Heat Radiation Effects Research Articles

Numerical treatment for the boundary layer flow of Sutterby nanofluid through porous medium with planktonic microorganisms over a stretching Riga cylindrical tube

The primary objective of this study is to create a novel mathematical model that accounts for the combined effects of heat radiation and the Sutterby nanofluid convection flow caused by a stretched Riga cylindrical tube that contains planktonic microorganisms utilizing the non-Darcy flow (Forchheimer model). Mathematically, the issue is modulated by a nonlinear partial differential equations system (PDEs), which are then converted into an ordinary differential equations system (ODEs) with the use of appropriate similarity transformations. Using MATHEMATICA software's built-in command (Parametric ND Solve), the generated ODEs system is resolved numerically. A series of figures are used to demonstrate numerically and graphically the influence of the physical parameters on the fluid behaviour. The performed numerical simulation indicated that thermal radiation is a property of temperature that decreases with the increase of thermal radiation parameter. Furthermore, as the temperature decreases, the diameter of the nanoparticles grows, resulting in an increase in the volume and concentration of the nanoparticle and making it more effective near to tumor tissues. Since it specifically targets tumour cells for localized destruction, it can be employed as a radiotherapy agent to cause localized increases in doses of radiation (Radiotherapy of oncology).

Impacts of Buoyancy and Joule Heating on Unsteady MHD Fluid Flow Along a Semi‐Infinite Vertical Porous Plate With Dufour, Chemical Reaction, and Radiation Effect

ABSTRACTAn analytical solution for unsteady, incompressible, laminar MHD fluid flow involving mass and heat transfer along a semi‐infinite vertical moving flat plate in a porous medium have been studied in this paper. Effects of heat radiation and absorption, Joule heating, Dufour, thermal and solutal buoyancy, and first order chemical reaction of are discussed under suitable physical conditions. It is postulated that the plate will migrate in the fluid's motion's direction due to the presence of a uniform magnetic field normal to the porous surface. The regular perturbation technique is used to solve the dimensionless governing equations. The mathematical derivations for fluid velocity, temperature, and concentration are evaluated; apart from that, skin friction, rate of mass and heat transfer at the plate are also expressed. The present outcomes are compared with previously obtained results and are found to be in excellent agreement. It is observed that the fluid velocity and temperature enhanced with thermal and solutal buoyancy forces as well as the Dufour effect. Also, with an increase in chemical reaction parameter, there is a decrease in fluid velocity, temperature, and concentration. Skin friction and Nusselt number increase with higher heat absorption parameter values. Schmidt number and chemical reaction parameter both lead to a rise in Sherwood number. Applications for these models have been observed in a number of industrial and technical methods.

Electrochemical Nanoimprinting of Colored Infrared Reflective Patterns for Radiative Heating

AbstractMetallic nanostructures hold immense promise for radiative heating technology because of their distinctive capability to simultaneously achieve high mid‐infrared reflectance and generate vibrant colors through structural or plasmonic effects. However, fabricating metallic nanostructures remains challenging using traditional top–down techniques. Here, the solid‐state superionic stamping (S4) process is demonstrated as a scalable and economical tool to electrochemically imprint metallic grid nano‐patterns onto flexible substrates. With precise control over grid width and length at the nanoscale, the S4 approach enables the fabrication of nano‐patterned grid coatings exhibiting a spectrum of colors. These coatings also show high mid‐infrared reflectance exceeding 80% at 9.5 µm, leading to radiative heating effects of 5.9 and 3.1 °C compared to bare skin and cotton, respectively. This work introduces a viable strategy for creating colored infrared‐reflective patterns, paving the way for diverse thermal management applications.

