Opposing Flow Case Research Articles

Stacking regression model approach to mixed convection flow of ternary- nanofluid over slanted surface with magnetic field, waste discharge concentration, and joule heating effects

The current work is carried out to investigate the mixed convection flow behavior of ternary-based nanofluid over an inclined surface in the presence of a magnetic field, waste discharge concentration, and joule heating effects. The governing equations with proper assumptions were converted into ordinary differential equations (ODEs) form by implementing suitable similarity constraints and solved with Runge Kutta Fehlberg 4th 5th order and shooting scheme. The stacking regression model approach is implemented along with the Runge Kutta Fehlberg 4th 5th order technique. The obtained outcomes are presented with graphs, and model correctness is assessed using the combination of Gaussian Process Regression (GPR), Extra Tree Regression (ETR), and Random Forest (RF). The consistency and stability of the model are demonstrated by the closely linked testing and training data. The study outcomes show that the rise in the magnetic constraint will improve the velocity profile while improved values of local pollutant external source and external pollutant source variation parameters will enhance the concentration profile. Enhancement in Eckart number and solid volume fraction values will improve the rate of thermal distribution. Ternary nanofluid shows significant improvement than nanofluid. The surface drag force is increased about 8 %-9 % in assisting flow case and 8 %-17 % for opposing flow case for different values of magnetic parameter, the rate of thermal distribution improved from 75.54 % to 11.55 % in assisting flow case and 16.87 % to 25.70 % in opposing flow case for different values of Eckert number. The study's results might contribute to the advancement of more effective heat exchangers and cooling systems for electronics and engines. Exploration and extraction of oil, as well as the creation of efficient water purification systems.

Heat transfer analysis of buoyancy opposing radiated flow of alumina nanoparticles scattered in water-based fluid past a vertical cylinder

Cooling and heating are two critical processes in the transportation and manufacturing industries. Fluid solutions containing metal nanoparticles have higher thermal conductivity than conventional fluids, allowing for more effective cooling. Thus, the current paper is a comparative exploration of the time-independent buoyancy opposing and heat transfer flow of alumina nanoparticles scattered in water as a regular fluid induced via a vertical cylinder with mutual effect of stagnation-point and radiation. Based on some reasonable assumptions, the model of nonlinear equations is developed and then tackled numerically employing the built-in bvp4c MATLAB solver. The impacts of assorted control parameters on gradients are investigated. The outcomes divulge that the aspect of friction factor and heat transport upsurge by incorporating alumina nanoparticles. The involvement of the radiation parameter shows an increasing tendency in the heat transfer rate, resulting in an enhancement in thermal flow efficacy. In addition, the temperature distribution uplifts due to radiation and curvature parameters. It is discerned that the branch of dual outcomes exists in the opposing flow case. Moreover, for higher values of the nanoparticle volume fraction, the reduced shear stress and the reduced heat transfer rate increased respectively by almost 1.30% and 0.0031% for the solution of the first branch, while nearly 1.24%, and 3.13% for the lower branch solution.

Dual solutions and linear temporal stability analysis of mixed convection flow of non-Newtonian special third grade fluid with thermal radiation

The present study aims to investigate the steady mixed convection stagnation-point flow of a special third grade fluid over a vertical stretching/shrinking sheet with the inclusion of suction and thermal radiation effects. The governing momentum and energy equations are transformed into a system of ordinary differential equations (ODEs) using the Lie scaling group of transformations. The resulting system of highly nonlinear boundary value problems (BVPs) is solved numerically with the help of Matlab solver ‘bvp4c’. Dual similarity solutions are found for the opposing flow case within the range λc≤λ<0, where λ is the buoyancy parameter. Emphasis has been given to conducting a temporal stability analysis to determine the practically reliable solution. The analysis reveals that the primary (upper) solution branch is stable while the other solution branch is unstable. It has been observed that the range of dual solutions and the magnitude of the critical point increase with the increasing value of the suction parameter. The increment of the thermal radiation parameter enhances fluid temperature in the upper solution branch, whereas temperature diminishes far away from the sheet in the lower solution branch.

