also exhibit substantial viscosity variation with temperature which can be exploited in solar collector designs. Modern manufacturing processes for such nano-rheological materials frequently employ stagnation flow dynamics under high temperature which invokes radiative heat transfer. Motivated by elaborating in further detail the nanoscale heat, mass and momentum characteristics, the present article presents a mathematical and computational study of the steady, two-dimensional, non-aligned thermo-fluid boundary layer transport of copper metal-doped water-based nano-polymeric sol gels under radiative heat flux. To simulate real nano-polymer boundary interface dynamics, thermal slip is analysed at the wall. A temperature-dependent viscosity is also considered. The conservation equations for mass, normal and tangential momentum and energy are normalized via appropriate transformations to generate a multi-degree, ordinary differential, non-linear, coupled boundary value problem. Numerical solutions are obtained via the stable, efficient Runge-Kutta-Fehlberg scheme with shooting quadrature in MATLAB symbolic software. Validation of solutions is achieved with a Variational Iterative Method (VIM) utilizing Langrangian multipliers. The impact of key emerging dimensionless parameters i.e. obliqueness parameter, radiation-conduction Rosseland number (Rd), thermal slip parameter (ALPHA), viscosity parameter (m), nanoparticles volume fraction (PHI) on non-dimensional normal and tangential velocity components, temperature, wall shear stress, local heat flux and streamline distributions is visualized graphically. Shear stress and temperature are boosted with increasing radiative effect whereas local heat flux is reduced. Increasing wall thermal slip parameter depletes temperatures

Numerical study of chemical reaction effects in magnetohydrodynamic Oldroyd B oblique stagnation flow with a non-Fourier heat flux model

Reactive magnetohydrodynamic (MHD) flows arise in many areas of nuclear reactor transport. Working fluids in such systems may be either Newtonian or non-Newtonian. Motivated by these applications, in the current study, a mathematical model is developed for electrically-conducting viscoelastic oblique flow impinging on stretching wall under transverse magnetic field. A non-Fourier Cattaneo-Christov model is employed to simulate thermal relaxation effects which cannot be simulated with the classical Fourier heat conduction approach. The Oldroyd-B non-Newtonian model is employed which allows relaxation and retardation effects to be included. A convective boundary condition is imposed at the wall invoking Biot number effects. The fluid is assumed to be chemically reactive and both homogeneous-heterogeneous reactions are studied. The conservation equations for mass, momentum, energy and species (concentration) are altered with applicable similarity variables and the emerging strongly coupled, nonlinear non-dimensional boundary value problem is solved with robust well-tested Runge-Kutta-Fehlberg numerical quadrature and a shooting technique with tolerance level of 10−4. Validation with the Adomian decomposition method (ADM) is included. The influence of selected thermal (Biot number, Prandtl number), viscoelastic hydrodynamic (Deborah relaxation number), Schmidt number, magnetic parameter and chemical reaction parameters, on velocity, temperature and concentration distributions are plotted for fixed values of geometric (stretching rate, obliqueness) and thermal relaxation parameter. Wall heat transfer rate (local heat flux) and wall species transfer rate (local mass flux) are also computed and it is observed that local mass flux increases with strength of heterogeneous reactions whereas it decreases with strength of homogeneous reactions. The results provide interesting insights into certain nuclear reactor transport phenomena and furthermore a benchmark for more general CFD simulations

Effects of ramped wall temperature and concentration on viscoelastic Jeffrey’s fluid flows from a vertical permeable cone

In thermo-fluid dynamics, free convection flows external to different geometries such as cylinders, ellipses, spheres, curved walls, wavy plates, cones etc. play major role in various industrial and process engineering systems. The thermal buoyancy force associated with natural convection flows can exert a critical role in determining skin friction and heat transfer rates at the boundary. In thermal engineering, natural convection flows from cones has gained exceptional interest. A theoretical analysis is developed to investigate the nonlinear, steady-state, laminar, non-isothermal convection boundary layer flows of viscoelastic fluid from a vertical permeable cone with a power-law variation in both temperature and concentration. The Jeffery’s viscoelastic model simulates the non-Newtonian characteristics of polymers, which constitutes the novelty of the present work. The transformed conservation equations for linear momentum, energy and concentration are solved numerically under physically viable boundary conditions using the finite-differences Keller-Box scheme. The impact of Deborah number (De), ratio of relaxation to retardation time (λ), surface suction/injection parameter (fw), power-law exponent (n), buoyancy ratio parameter (N) and dimensionless tangential coordinate (Ѯ) on velocity, surface temperature, concentration, local skin friction, heat transfer rate and mass transfer rate in the boundary layer regime are presented graphically. It is observed that increasing values of De reduces velocity whereas the temperature and concentration are increased slightly. Increasing λ enhance velocity however reduces temperature and concentration slightly. The heat and mass transfer rate are found to decrease with increasing De and increase with increasing values of λ. The skin friction is found to decrease with a rise in De whereas it is elevated with increasing values of λ. Increasing values of fw and n, decelerates the flow and also cools the boundary layer i.e. reduces temperature and also concentration. The study is relevant to chemical engineering systems, solvent and polymeric processes