Heat transfer enhancement in magnetohydrodynamic hybrid nanofluids over a Bi-directional extending sheet with slip and convective conditions

The hybrid nanofluids can enhance cooling systems in microelectronics by enhancing heat dissipation from processes which makes them vital for maintaining optimal performance. They are also beneficial in solar systems where efficient heat transfer is essential for exploiting the energy detention. Thus, this study has studied the three-dimensional flow of a water-based hybrid nanofluid comprising of Fe3O4 and CuO nanoparticles on a bi-directional extending sheet. The bi-directional extending sheet is subjected to thermal convective and velocity slip conditions. In addition, the effects of heat source, magnetic field, thermal radiation, viscous dissipation, and Joule heating are employed. The partial differential equations (PDEs) that represent the mathematical model are subsequently converted to ordinary differential equations (ODEs) by applying the appropriate similarity variables. The shooting technique is incorporated to determine the computational solution of the converted ODEs. The effectiveness of the current study is confirmed by published results, which also validate the current outcomes. Based on the results, it is concluded that CuO and Fe3O4 solid nanoparticle volume fractions improved the thermal distribution while decreasing the velocity distributions along x and y-axes. The thermal distribution is improved by the thermal heat source, thermal radiation, thermal Biot number, and thermal Eckert numbers. CuO-water nanofluid has a higher velocity panel than CuO-Fe3O4/water hybrid nanofluid. Conversely, the CuO-Fe3O4/water hybrid nanofluid has a higher thermal profile than the CuO-water nanofluid. CuO-water nanofluid flow has higher surface drags than CuO-Fe3O4/water hybrid nanofluid flow. CuO-water nanofluid has a lower heat transfer rate than CuO-Fe3O4/water hybrid nanofluid.

Effects of exponentially stretching sheet for MHD Williamson nanofluid with chemical reaction and thermal radiative

This paper explores the combined effects of heat radiation, viscous dissipation, and chemical reactions on the steady flow of Williamson nanofluid over an exponentially stretched sheet. The Governing non-linear Partial Differential Equations (PDE's), converted to couple nonlinear Ordinary ODE's by using similarity transformation, which are solved numerically using the Runge-Kutta-Fehlberg method along with the shooting technique. The study shows detailed analysis of the behaviour of Williamson nanofluid under the influence of thermal radiation and magnetic fields, having relevant industrial applications in cooling technologies and polymer processing. The results show that increasing the magnetic field parameter reduces the fluid velocity, while higher thermal radiation and Brownian motion parameters significantly enhance heat transfer rate withing the boundary region.

Thermal diffusivity measurement of polymer microfibers while eliminating the effect of heat radiation

The thermal transport properties of polymer fibers are important for heat dissipation in apparel, matrix of wearable devices, and so on. However, it is difficult to precisely determine the thermal properties of a single polymer fiber because of non-negligible thermal radiation due to its relatively low thermal conductivity and high surface-area-to-volume ratio. Here, we developed a system in which the apparent thermal diffusivity and size of microfibers can be measured to estimate their intrinsic thermal diffusivity. We determined the thermal diffusivities of three fibrous materials: silk, spider silk, and cellulose microfibers to be 4.2 (±0.8)×10−7, 1.8 (±0.7)×10−7, and 4.7 (±0.5)×10−7, respectively. For all fibers, the apparent thermal diffusivity strongly depended on the fiber size, indicating that eliminating the radiation effect is indispensable for determining the thermal transport properties of polymer microfibers.

Investigation of heat generation and radiation effects on boundary layer flow of Prandtl liquid with Cattaneo–Christov double diffusion models