Numerical investigation of forced convective heat transfer of nanofluids within an enclosure

Heat transfer applications normally observed day-to-day are mainly focused on forced convection such as the transfer of hot fluid being pumped through pipes, shell and tube heat exchanger and power plants. The heat transfer characteristics of nanofluids present within a cubical enclosure subjected to forced convection is analysed here. Assisting and opposing forced convection flows are being compared. The inlet through which a nanofluid enters the cubical enclosure at a uniform velocity is positioned at the lower portion of the left wall for the assisting case and situated at the upper portion of the left wall for the opposing case. An in-house solver based on finite difference method is developed using simplified marker and cell algorithm (SMAC) through which the simulation is performed. The nanofluid chosen here is a water-based one with various nanoparticles such as aluminium (Al), silver (Ag), aluminium oxide (Al2O3) and singled wall carbon nanotubes (SWCNT) which are investigated for a Reynolds number range of 103 to 105. Other parametric studies like the volume concentration is also being varied from 0% to 3%. The results of this paper tend to show that heat transfer characteristics increase with an increase in both Reynolds number and volume concentration. Forced convection occurring through assisting flow case is showing better heat transfer than in the opposing flow case.

Stagnation point flow of a micropolar fluid filled with hybrid nanoparticles by considering various base fluids and nanoparticle shape factors

PurposeThe boundary-layer analysis is required to reveal the fluid flow behavior in several industrial processes and enhance the products’ effectiveness. Therefore, this research aims to investigate the buoyancy or mixed convective stagnation-point flow (SPF) and heat transfer of a micropolar fluid filled with hybrid nanoparticles over a vertical plate. The nanoparticles silver (Ag) and titanium dioxide (TiO2) are scattered into various base fluids to form a new-fangled class of (Ag-TiO2/various base fluid) hybrid nanofluid along with different shape factors.Design/methodology/approachThe self-similarity transformations are used to reformulate the leading requisite partial differential equations into renovated non-linear dimensionless ordinary differential equations. The numerical dual solutions are gained for the transmuted requisite equations with the help of the bvp4c built-in package in MATLAB software. The results are validated by comparing them with previously available published data for a particular case of the present study.FindingsThe impact of various pertaining parameters such as nanoparticle volume fraction, material parameter, shape factor and mixed convective on temperature, heat transfer, fluid motion, micro-rotation and drag force are visualized and scrutinized through tables and graphs. It is observed that dual or non-uniqueness outcomes are found for the case of buoyancy assisting flow, whereas the solution is unique in the buoyancy opposing flow case. Additionally, the fluid motion and micro-rotation profiles decelerate in the presence of nanoparticle volume fraction, while the temperature augments.Originality/valueThe mixed convective stagnation point flow conveying TiO2/Ag hybrid nanofluid with micropolar fluid with various shape factors is the significant originality of the current investigation where multiple outcomes are obtained for the assisting flow. The various base fluids such as glycerin, water and water–ethylene glycol (50%:50%) are considered in the present problem. The bifurcation values of the considered problem do not exist, probably because of various base fluids. To the best of the authors’ knowledge, this work is new and original which were not previously reported.

Dynamics of chemically reactive Jeffery fluid embedded in permeable media along with influence of magnetic field on associated boundary layers under multiple slip conditions

The prime goal of the current pagination is to scrutinize behavior of mixed convective Jeffrey nanoliquid (JNL) flowing over an exponentially stretching sheet by using possessions of radiative energy flux, non-uniformly heated source/sink, slip boundary condition, and modified Arrhenius energy function. The governing physical expression (PDEs) are converted in view of similar ODE’s. Solution of constructed problem is heeded by employing shooting technique. Graphical and tabular results are designed for assisting flow, opposing flow and forced convection cases to scrutinize the performance of miscellaneous significant variables. The results attained exhibited worthy agreement with the preceding remarkable works. The noteworthy finding is Opposing flow case demonstrations higher temperature and concentration profile compared to assisting flow and forced convection case.