Finite element analysis of viscoelastic nanofluid flow with energy dissipation and internal heat source/sink effects

A numerical study is conducted of laminar viscoelastic nanofluid polymeric boundary layer stretching sheet flow. Viscous dissipation, surface transpiration (suction/injection), internal heat generation/absorption and work done due to deformation are incorporated using a second grade viscoelastic non-Newtonian nanofluid with non-isothermal associated boundary conditions. The nonlinear boundary value problem is solved using a higher order finite element method. The influence of viscoelasticity parameter, Brownian motion parameter, thermophoresis parameter, Eckert number, Lewis number, Prandtl number, internal heat generation and also wall suction on thermofluid characteristics is evaluated in detail. Validation with earlier non-dissipative studies is also included. The hp-finite element method achieves the desired accuracy at p=8 with comparatively less CPU cost per iteration (with less degrees of freedom, DOF) as compared to lower order finite element methods. The simulations have shown that greater polymer fluid viscoelasticity (k1) accelerates the flow. A rise in Brownian motion parameter (Nb) and thermophoresis parameter (Nt) elevates temperatures and reduce the heat transfer rates (local Nusselt number function). Increasing Eckert number increases temperatures whereas increasing Prandtl number (Pr) strongly lowers temperatures. Increasing internal heat generation (Q > 0) elevates temperatures and reduces the heat transfer rate (local Nusselt number function) whereas heat absorption (Q 0) reduces velocities and temperatures but elevates enhances mass transfer rates (local Sherwood number function), whereas increasing injection (fw <0) accelerate the flow, increases temperatures and depresses wall mass transfer rates. The study finds applications in rheological nano-bio-polymer manufacturing

Effects of thermophoresis and Brownian motion for thermal and chemically reacting Casson nanofluid flow over a linearly stretching sheet

The current research explores the problem of steady laminar flow of nanofluid on a two dimensional boundary layer using heat transfer of Cassona cross the linearly stretching sheet. The governing equations are partial differential equations which are transformed into non-linear ordinary differential equations by using some similarity transformation. The converted form of the combined non-linear higher-order ODEswith a set of boundary conditions are solved by means of Runge-Kutta 4th-order approach along with the shooting method. The nanoparticle concentration profiles, velocity, and temperature are examined by taking account of their influence of Prandtl number, "Brownian motion parameter ", Lewis number, thermophoresis, and Casson fluid parameter. It is reported that the temperature increase as Nt and Nb increases which causes thickening of the thermal boundary layer. Also it is observed that, there is increment in temperature profile for increasing values of Brownian motion parameter and the energy distribution grows with increment in the values of Thermophoresis parameter. The comparison for the local Nusselt & local Sherwood number has been tabulated with respect to variation of the Brownian Motion Parameter and Thermophoresis parameter. All the findings of the results are graphically represented and discussed.Funding The work of U.F.-G. was supported by the government of the Basque Country for the ELKARTEK21/10 KK-2021/00014 and ELKARTEK22/85 research programs, respectively

Differential transform solution for hall and ion slip effects on radiative-convective casson flow from a stretching sheet with convective heating

Magnetohydrodynamic (MHD) materials processing is becoming increasingly popular in the 21st century since it offers significant advantages over conventional systems including improved manipulation of working fluids, reduction in wear and enhanced sustainability. Motivated by these developments, the present work develops a mathematical model for Hall and Ion slip effects on non-Newtonian Casson fluid dynamics and heat transfer towards a stretching sheet with a convective heating boundary condition under a transverse magnetic field. The governing conservation equations for mass, linear momentum and thermal (energy) are simplified with the aid of similarity variables and Ohm’s law. The emerging nonlinear coupled ordinary differential equations are solved with an analytical technique known as the differential transform method (DTM). The impact of different emerging parameters is presented and discussed with the help of graphs and tables. Generally aqueous electro-conductive polymers are considered for which a Prandtl number of 6.2 is employed. With increasing Hall parameter and ion slip parameter the flow is accelerated whereas it is decelerated with greater magnetic parameter and rheological (Casson) fluid parameter. Skin friction is also decreased with greater magnetic field effect whereas it is increased with stronger Hall parameter and ion slip parameter values

