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Mathematical modelling of MHD hybrid nanofluid flow in a convergent and divergent channel under variable thermal conductivity effect

  • Abdulaziz H. Alharbi EMAIL logo
Published/Copyright: January 21, 2025
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Applied Rheology
From the journal Applied Rheology Volume 35 Issue 1

Abstract

The aim of this research is to analyse the combined effect of variable thermal conductivity and nonlinear thermal radiation on magnetohydrodynamic (MHD) hybrid nanofluid flow in convergent-divergent channels. The effects of two nanoparticles (i.e. ZrO 2 and SiO 2 ) in base fluid (i.e. H 2 O ) are considered in this work. The partial differential equations modelling the problem are reduced to ordinary differential equations following the application of the similarity transformations. The system has been solved analytically with the differential transform method and numerically with the Runge–Kutta–Fehlberg 4th–5th order method with the assistance of the shooting technique. Comprehensive analysis and discussion have been conducted regarding the impact of multiple governing parameters on the dimensionless velocity and temperature distributions. These parameters include variable thermal conductivity, nonlinear thermal radiation, Hartman number, and hybrid nanoparticle volume fraction. Finally, this method will provide some insights into the usefulness of MHD hybrid nanofluid flow in convergent-divergent channels, and the results produced by the analytical data have also been strengthened and verified by the use of numerical data as well as data from the literature.

Keywords: variable thermal conductivity; hybrid nanofluid; DTM, Runge; Kutta; Fehlberg; convergent/divergent channel

Symbols

a and b

constants

B 0 … . . B 4

constants

B

magnetic field (T)

B 0

strength of magnetic field (T)

Br

Brinkman number

C f  

skin friction coefficient ( J/kg K)

C p

effective specific heat of fluid ( J/kg K)

Ec 

Eckert number

F

dimensionless velocity

Ha

Hartmann number

K

thermal conductivity (W/m K)

k ⁎

mean absorption coefficient

Nu 

Nusselt number or nonlinear term

P

fluid pressure ( N/m 2 )

Pr 

Prandtl number

q r ; q θ

heat flux radiative ( W/m 2 )

r

radial coordinate

Re 

Reynolds number

Rd

thermal radiation parameter

T

fluid temperature (K)

T w

wall temperature (K)

V c

rate of movement at the centreline of channel ( m/s )

V max

maximal velocity ( m/s )

V r ; V θ ; V z

radial, azimuthal, axial velocity ( m/s )

Greek symbols

α

channel half-angle

η

dimensionless

θ

dimensionless temperature

φ

nanoparticle volume fraction

µ

dynamic viscosity ( kg/m)

ν

kinematic viscosity ( m 2 /s )

ρ

density ( kg/m 3 )

σ

electrical conductivity ( 1/Ω m )

σ ⁎

Stefan–Boltzmann constant

ε

variable thermal conductivity parameter

1 Introduction

Nanofluids have garnered attention and large numbers of investigations owing to their advantageous characteristics relative to conventional fluids. These fluids possess remarkable thermal conductivity, rendering them more advantageous for practical applications. The incorporation of uniformly distributed nanoparticles to the host fluid enhances the thermal conductivity of the resulting fluid. The improved attributes render hybrid nanofluids more effective than nanoliquids [1,2,3].