Enhanced magnetohydrodynamic thermal convection in a partially driven cavity packed with a nanofluid‐saturated porous medium

Convective heat transfer characteristics in the purview of fundamentals of flow physics in a two‐sided partially driven cavity (PDC) are addressed in this work. The effect of partial translational motion on the sidewalls of PDC can significantly alter the convective heat transfer characteristics. To explore this novel idea, a square enclosure packed with Cu–water nanofluid‐saturated porous media under the influence of the external magnetic field, heated around a protruded heater mounted at the bottom wall. The cavity is cooled at the upper half of the two sidewalls—partially translating upward or downward direction. Fundamentals of the evolved flow physics and mixed convection heat transfer characteristics are analyzed numerically using extensively validated FORTRAN code based on the finite volume approach. The impacts of the relevant parameters on fluid flow and heat transfer are investigated systematically. The governing parameters are wall speed (Reynolds number) and its direction, convection regime (Richardson number), permeability (Darcy number and porosity), magnetic field strength (Hartmann number), and nanoparticles volume concentration. The results show that the thermal performance of PDC is greatly influenced by all of the above parameters. Heat transfer is enhanced significantly at higher Reynolds number, Richardson number, Darcy number, and porosity and increases in the nanoparticles volume fraction for the opposing flow case.

Effect of dispersion on thermally stable stratified power‐law fluids over the vertical frustum of a cone in a non‐Darcy porous medium: Flow separation

AbstractThe present problem shares out the influences of convective heating and thermal dispersion on thermally stable stratified power‐law fluid flow over the vertical frustum of a cone situated in a non‐Darcy porous medium. For the first time, it is considered in both aiding and opposing flow cases as it is readily applicable in realistic, practical situations. The local nonsimilarity approach, along with the spectral local linearization method, is used to analyze the fluid behavior and heat transfer within the boundary layer region. In addition, error analysis and comparison with the existing results are also included to validate the obtained results wherever feasible. It is significant to perceive the existence of flow separation in this study as more gain of the velocity of a power‐law fluid is seen for aiding flow case in comparison with the opposing flow case. Also, it is evident from these results that the separation of flow is less in the presence of thermal stratification, but it is more in the absence of thermal stratification. Finally, thermal stratification significantly affects the heat transfer rate of power‐law fluids besides delaying the boundary layer separation.

Convective Effect on Magnetohydrodynamic (MHD) Stagnation Point Flow of Casson Fluid over a Vertical Exponentially Stretching/Shrinking Surface: Triple Solutions

In the current study, the characteristics of heat transfer of a steady, two-dimensional, stagnation point, and magnetohydrodynamic (MHD) flow of shear thickening Casson fluid on an exponentially vertical shrinking/stretching surface are examined in attendance of convective boundary conditions. The impact of the suction parameter is also considered. The system of governing partial differential equations (PDEs) and boundary conditions is converted into ordinary differential equations (ODEs) with the suitable exponential similarity variables of transformations and then solved using the shooting method with the fourth order Runge–Kutta method. Similarity transformation is an important class of phenomena in which scale symmetry allows one to reduce the number of independent variables of the problem. It should be noted that solutions of the ODEs show the symmetrical behavior of the PDES for the profiles of velocity and temperature. Similarity solutions are obtained for the case of stretching/shrinking and suction parameters. It is revealed that there exist two ranges of the solutions in the specific ranges of the physical parameters, three solutions depend on the opposing flow case where stagnation point (A) should be equal to 0.1, two solutions exist when λ1 = 0 where λ1 is a mixed convection parameter and A &gt; 0.1, and a single solution exists when λ1 &gt; 0. Moreover, the effects of numerous applied parameters on velocity, temperature distributions, skin friction, and local Nusselt number are examined and given through tables and graphs for both shrinking and stretching surfaces.

A Novel Investigation and Hidden Effects of MHD and Thermal Radiations in Viscous Dissipative Nanofluid Flow Models

Hidden effects of MHD and thermal radiations for a viscous dissipative nanofluids (Al_2 O_3-H_2 O, and γAl_2 O_3-H_2 O) are taken under consideration. The models are formulated by implementing the suitable similarity transformations. Then, two models are discussed mathematically by using RK scheme together with shooting method. The results for flow regimes, coefficient of skin friction, thermophysical characteristics and heat transfer coefficient are pictured and discussed comprehensively by changing the pertinent flow parameters. It is observed that the nanofluids velocity increases abruptly for higher Hartree pressure gradient. For assisting flow situation, the velocity F'(η) increases and abrupt decreasing behavior is examined for opposing flow case. The composition of Al_2 O_3-H_2 O, and γAl_2 O_3-H_2 O becomes more dense for high volume fraction therefore, drops in the velocity field is noted. The temperature of Al_2 O_3-H_2 O, and γAl_2 O_3-H_2 O rises rapidly by varying opposing flow parameter γ<0 and high volume fraction ϕ. Also, the temperature β(η) declines abruptly for parameter λ.