A numerical study of magnetohydrodynamic transport of nanofluids from a vertical stretching sheet with exponential temperature-dependent viscosity and buoyancy effects

In this paper, a mathematical study is conducted of steady incompressible flow of a temperature-dependent viscous nanofluid from a vertical stretching sheet under applied external magnetic field and gravitational body force effects. The Reynolds exponential viscosity model is deployed. Electrically-conducting nanofluids are considered which comprise a suspension of uniform dimension nanoparticles suspended in viscous base fluid. The nanofluid sheet is extended with a linear velocity in the axial direction. The Buonjiornio model is utilized which features Brownian motion and thermophoresis effects. The partial differential equations for mass, momentum, energy and species (nano-particle concentration) are formulated with magnetic body force term. Viscous and Joule dissipation effects are neglected. The emerging nonlinear, coupled, boundary value problem is solved numerically using the Runge–Kutta fourth order method along with a shooting technique. Graphical solutions for velocity, temperature, concentration field, skin friction and Nusselt number are presented. Furthermore stream function plots are also included. Validation with Nakamura’s finite difference algorithm is included. Increasing nanofluid viscosity is observed to enhance temperatures and concentrations but to reduce velocity magnitudes. Nusselt number is enhanced with both thermal and species Grashof numbers whereas it is reduced with increasing thermophoresis parameter and Schmidt number. The model is applicable in nano-material manufacturing processes involving extruding sheets

Radiative and magnetohydrodynamics flow of third grade viscoelastic fluid past an isothermal inverted cone in the presence of heat generation/absorption

A mathematical analysis is presented to investigate the nonlinear, isothermal, steady-state, free convection boundary layer flow of an incompressible third grade viscoelastic fluid past an isothermal inverted cone in the presence of magnetohydrodynamic, thermal radiation and heat generation/absorption. The transformed conservation equations for linear momentum, heat and mass are solved numerically subject to the realistic boundary conditions using the second-order accurate implicit finite-difference Keller Box Method. The numerical code is validated with previous studies. Detailed interpretation of the computations is included. The present simulations are of interest in chemical engineering systems and solvent and low-density polymer materials processing

Chemical reaction and Soret effects on hydromagnetic micropolar fluid along a stretching sheet

AbstractFree convection effects of a micropolar fluid along a stretching sheet embedded in a porous medium in the presence of a volumetric non-uniform heat source is investigated in the present paper. Thermal diffusion and first order chemical reaction are also considered in the present study to govern the flow characteristic. The generalization of the earlier studies centers round: (i) The magnetohydrodynamic flow is made to pass through a porous medium characterized by a non-Darcian drag coefficient affecting the momentum equation. (ii) The energy equation is modified with the interplay of non-uniform heat source. (iii) Consideration of chemically reactive species characterized by first order chemical reaction and thermal diffusion i.e. Soret modifying the equation of species concentration. Similarity transformation technique is used to transform the governing nonlinear partial differential equations into ordinary differential equations. The numerical solutions are achieved showing the effects of pertinent parameters. For verification of the present findings the results of this study have been compared with the earlier works in particular cases

Analysis of nonlinear convection-radiation in chemically reactive Oldroyd-B nanoliquid configured by a stretching surface with Robin conditions: applications in nano-coating manufacturing

Motivated by emerging high-temperature manufacturing processes deploying nanopolymeric coatings, the present communication studies nonlinear thermally radiative OldroydB viscoelastic nanoliquid stagnant-point flow from a heated vertical stretching permeable surface. Robin (mixed derivative) conditions are utilized to better represent coating fabrication conditions. The nanoliquid analysis is based on Buongiorno's two-component model which elaborates Brownian movement and thermophoretic attributes. Nonlinear buoyancy force and thermal radiation formulations are included. Chemical reaction (constructive and destructive) is also considered since coating synthesis often features reactive transport phenomena. Via a similarity approach, an ordinary differential equation model is derived from the primitive partial differential boundary value problem. Analytical solutions are achieved employing homotopy analysis scheme. The influence of emerging dimensionless quantities on transport characteristics is comprehensively elaborated with appropriate data. The obtained analytical outcomes are compared with available limiting studies and good correlation is achieved. The computations show that the velocity profile is diminished with increasing relaxation parameter whereas it is enhanced when retardation parameter is increased. Larger thermophoresis parameter induces temperature and concentration enhancement. The heat and mass transfer rates at the wall are increased with an increment in temperature ratio and first order chemical reaction parameters while contrary effects are observed for larger thermophoresis, fluid relaxation and Brownian motion parameters. The simulations find applications in stagnation nano-polymeric coating of micromachines, robotic components and sensor