Hamilton and Crosser [4] were the pioneers in experimenting with the concept of developing an improved heat transfer fluid. They distributed micro sized particles in base liquids to enhance the thermal conductivity of the colloidal solution. The results of their experimental discoveries enhanced the thermal performance of the developed fluid; however, they identified that the issue of coagulation hindered its application in industrial contexts. Madhukesh et al. [5] introduced an innovative and thorough model for examining heat and solutal transportation in non-Newtonian flow of nanofluid over a Riga surface influenced by waste release concentration. Srinivas et al. [6] investigated the hydromagnetic flow of nanofluids in a two-dimensional permeable domain. The analysis of several parameters revealed that nanoparticle concentration is directly connected with the Brownian factor. Hemmat Esfe and Saedodin [7] examined the thermal conductivity and its influence on the heat transmission of MgO/water nanofluid. Al-Zahrani et al. [8] presented a compelling analytical investigation of (Ag-Graphene)/blood hybrid nanofluid affected by platelet cylindrical nanoparticles and Joule heating. This work is distinguished by its multidisciplinary approach, integrating nanotechnology, bio-fluid dynamics, and mathematical modelling to examine complex phenomena. Ramesh et al. [9] examined the effects of a ternary nanofluid with HS–S and permeable media in a stretched divergent/convergent channel. Fakour et al. [10] investigated the process of heat transfer mechanism as well as laminar fluid flow among two parallel porous plates. The impact of non-dimensional factors on the dimensionless velocity as well as temperature profiles was examined. Mohammadi and Nassab [11] developed complicated geometry within a cavity and analysed the effects of radiative parameters and magnetic fields under constant Rayleigh numbers. Ullah et al. [12] examined the flow of a modified hybrid nanofluid within stretching or shrinking CD channels, considering the continual heat absorption or creation, ohmic heating, and viscous dissipation. Ramesh et al. [13] analysed the flow of hybrid nanomaterials in a convergent/divergent channel. Chamkha et al. [14] examined the process of heat transfer in hybrid nanofluid flow inside a rotating structure between elastic surfaces. They found that the rate of heat transfer increases through the improvement of injection and radiation factors. Conversely, researchers have also conducted numerical studies. For example, Waini et al. [15] explained a numerical analysis of the transient flow of hybrid nanofluid over a curved stretching and shrinking surface. Furthermore, Anitha et al. [16] studied the thermal properties of a tangent hyperbolic fluid as it traverses a vertical microchannel. In addition, Anitha and Gireesha [17] investigated the irreversibility and thermal characteristics of the Jeffrey nanofluid within a vertical porous microchannel. Moreover, Chamkha [18] conducted a theoretical study on the influence of solar radiation on natural convection within a porous media in a flat-plate collector. The author determined that the Nusselt number increased with an elevation in the Prandtl number, while a decrease was observed due to enhancements in the coefficient of heat transfer, tangential distance, inverse Darcy number, and medium inertia. For more information, we refer the readers to previous studies [19,20,21,22,23,24].

The novelty and significance of this work are emphasized by the lack of prior research on this particular subject. Understanding how heat transfer behaves in flow between convergent–divergent channels with hybrid nanofluid (such as ZrO 2 and SiO 2 ) in base fluid (such as H 2 O ) under changing thermal conductivity, nonlinear thermal radiation, and magnetic fields is essential for biomedical applications. The differential transform method (DTM) and the Runge–Kutta–Fehlberg 4th–5th order (RKF45) method with the help of the shooting technique were used to generate the numerical and analytical solutions, respectively. On the other hand, the integration of H 2 O and hybrid nanofluid (such as ZrO 2 and SiO 2 ) provides a unique nanofluid with remarkable thermal properties, making it a strong competitor for boosting heat transfer efficiency in varied industries. This study can help build more sustainable and efficient technologies with a wide range of applications in energy, heat exchangers, and thermal management systems by advancing our comprehension of nanofluid and heat transfer dynamics in complex geometries.

2 Problem formulation

The study examines the effect of variable thermal conductivity on incompressible magnetohydrodynamic (MHD) flow of hybrid nanofluid in convergent and divergent channels. The geometry of the flow model is given in Figure 1.

Figure 1 MHD Jeffery–Hamel (J-H) flow.
Figure 1

MHD Jeffery–Hamel (J-H) flow.

The Lorentz force is a force affected by the external magnetic field B , electrical field E , and fluid velocity V , which are typically supplied by

(1) f B = J × B .

According to Ohm’s Law, the constancy of electrical current is provided by

(2) J = σ ( E + V × B ) ,

where E represents the electric field and indicates the electrical conductivity. Due to the irrotational nature of the electric field E, it follows that E = 0 in the absence of any free electric charge. Moreover, assuming a low magnetic Reynolds number, the resultant magnetic field B is approximately equal to B 0 . The Lorentz force is given in this context by

(3) f B = σ [ ( V × B 0 ) × B 0 ] .