Stability Analysis and Dual Solutions of Micropolar Nanofluid over the Inclined Stretching/Shrinking Surface with Convective Boundary Condition

The present study accentuates the heat transfer characteristics of a convective condition of micropolar nanofluid on a permeable shrinking/stretching inclined surface. Brownian and thermophoresis effects are also involved to incorporate energy and concentration equations. Moreover, linear similarity transformation has been used to transform the system of governing partial differential equations (PDEs) into a set of nonlinear ordinary differential equations (ODEs). The numerical comparison has been done with the previously published results and found in good agreement graphically and tabular form by using the shooting method in MAPLE software. Dual solutions have been found in the specific range of shrinking/stretching surface parameters and the mass suction parameter for the opposing flow case. Moreover, the skin friction coefficient, the heat transfer coefficient, the couple stress coefficient, and the concentration transfer rate decelerate in both solutions against the mass suction parameter for the augmentation of the micropolar parameter respectively. The first (second) solution is the stable (unstable) solution and can (not) be considered as a real solution as the values of the smallest eigenvalues are positive (negative).

CFD Analysis of Turbulent Heat Transfer Characteristics in Cubical Enclosure

In this paper we present the turbulent flow and convective heat transfer phenomena inside a cubical enclosure with an internal heat source. The enclosure is designed with an inlet and outlet vent and the heat source is mounted on the bottom wall. The turbulent flow is modeled by the computational fluid dynamics (CFD) approach using Lambremhorst k- ε turbulence model. A finite difference method is used to discretize the governing equations and an in- house CFD used is developed for simulating the turbulent characteristics . The parametric study is performed for the assisting and opposing flow character stics inside the enclosure by varying the Grashof (Gr) and Reynolds (Re) number in the range of 105 ≤ Gr ≤ 1010 and 102 ≤ Re ≤ 106. The present study emphasises that the inertial force and buoyancy force has significant impact on the recirculation flow p attern inside the enclosure . The heat transfer rate is drastically influenced by the assisting and opppsing flow behavior developed inside the enclosure. It is observed that the mass flow rate across the outlet vent increases linearly with the Reynolds nu mber. The flow behavior is highly chaotic with the development of instabilities inside the enclosure . The streamlines and temperature distribution patterns inside the enclosure indicated that the assisting flow enhanced the heat transfer rate by 48% while the opposing flow suppressed the heat transfer rate by 45% inside the enclosure. A multi recirculating convective cell pattern is formed at higher Grashof number and the size of the cell increases with increase in Grashof number . It is also found that the mass flow rate across the outlet vent increases linearly for assisting flow case while it decreases for the opposing flow case. It is evident from the present study that the assisting flow case is best suited for heat transfer enchancement in cubical enclosure.

Steady incompressible magnetohydrodynamics Casson boundary layer flow past a permeable vertical and exponentially shrinking sheet: A stability analysis

AbstractSteady incompressible magnetohydrodynamic mixed convection boundary layer flow of a Casson fluid on an exponentially vertical shrinking sheet using the non‐Newtonian heating equation is investigated in this paper. There are three main objectives of this study, namely, to develop a new mathematical model, to obtain multiple solutions, and to perform stability analysis. The governing partial differential equations have been changed into nonlinear ordinary differential equations. The resultant equations of boundary value problems are then converted into the equivalent initial value problems using the shooting method before they can be solved using Runge‐Kutta of order four. The numerical results are obtained and found to be in good agreement with the published literature. The results also indicate that the velocity boundary layer becomes thinner as the magnetic, slip, and Casson parameters increase. Dual solutions for temperature and velocity distributions are obtained. Furthermore, the results suggest that the presence of the force of buoyancy (opposing flow case) would cause the occurrence of dual solutions. However, based on the stability analysis, only the first solution is stable.