In this analysis, a bidirectional stretched sheet is used to produce a 3D\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{D}$$\\end{document} flow of Prandtl liquid with improve mass diffusion and heat conduction models. This study advances knowledge of magnetohydrodynamics, radiation impacts, and heat production in fluid dynamics and transport processes. The Prandtl fluid model is critical for modeling non-Newtonian fluids, capturing its viscoelastic features, and allowing for precise simulation in industrial applications. It gives a mathematical foundation for analyzing complex fluid behaviors, which is necessary for optimizing operations utilizing such fluids. It uses the boundary layer method to simplify the fundamental equations and Cattaneo–Christov double diffusion models. The optimal homotopy analysis method is used to solve nonlinear ODEs caused by non-dimensional similarity variables. This investigation undertakes the calculation of drag coefficient for surfaces mass transfer rates and heat transfer rates proximate to the solid boundary. Furthermore, it conducts a comprehensive analysis of the influences exerted by various parameters on concentration and temperature profiles employing graphical representations for a rigorous examination. The Prandtl fluid model describes the viscoelastic characteristics of non-Newtonian fluids through constitutive equations, dimensional evaluation, and numerical simulations, which are frequently validated by experiments. The results show that changes in thermal and concentration relaxation parameters are accompanied by a decline in temperature. Temperature field rises as the thermal radiation parameter and heat generation increases. The work's novelty consists in its advanced modeling of Prandtl non-Newtonian fluids via Cattaneo–Christov double diffusion models, which incorporate magnetohydrodynamics and radiation effects and use optimal homotopy analysis for accurate parametric analyses of heat and mass transfer.

Study on the electromagnetic-thermal-mechanical coupling damage of concrete under microwave irradiation

The paper aims to explore the thermal response of three-dimensional random aggregate concrete model under microwave irradiation. The multi-field distribution in concrete by coupling of the electromagnetics, heat transfer and solid mechanics in COMSOL Multiphysics software under microwave irradiation was investigated. The results shown that the different in dielectric properties and thermal expansion coefficients between aggregate and mortar resulted in the generation of temperature gradients and stress concentration at interface. In addition, due to the larger expansion coefficient of aggregate compared to mortar, stress concentration was formed at interface, promoting the damage of concrete. Microwave power exhibited a notable influence on thermal accumulation and thermal stress. Higher microwave power correlating to higher growth rates of temperature and stress. The Von Mises stress in mortar was significantly greater than that in aggregate, as energy absorption reached a certain threshold, damage occurred in mortar. In addition, microwave frequency significantly influenced the distribution of electric field within the cavity, and also the energy conversion ratio of aggregate within concrete. The study could provide a comprehensive understanding of heating effects of microwave radiation on concrete, providing the mechanical basis for microwave-assisted concrete recovery.

A simple model linking radiative–convective instability, convective aggregation and large-scale dynamics

Abstract. A simple model is presented which is designed to analyse the relation between the phenomenon of convective aggregation at small scales and larger-scale variability that results from coupling between dynamics and moisture in the tropical atmosphere. The model is based on single-layer dynamical equations coupled to a moisture equation to represent the dynamical effects of latent heating and radiative heating. The moisture variable q evolves through the effect of horizontal convergence, nonlinear horizontal advection and diffusion. Following previous work, the coupling between moisture and dynamics is included in such a way that a horizontally homogeneous state may be unstable to inhomogeneous disturbances, and, as a result, localised regions evolve towards either dry or moist states, with divergence or convergence respectively in the horizontal flow. The time evolution of the spatial structure of the dry and moist regions is investigated using a combination of theory and numerical simulation. One aspect of the evolution is a spatial coarsening that, if moist regions and dry regions are interpreted as convecting and non-convecting respectively, represents a form of convective aggregation. When the weak temperature gradient (WTG) approximation (i.e. a local balance between heating and convergence) applies, and horizontal advection is neglected, the system reduces to a nonlinear reaction–diffusion equation for q, and the coarsening is a well-known aspect of such systems. When nonlinear advection of moisture is included, the large-scale flow that arises from the spatial pattern of divergence and convergence leads to a distinctly different coarsening process. When thermal and frictional damping and f-plane rotation are included in the dynamics, there is a dynamical length scale Ldyn that sets an upper limit for the spatial coarsening of the moist and dry regions. The f-plane results provide a basis for interpreting the behaviour of the system on an equatorial β plane, where the dynamics implies a displacement in the zonal direction of the divergence relative to q and hence to coherent equatorially confined zonally propagating disturbances, comprising separate moist and dry regions. In many cases the propagation speed and direction depend on the equatorial wave response to the moist heating, with the relative strength of the Rossby wave response to the Kelvin wave response determining whether the propagation is eastward or westward. Within this model, the key overall properties of the propagating disturbances, the spatial scale and the phase speed, depend on nonlinearity in the coupling between moisture and dynamics, and any linear theory for such disturbances therefore has limited usefulness. The model described here, in which the moisture and dynamical fields vary in two spatial dimensions and important aspects of nonlinearity are captured, provides an intermediate model between theoretical models based on linearisation and one spatial dimension and general circulation models (GCMs) or convection-resolving models.