The continuity and N-S equations of hybrid nanofluid J-H flow for cylindrical coordinates (r, θ, z) are expressed by

(4) 1 r ∂ ∂ r ( r V r ) = 0 ,

(5) V r ∂ V r ∂ r = − 1 ρ hnf ∂ p ∂ r + ν hnf ∂ 2 V r ∂ r 2 + 1 r ∂ V r ∂ r + 1 r 2 ∂ 2 V r ∂ Θ 2 − V r r 2 + σ hnf ρ hnf r 2 ( − B 2 V r ) ,

(6) − 1 ρ hnf ∂ p r ∂ Θ + 2 ν thnf r 2 ∂ V r ∂ Θ = 0 .

And the expressions of energy equation in cylindrical coordinates under external magnetic field, radiation, and heat source are as follows:

(7) ( ρ c p ) hnf V r ∂ T ∂ r = 1 r 2 ∂ ∂ Θ k ˆ hnf ( T ) ∂ T ∂ Θ + μ hnf 2 . ∂ V r ∂ r 2 + V r r 2 + 1 r ∂ V r ∂ r 2 − 1 r 2 ∂ q θ ∂ r + 1 r ∂ r q r ∂ r .

Rosseland approximation gives

(8) q r = − 16 3 σ ⁎ T w 3 k ⁎ ∂ T ∂ r q θ = − 16 3 σ ⁎ T w 3 k ⁎ ∂ T ∂ θ .

The boundary conditions are as follows:

(9) At → θ = 0 V r = V c r , ∂ V r ∂ Θ = 0 and ∂ T ∂ Θ = 0 At → θ = ± α V r = 0 and T = T w r 2 .

The properties of hybrid nanofluid and the thermophysical characteristics of nanoparticles and water are expressed in Tables 1 and 2, respectively.

Table 1

Characteristics of ternary nanofluids

Dynamic viscosity μ hnf = μ f ( 1 ‒ φ 1 ) 2.5 ( 1 ‒ φ 2 ) 2.5
Density ρ hnf = ( 1 ‒ φ 2 ) ( ( 1 ‒ φ 1 ) + φ 1 ⋅ ρ 1 ) + φ 2 ⋅ ρ 2
Specific heat ( ρ C p ) hnf = ( 1 ‒ φ 2 ) ( ( 1 ‒ φ 1 ) + φ 1 ⋅ ( ρ C p ) 1 ) + φ 2 ⋅ ( ρ C p ) 2
Electrical conductivity σ hnf σ nf = σ 1 + 2 σ nf ‒ 2 φ 1 ( σ nf ‒ σ 1 ) σ 1 + 2 σ nf ‒ φ 1 ( σ nf ‒ σ 1 ) σ nf σ f = σ 2 + 2 σ f ‒ 2 φ 2 ( σ f ‒ σ 2 ) σ 2 + 2 σ f ‒ φ 2 ( σ f ‒ σ 2 )
Thermal conductivity k hnf k nf = k 1 + 2 k nf ‒ 2 φ 1 ( k nf ‒ k 1 ) k 1 + 2 k nf ‒ φ 1 ( k nf ‒ k 1 ) k nf k f = k 2 + 2 k f ‒ 2 φ 2 ( k f ‒ k 2 ) k 2 + 2 k f ‒ φ 2 ( k f ‒ k 2 )
Table 2

Thermophysical properties of nanoparticles and liquid-based H 2 O

Physical properties ρ C p k σ Pr
H 2 O 997.1 4,179 0.613 5.5 × 106 6.2
ZrO 2 → φ 1 5,680 502 1.7 3.5 × 106 ‒
SiO 2 → φ 2 2,650 730 1.5 3.5 × 106 ‒

Introduce non-dimensional terms in the form:

(10) η = Θ α F ( η ) = f ( Θ ) f max θ ( η ) = r 2 T T w k ˆ hnf ( T ) = k hnf 1 + ε T T w .