Unsteady MHD slip flow of a ferrofluid over an impulsively stretched vertical surface

Investigation of unsteady magnetohydrodynamic (MHD) mixed convective ferrofluid flow over an impulsively stretchable surface is modeled with convective boundary conditions and partial slip impacts. Employing a finite-difference method, the governing non-similar equations are solved computationally. The sway of different considerable parameters on flow and heat transfer are demonstrated in graphical forms and discussed. The results show that the increment in the volume fraction leads to decrease the velocity and the temperature as well as the skin-friction coefficient and Nusselt number. Moreover, in the assisting flow case both the velocity and skin friction coefficient increase as Biot number increases, while they have the opposite behaviour in the opposing flow case. Also, both the temperature and local Nusselt number increase as Biot number increases for assisting and opposing flows.

The influence of heat radiation on mixed convection boundary layer flow of a viscoelastic fluid over a circular cylinder with constant surface temperature

The influence of mixed convection boundary layer flow of a viscoelastic fluid over an isothermal horizontal circular cylinder has been analyzed. The boundary layer equations governing the problem are reduced to dimensionless nonlinear partial differential equations and then solved numerically using Keller-box method. Skin friction coefficient and Nusselt number are emphasized specifically. These quantities are displayed against curvature parameter. Effects of mixed convection parameter and radiation-conduction parameter on skin friction coefficient and Nusselt number are illustrated through graphs and table. The boundary layer separation points along the surface of cylinder are also calculated with/without radiation, and a comparison is shown. The presence of radiation helps to reduce the skin friction coefficient in opposing flow case and enhances it for assisting flow case. The increase in value of radiation-conduction parameter helps increase the value of skin friction coefficient and Nusselt number for viscoelastic fluids. The boundary layer separation delays due to thermal radiation.

Oblique stagnation-point flow of a nanofluid past a shrinking sheet

Purpose – The laminar two-dimensional stagnation-point flow and heat transfer of a viscous incompressible nanofluid obliquely impinging on a shrinking surface is formulated as a similarity solution of the Navier-Stokes, energy and concentration equations. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The effect of the dimensionless strain rate, shrinking parameter, Brownian motion parameter and thermophoresis parameter on the flow, temperature and nanoparticle volume fraction is investigated in details. The paper aims to discuss these issues. Design/methodology/approach – The transformed system of ordinary differential equations was solved using the function bvp4c from Matlab. The relative tolerance was set to 10−10. Findings – It is found that dimensionless strain rate and shrinking parameter causes a shift in the position of the point of zero skin friction along the stretching sheet. Obliquity of the flow toward the surface increases as the strain rate intensifies. The results indicate that dual solutions exist for the opposing flow case. Research limitations/implications – The problem is formulated for an incompressible nanofluid with no chemical reactions, dilute mixture, negligible viscous dissipation and negligible radiative heat transfer assuming nanoparticles and base fluid are locally in thermal equilibrium. Beyond the critical point λ c to obtain further solutions, the full basic partial differential equations have to be solved. Originality/value – The present results are original and new for the oblique stagnation-point flow of a nanofluid past a shrinking sheet. Therefore, this study would be important for the researchers working in the relatively new area of nanofluids in order to become familiar with the flow behavior and properties of such nanofluids.

Magnetohydrodynamic (MHD) mixed convection stagnation point flow of a nanofluid over a vertical plate with viscous dissipation

In this study, magnetohydrodynamic effects on the mixed convection flow of nanofluid particles, namely, Cu (copper) and Al2O3 (alumina) near a stagnation region over a vertical plate in the presence of viscous dissipation is investigated. The governing equations of the nanofluid flow model proposed by Tiwari and Das (Int. J. Heat Mass Transfer, 50, 2002 (2007). doi:10.1016/j.ijheatmasstransfer.2006.09.034) are converted into a dimensionless nonlinear system of ordinary differential equations by using the similarity transformation. The solution of the resulting equations is obtained numerically by using a very efficient implicit scheme known as the Keller box method. A comparison with previous studies is shown in tabular form and excellent agreement is found. The effects of pertinent parameters like magnetic parameter M, Eckert number Ec, and volume fraction parameter ϕ on velocity, temperature, skin friction coefficient, and local Nusselt number with fixed value of Prandtl number Pr = 6.2 are shown graphically and discussed. These results show that the skin friction coefficient increases for both nanoparticles in assisting and opposing flow cases because of increasing absolute values of M and Ec, on the other hand heat transfer rate is enhanced in the opposing flow case and reduced in the assisting flow case. The values of skin friction coefficient for both nanoparticles, namely, Cu and Al2O3 increase with the increase in volume fraction parameter ϕ in both assisting and opposing flow cases and Cu has a higher value than Al2O3. The same behavior is observed for local Nusselt number in opposing flow, but in assisting flow the value of local Nusselt number decreases with the increase of ϕ in the presence of magnetic and viscous dissipation effects and Cu has a smaller value than Al2O3.