Why Does Atmospheric Radiative Heating Weaken Midlatitude Cyclones?

AbstractRecent work has indicated that atmospheric radiative heating reduces the kinetic energy of large‐scale eddies in the midlatitudes. However, a physical mechanism that connects radiation to the midlatitude eddy kinetic energy is still uncertain. Using a high‐resolution general circulation model we perform an experiment in which the radiative cooling profile at each model time step is overwritten with the climatological mean, computed from a control simulation. This approach separates the mean and transient effects of radiative heating on the extratropical circulation. We find that, when radiative heating is fixed, the globally‐averaged eddy kinetic energy is enhanced by ∼6%. We show that thermal radiation dampens temperature anomalies near the surface and tropopause in low‐pressure systems, destroying eddy available potential energy and eddy kinetic energy. We identify this as a possible mechanism by which atmospheric radiative heating weakens midlatitude cyclones.

Convective diffusive thermal flow over an inclined surface with viscous dissipation and aligned magnetic field applications

This investigation incorporating the fluctuation in heat and mass transfer associated to the mixed convection magnetized flow of viscous fluid due to inclined surface with porous media. The contribution of Soret effects and viscous dissipation appliances is addressed. Furthermore, the heat transfer improvement is also assessed by thermal radiation, heat source and joule heating effects. The chemical reaction enrollment is also studied for concentration phenomenon. The convection of problem into non-dimensional framework is based on implication of new variables. The perturbation technique is followed to tracking the analytical outcomes. Physical visualization and interpretation of results under the influence of perturbed parameters have been studied. It is observed that heat and mass transfer enhances due to Soret number. Presence of chemical reaction leads to decrement of concentration profile. Claimed results presents applications in heat and mass transfer processes, chemical reaction, manufacturing systems, chemical engineering, extrusion processes etc.

Investigation of Third-Grade fluid flow in an inclined Microchannel: Utilizing the Hermite wavelet technique for second law analysis

Microfluidics serves as an interdisciplinary bridge between thermal and engineering fields, offering flexible solutions for addressing heat transport obstacles across diverse sectors. This study explores entropy production in the flow of a third-grade fluid through an inclined microchannel, considering radiation and convective heating effects. The analysis includes various factors such as viscous dissipation, natural convection, Joule heating, magnetic fields, and a uniform heat source/sink. The aim is to assess the energy efficiency of the system by minimizing entropy generation. To achieve this, governing equations are transformed into dimensionless forms using non-dimensional parameters. These equations are then solved using the Hermite wavelet method, a novel approach in this field. The impact of the Biot number on temperature exhibits a dual nature: temperature increases towards the upper plate of the channel while decreasing towards the lower plate. Similarly, entropy generation displays a dual behavior for higher values of Qt and Re, decreasing at the lower plate and increasing at the upper plate. This research offers valuable insights for optimizing energy efficiency in various applications, including pumps, heat exchangers, and energy systems, with potential applications in electronics cooling and renewable energy collection.