Using equation (10) in (4)–(7) gives

(11) ℱ ‴ + 2 Re α B 0 B 1 ℱ ℱ ′ + ( 4 − B 0 B 2 H a ) α 2 ℱ ′ = 0 ,

(12) ( 1 + Rd + ε θ ) θ ″ + ε θ ′ 2 + 2 α 2 2 Rd + 2 + Pr B 3 B 4 ℱ θ + 1 B 0 B 4 Br Re ( 4 α 2 ℱ 2 + ℱ ′ 2 ) + B 2 B 4 BrHa ℱ 2 = 0 .

The boundary conditions are as follows:

(13) At → η = 0 ℱ = 1 , ℱ ′ = 0 and θ ′ = 0 At → η = ± 1 ℱ = 0 and θ = 1 .

From equation (9), the quantities B 0 , B 1 , B 2 , B 3 , and B 4 are as follows:

B 0 = ( 1 − φ 1 ) 2.5 ( 1 − φ 2 ) 2.5 B 1 = ( 1 − φ 2 ) ( 1 − φ 1 ) + φ 1 . ρ 1 ρ f + φ 2 . ρ 2 ρ f B 2 = σ hnf σ f B 3 = ( 1 − φ 2 ) ( 1 − φ 1 ) + φ 1 . ( ρ C p ) 1 ( ρ C p ) f + φ 2 . ( ρ C p ) 2 ( ρ C p ) f B 4 = k hnf k f .

The skin friction coefficient and Nusselt local numbers are as follows:

(14) C f = 1 B 0 F ′ | η = 1

(15) Nu = − ( B 4 + Rd ) θ ′ | η = 1 .

3 Implementation of the DTM

By using the DTM, a differential equation can be converted into a set of readily solved algebraic equations. The DTM procedure is shown in a flow chart form in Figure 2.

Figure 2 DTM procedure for the present problem.
Figure 2

DTM procedure for the present problem.

4 Results and discussion

One of the goals of this research is to investigate the effect of multiple governing parameters on the dimensionless velocity, temperature distributions, and heat transfer rate inside the channel width. These parameters include variable thermal conductivity, nonlinear thermal radiation, Hartman number, and hybrid nanoparticle volume fraction, a set of values for parameters are considered as Re = 102 , Rd = 1 , α = ± 7 ° , Ec = 0.5 , Ha = 0 , Br = 2 , φ 1 = φ 2 = 2 % , Ha = 0 and ϵ = 0.1 .

4.1 Effect of active parameters on velocity and temperature profile

Figure 3 shows the velocity and temperature changes in divergent and converging channels with different nanoparticle concentrations. Concentration does not significantly affect velocity in both channels. Velocity towards the centre has larger values, and convergent channels have more intense velocity changes. Concentration changes significantly affect channel temperature, with more intensity towards the centre. Physically, the basic liquid becomes denser and the nanoliquid density increases when nanoparticles are added. As a result, moving through the canal is more challenging.

Figure 3 f ( η ) and θ ( η ) f(\eta )\hspace{.5em}\text{and}\hspace{.5em}\theta (\eta ) profile vs φ hnf {\varphi }_{\text{hnf}} for both channels (right: Converging channel; left: Divergent channel).
Figure 3

f ( η ) and θ ( η ) profile vs φ hnf for both channels (right: Converging channel; left: Divergent channel).

Figure 4 shows the effect of Reynolds parameter on velocity and temperature of the hybrid nanofluid in both channels. The Reynolds parameter increases velocity on the wall, affecting velocity variations and temperature conditions in the diverging channel, with the effect being more intense at a certain distance from the wall. In addition, the temperature decreases in the divergent channel causing the thermal boundary layer to increase. However, in a convergent channel, the velocity profile remains constant while the thickness of the momentum boundary layer drops, the thermal boundary layer raises with a significant drop in temperature magnitude.