Mixed convection boundary layer flow past a vertical flat plate embedded in a non-Darcy porous medium saturated by a nanofluid

Purpose – The purpose of this paper is to numerically solve the problem of steady mixed convection boundary layer flow past a vertical flat plate embedded in a fluid-saturated porous medium filled by a nanofluid. The non-Darcy equation model along with the mathematical nanofluid model proposed by Tiwari and Das (2007) has been used. Design/methodology/approach – Using appropriate similarity transformations, the basic partial differential equations are transformed into ordinary differential equations. These equations have been solved numerically for different values of the nanoparticle volume fraction, the mixed convection and the non-Darcy parameters using the bvp4c function from Matlab. A stability analysis has been also performed. Findings – Numerical results are obtained for the reduced skin-friction, heat transfer and for the velocity and temperature profiles. The results indicate that dual solutions exist for the opposing flow case (λ&lt;0). The stability analysis indicates that for the opposing flow case, the lower solution branch is unstable, while the upper solution branch is stable. In addition, it is shown that for a regular fluid (φ=0) a very good agreement exists between the present numerical results and those reported in the open literature. Research limitations/implications – The problem is formulated for three types of nanoparticles, namely, copper (Cu), alumina (Al2O3) and titania (TiO2). However, the paper present results here only for the Cu nanoparticles. The analysis reveals that the boundary layer separates from the plate. Beyond the turning point it is not possible to get the solution based on the boundary-layer approximations. To obtain further solutions, the full basic partial differential equations have to be solved. Practical implications – Nanofluids have many practical applications, for example, the production of nanostructured materials, engineering of complex fluids, for cleaning oil from surfaces due to their excellent wetting and spreading behavior, etc. Social implications – Nanofluids could be applied to almost any disease treatment techniques by reengineering the nanoparticle properties. Originality/value – The present results are original and new for the boundary-layer flow and heat transfer past a vertical flat plate embedded in a porous medium saturated by a nanofluid. Therefore, this study would be important for the researchers working in porous media in order to become familiar with the flow behavior and properties of such nanofluids.

Mixed Convection Stagnation-Point Flow Past a Vertical Flat Plate With a Second Order Slip

An exact similarity solution of the steady mixed convection flow of a viscous and incompressible fluid in the vicinity of two-dimensional stagnation-point with a second-order slip condition has been investigated. Using appropriate similarity variable, the Navier–Stokes equations coupled with the energy equation governing the flow and heat transfer are reduced to a system of nonlinear ordinary (similarity) equations, which are well-posed. These equations are solved numerically in the buoyancy assisting and opposing flow regions. It is found that a reverse flow region develops in the buoyancy opposing flow case, and dual (upper and lower branch) solutions are found to exist in the case of opposing flow region for a certain range of the negative values of the mixed convection parameter. A stability analysis has been performed, which shows that the upper branch solutions are stable and physically realizable in practice, while the lower branch solutions are not stable and, therefore, not physically realizable in practice. The numerical results have been compared with those reported in the literature, the agreement being excellent.

Unsteady MHD mixed convection flow of a micropolar fluid along an inclined stretching plate

AbstractIn this research, the unsteady magnetohydrodynamic mixed convection flow of a micropolar fluid over an inclined plate has been investigated. The problem is reduced to a system of non‐dimensional partial differential equations, which are solved numerically using the implicit finite‐difference scheme. Velocity profiles, temperature profiles, concentration profiles, the skin friction coefficient, the rate of heat transfer, and the rate of mass transfer are computed numerically for various values of different physical parameters. In this study, we consider both assisting and opposing flow. It is found that in the assisting flow case, a solution could be obtained for all positive values of the buoyancy parameter λ, while in the opposing flow case the solution terminated at $\lambda = {\lambda _c}(\lambda &lt; 0)$. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21034