Investigation of heat transfer phenomenon in a complex wavy divergent channel under the effects of thermal radiation, joule heating and electroosmosis

The heat transfer analysis in electro osmotic flow of nanofluid is studied through the complex wavy channel under the consideration of joule heat and thermal radiation effects. The Ellis fluid is considered a base fluid and gold particles are suspended in them. The complex system of equations is converted to dimensionless form with the help of dimensionless transformation and parameters. The concepts of longer wavelength and lower Reynolds number are utilized to simplify the problem and obtain the exact solution of velocity and temperature distribution by using the built-in command DSolve in the mathematical software MATHEMATICA 13.3. The graphs are plotted with the same software to check the effects of various parameters on velocity, temperature, heat transfer rate, and streamlines with the following range of parameters − 5 ≤ U H S ≤ 5 , 0 ≤ β ≤ 5 , 0 ≤ α ≤ 3 , 0 < k ≤ 5 , 0 ≤ ϕ ≤ 0.04 , 20 ≤ P r ≤ 28 , 0 ≤ R n ≤ 5 . The computational results reported that the electroosmotic parameter, Helmholtz-Smoluchowski velocity, and material parameter reduce the velocity in the initial region and enhance the final region of the channel. It is also noted that the velocity profile exhibits increasing and decreasing behavior in the initial and final region respectively with upgrading the values of volumetric concentration of nanoparticles. The heat transfer rate is strongly affected by material parameters α and β , thermal radiation parameter, Prandtl number, and joule heating and these parameters promote the heat transfer rate of the system. The novel research of the current study shows the examination of the heat transfer analysis of blood-gold nanofluid in the presence of an electrical double layer and thermal radiation with the help of the Ellis nanofluid flow model through a complex symmetric wavy channel. The results of the present investigation are useful for the early detection of renal diseases and monitoring of disease progression because of the unique properties of gold nanoparticles. The role of gold nanoparticles as imaging agents, drug delivery antioxidant properties, biosensing, targeted therapy, and renal clearance makes them the perfect choice for renal diseases.

Magnetic field, radiation, and Joule heating effects on natural convection Williamson fluid flow through a vertical channel using Levenberg–Marquardt algorithm

The study examined the natural convection flow of Williamson fluid through a vertical channel under the influence of the magnetic field, radiation, and joule heating effects. The governing partial differential equations are turned into ordinary differential equations using suitable transformations and solved by using the spectral quasi-linearization method (SQLM). The study explained a neural network algorithm called feed-forward back-propagation using the Levenberg–Marquardt technique (BPFF-LMT). Furthermore, a reference dataset is created for several parameters, including the magnetic parameter, Hall parameter, radiation parameter, Weissenberg number, Biot number, and Joule heating parameter. This dataset encompasses velocity and temperature profiles for different scenarios, employing the SQLM. The BPFF-LMT method’s accuracy was evaluated through a comprehensive analysis involving training, validation, and testing phases, along with mean squared error, error histograms, and performance and regression graphs. The artificial neural network’s result shows good accuracy when compared to the SQLM solution numerically. The results are presented visually through graphical representation and further analyzed quantitatively concerning the active parameters featured in the mathematical formulations. The result indicates that increasing values of the magnetic parameter result in decreased velocity and temperature profiles. Additionally, the heat transfer rate increases in the left channel. Both the radiation parameter and Weissenberg number contribute to higher velocity and temperature profiles, leading to increased skin friction in the left channel. The accuracy of the BPFF-LMT method is illustrated through graphs displaying the absolute error falling within the range of [Formula: see text] to [Formula: see text].

Investigation of thermal radiation and joule heating effects on variable viscosity Casson nanofluid flow over a stretching sheet in Darcy–Forchheimer porous medium