Figure 4 f ( η ) and θ ( η ) f(\eta )\hspace{.5em}\text{and}\hspace{.5em}\theta (\eta ) profile vs Re for both channels (right: Converging channel; left: Divergent channel).
Figure 4

f ( η ) and θ ( η ) profile vs Re for both channels (right: Converging channel; left: Divergent channel).

Figure 5 shows the effect of Ha parameter on velocity and temperature of the hybrid nanofluid in both channels. As the parameter increases, the Lorentz force, a force resulting from the interaction between the magnetic field and the hybrid nanofluid, becomes more significant, causing deviations from traditional flow patterns. On the other hand, this is mainly explained by the stabilizing influence of an external magnetic field, which creates a Lorentz force opposed to the direction of flow. Consequently, the backflow phenomenon entirely vanishes at both the upper and bottom walls of divergent and convergent flow. This force also affects temperature distribution by altering thermal conductivity and heat dissipation, particularly near the walls.

Figure 5 f ( η ) and θ ( η ) f(\eta )\hspace{.5em}\text{and}\hspace{.5em}\theta (\eta ) profile vs Ha for both channels (right: Converging channel; left: Divergent channel).
Figure 5

f ( η ) and θ ( η ) profile vs Ha for both channels (right: Converging channel; left: Divergent channel).

Figure 6 shows the effect of variable thermal conductivity parameter ε on temperature of the hybrid nanofluid in both channels. The ε parameter increases and the temperature profile plot in the computational domain flattens, indicating a decrease in temperature gradient. The dependence of temperature on ε is stronger for divergent channels, suggesting that channel geometry influences the temperature profiles.

Figure 6 f ( η ) and θ ( η ) f(\eta )\hspace{.5em}\text{and}\hspace{.5em}\theta (\eta ) profile vs ϵ {\epsilon } for both channels (right: Converging channel; left: Divergent channel).
Figure 6

f ( η ) and θ ( η ) profile vs ϵ for both channels (right: Converging channel; left: Divergent channel).

Figure 7 shows the effect of Br parameter on temperature profiles of the hybrid nanofluid in both channels. The temperature of the hybrid nanofluid in a divergent channel is significantly enhanced by increasing Br parameter.

Figure 7 f ( η ) and θ ( η ) f(\eta )\hspace{.5em}\text{and}\hspace{.5em}\theta (\eta ) profile vs Br for both channels (right: Converging channel; left: Divergent channel).
Figure 7

f ( η ) and θ ( η ) profile vs Br for both channels (right: Converging channel; left: Divergent channel).

Figure 8 shows the effect of thermal radiation parameter on temperature profiles of the hybrid nanofluid in both channels. This figure of the channel’s temperature leads us to the conclusion that thermal radiation has a greater effect on the temperature close to the wall. As one moves from the wall to the centre of the channel, the radiation impacts actually get smaller.

Figure 8 f ( η ) and θ ( η ) f(\eta )\hspace{.5em}\text{and}\hspace{.5em}\theta (\eta ) profile vs Rd for both channels (right: Converging channel; left: Divergent channel).
Figure 8

f ( η ) and θ ( η ) profile vs Rd for both channels (right: Converging channel; left: Divergent channel).

4.2 Effect of active parameters on heat transfer rate Nu

Figure 9 shows unequivocally how a rise in parameter ε values leads to an increase in the Nusselt number of the hybrid nanofluid in both channels, or in other words, with an increase in the parameter ε, Nu is seen to reduce overall hinting towards lesser fluid flow resistance and heat transfer rate in both channels. It appears that the action of thermal radiation parameter depends on variable thermal conductivity parameter, where performance of Nusselt number can be either enhanced. Possible reason seen is nonlinear thermal radiation.

Figure 9 Nu vs Ra and ϵ for both channels (right: Converging channel; left: Divergent channel).
Figure 9

Nu vs Ra and ϵ for both channels (right: Converging channel; left: Divergent channel).