Nanofluids possess unique thermal and rheological properties that offer significant advantages in enhancing heat transfer efficiency in various applications, such as heat exchangers, cooling systems, and microdevices. In this study, we investigate the combined effects of thermal radiation, Joule heating, variable viscosity, and a two-phase model on the flow behavior and heat transfer characteristics of a magnetohydrodynamic Casson nanofluid flowing over a stretching sheet in Darcy-Forchheimer porous media. The governing partial differential equations are converted into a system of first-order ordinary differential equations numerically solved using the bvp5c package in MATLAB. Consequently, the result indicates that the velocity profile increases with thermal radiation, variable viscosity, and viscous dissipation, decreasing with the magnetic field, permeability index, and Forchheimer coefficient. Also, the temperature profile shows an increase with the permeability index, viscous dissipation, and thermal radiation, but a decrease with the Forchheimer Coefficient, variable viscosity, and magnetic field. Additionally, the concentration profile exhibits an increase with the Forchheimer coefficient and permeability index, and variable viscosity while it decreases with viscous dissipation, magnetic field, and thermal radiation. Analyzing the skin friction coefficient reveals an increase with magnetic field and thermal radiation and a decrease with permeability index and Forchheimer coefficient as well as variable viscosity. Moreover, the local heat transfer rate demonstrates an increase with the variable viscosity, and magnetic field as well as the Forchheimer coefficient and permeability index. At the same time, it decreases with the viscous dissipation. Furthermore, the local mass transfer rate displays an increase with the magnetic field and thermal radiation and viscous dissipation, while it decreases with the variable viscosity as well as permeability index, viscous dissipation, and Forchheimer coefficient. Finally, the current findings are compared with that of the existing literature and a sound agreement was established.

Thermal improvement of the porous system through numerical solution of nanofluid under the existence of activation energy and Lorentz force

Background: The important physical phenomenon under the action of microgravity is called Marangoni convection. This convection occurs due to the surface tension gradient of the interface, which has various applications, such as crystal growth melt. Objective: This research aims to explore the effects of heat radiation, heat generation, viscous dissipation, and activation energy on the Marangoni flow of nanofluids. The development of the mathematical model takes into account the activation energy and uniform liquid properties. The Darcy–Forchheimer model is also used to emphasize the influence of porous media parameters. Method: The numerical algorithm of the shooting method based on Newton’s Raphson method is developed in MATLAB and used to find the numerical solution of the obtained equations. Findings: The temperature field is enhanced by thermophoresis parameters, Brownian motion parameters, Schmitt number, and magnetic number, but decreases in the range where the Marangoni ratio increases. The Nusselt and Sherwood numbers are increased and decreased via the Marangoni ratio parameter, respectively. Research gap: The numerical solution of the Marangoni flow of nanofluids in a porous medium under the effects of heat radiation, heat generation, viscous dissipation, and activation energy was not discussed before.

Heat and mass transfer analysis of non‐miscible couple stress and micropolar fluids flow through a porous saturated channel

AbstractThis study examines the flow rate, Bejan number transportation, concentration distribution and thermal characteristics of an immiscible couple stress‐ micropolar fluids within a porous channel. The authors focus on the effects of heat radiation and an angled magnetic field on the thermal dispersion, concentration distribution and entropy formation of two different types of incompressible immiscible micropolar and couple stress fluids inside a porous channel. Here, the static walls of the channel are isothermal, and the pressure gradient in the flow domain's entrance zone is constant. In this flow problem, we tried to simulate thermal radiation in the energy equation by applying Rosseland's diffusion approximation. To solve the problem, the authors have used no‐slip conditions at the channel's immovable walls, a continuity of temperature profile, shear stresses, thermal flux, linear velocity, and micro‐rotational velocity over the fluid‐fluid interface. The equations that govern the flow of immiscible fluids are solved using a well‐defined methodology and both the temperature and flow field are then evaluated using a closed‐form solution. The mathematical results of the thermal distribution and flow velocity are used to derive the Bejan number distribution and the entropy generation number. Graphical discussions are used to illustrate the impact of different emerging factors on the model's flow and thermal properties, which describe the major impact of the proposed model. These variables involve the micropolarity parameter, Reynolds number, inclination angle parameter, radiation parameter, and Hartmann number. The outcomes of the present models are corroborated by previously established results available in the literature.

On the thermal performance of radiative stagnation-point hybrid nanofluid flow across a wedge with heat source/sink effects and sensitivity analysis

The present article aims to examine the thermal performance and the sensitivity analysis of a GO−TiO2/water hybrid nanofluid in the presence of different nanoparticle shapes along with heat absorption and thermal radiation effects over a wedge geometry. Analyzing the effects of heat generation and radiation effects is one of the key studies conducted by researchers in various nanofluid flows over some required geometries. However, a combined study of these effects has yet to be studied over a moving wedge, and that combination defines the novelty of the work. Similarity transformations are implemented to the governing equations to obtain the final set of nondimensional equations, which are solved using the bvp4c code in MATLAB. The results obtained were in close agreement with the published results. The Nusselt number decreased with an increase in the heat source parameter Q, and it increased with an increasing Hartree pressure gradient β and thermal radiation parameter Rd. The sensitivity is statistically analyzed for the variations in radiation effect, heat source, and pressure gradient parameters on the Nusselt number. The high values for R2=99.99% and Adj R2=99.96% validate the ANOVA results obtained using a Box–Behnken design (BBD) model in the response surface methodology (RSM) with 14 degrees of freedom. The input parameters Rd and β show positive sensitivity, while Q shows negative sensitivity toward the skin friction. The Nusselt number proves to be most sensitive toward the pressure gradient parameter. TiO2, graphene (Gr), and the derivative forms of graphene, are gaining much importance due to their wide applications in the oil and petroleum industries. Thus, this study contributes to lubrication purposes, emulsion stabilizers, oxalic acid removal, anti-corrosive properties, etc.

Global aviation contrail climate effects from 2019 to 2021

Abstract. The current best-estimate of the global annual mean radiative forcing (RF) attributable to contrail cirrus is thought to be 3 times larger than the RF from aviation's cumulative CO2 emissions. Here, we simulate the global contrail RF for 2019–2021 using reanalysis weather data and improved engine emission estimates along actual flight trajectories derived from Automatic Dependent Surveillance–Broadcast telemetry. Our 2019 global annual mean contrail net RF (62.1 mW m−2) is 44 % lower than current best estimates for 2018 (111 [33, 189] mW m−2, 95 % confidence interval). Regionally, the contrail net RF is largest over Europe (876 mW m−2) and the USA (414 mW m−2), while the RF values over East Asia (64 mW m−2) and China (62 mW m−2) are close to the global average, because fewer flights in these regions form persistent contrails resulting from lower cruise altitudes and limited ice supersaturated regions in the subtropics due to the Hadley Circulation. Globally, COVID-19 reduced the flight distance flown and contrail net RF in 2020 (−43 % and −56 %, respectively, relative to 2019) and 2021 (−31 % and −49 %, respectively) with significant regional variations. Around 14 % of all flights in 2019 formed a contrail with a net warming effect, yet only 2 % of all flights caused 80 % of the annual contrail energy forcing. The spatiotemporal patterns of the most strongly warming and cooling contrail segments can be attributed to flight scheduling, engine particle number emissions, tropopause height, and background radiation fields. Our contrail RF estimates are most sensitive to corrections applied to the global humidity fields, followed by assumptions on the engine particle number emissions, and are least sensitive to radiative heating effects on the contrail plume and contrail–contrail overlapping. Using this sensitivity analysis, we estimate that the 2019 global contrail net RF could range between 34.8 and 74.8 mW m−2.

Effects of Heat Generation and Radiation on Darcy Convective Non-Newtonian Power Law Liquid with Yield Stress over a Vertical Plate

The effects of heat flux, and thermal buoyancy on mixed convective flow for a non-Newtonian power law liquid with yield stress via a vertical plate filled with a porous material under the influence of thermal radiation, and heat production are investigated in this topic. For this model, The PDE's that govern the flow are constructed and converted to a set of ODE's using appropriate transformation and the resultant ODEs are quantitatively determined using Shooting technique. The impacts of different flow regulating factors such as index parameter, yield stress, radiation, and heat generation are illustrated through graphical representation for fluid properties. This research shows that the velocity distribution, Nusselt and Sherwood numbers declines as the dimensionless rheological parameter rise, but temperature and concentration profiles exhibit the reverse tendency. Also, the velocity, temperature curves and mass flux grow as the radiation parameter rises, whereas the concentration curves and heat flux fall as the radiation parameter rises. For a specific case, a comparison with Lakshmi Narayana et al.,13 was made, and a great agreement was established.