The Nusselt number evolution is affected by several parameters such as magnetic field and variable thermal conductivity parameter, as shown in Figure 10. It appears that when Hartman number increases, the Nusselt number evolution increases. Furthermore, when we increase the variable thermal conductivity parameter, the Nusselt number shows a little decrease. The Nusselt number evolution is affected by several factors such as Reynolds parameter and variable thermal conductivity parameter, as shown in Figure 11. Clearly, when both the parameters increase, the Nusselt number evolution decreases.

Figure 10 Nu vs Ha and ϵ for both channels (right: Converging channel; left: Divergent channel).
Figure 10

Nu vs Ha and ϵ for both channels (right: Converging channel; left: Divergent channel).

Figure 11 Nu vs Re and ϵ for both channels (right: Converging channel; left: Divergent channel).
Figure 11

Nu vs Re and ϵ for both channels (right: Converging channel; left: Divergent channel).

4.3 Validation and comparison

Tables 3 and 4 show the results of the comparison between the current results (i.e. both methods: analytical method [DTM] and the homotopy analysis method [HAM]) and those available in previous literature [25–28] for velocity values F when α = −5° and α = +5°, respectively. It is observed that there is an exceptional correlation of the obtained analytical outcomes through the DTM with those available in previous studies [25–28].

Table 3

Comparison between DTM technique and those available in the literature for F ″ ( 0 ) in a converging channel when α = −5°

Re F ″ ( 0 ) [17] F ″ ( 0 ) [18] F ″ ( 0 ) [19] F ″ ( 0 ) [20] DTM HAM-package
10 1.784547 1.784546 1.78454676648462 1.78454676647621 1.78454676647543 1.784546766475
30 1.413692 1.413692 1.41369209135674 1.41369209136534 1.41369209136619 1.413692091366
50 1.121989 1.121989 1.2198919535324 1.21989195351279 1.21989195351651 1.219891953516

The bold value shows the results of the (i.e. both methods: analytical method [DTM] and the homotopy analysis method [HAM]) while the rest are values available in previous literature [25–28] for velocity values F when α = −5° and α = +5°, respectively.

Table 4

Comparison between DTM technique and those available in the literature for F ' ' ( 0 ) in a diverging channel when α = +5°

Re F ″ ( 0 ) [17] F ″ ( 0 ) [18] F ″ ( 0 ) [19] F ″ ( 0 ) [20] DTM HAM-package
10 2.527192 2.527192 2.5271921099786 2.5271921099672 1.78454676647431 1.784546766474
30 3.942140 3.942140 3.9421401298765 3.9421401298543 1.41369209136983 1.413692091369
50 5.869165 5.869165 5.8691652309549 5.8691652309231 1.21989195351178 1.219891953511

The bold value shows the results of the (i.e. both methods: analytical method [DTM] and the homotopy analysis method [HAM]) while the rest are values available in previous literature [25–28] for velocity values F when α = −5° and α = +5°, respectively.

5 Conclusion

This study focuses on the behaviour of variable thermal conductivity within the MHD framework, with key findings summarizing the research’s significant findings.

  • Both channels’ velocity is not greatly impacted by concentration, but convergent channels have more dramatic variations in velocity, and channel temperature is greatly impacted by concentration fluctuations.

  • The variable thermal conductivity influences flow patterns and temperature stratification in nanofluids, highlighting the importance of these parameters in practical applications.

  • It is noticed that the hybrid nanofluid has higher thermal conductivity and better heat transfer attributes as contrasted to the base fluid, especially at different flow rates.

  • The evolution of the Nusselt number increases with increase in the Hartman number, while a slight decrease occurs with an increase in the variable thermal conductivity parameter.

  • The numerical solution using the RKF45 method demonstrates the efficacy of the DTM in solving nonlinear differential equations, matching it precisely.

6 Future work

Future work may be extended from this work as follows:

  1. Investigation of the impact of both variable conductivity (i.e. electrically and thermically) effects.

  2. Artificial neural network scheme can be used to fetch the numerical solution.

  1. Funding information: The author states no funding involved.

  2. Author contributions: The author confirms the sole responsibility for the conception of the study, presented results, and manuscript preparation.

  3. Conflict of interest: The author states no conflict of interest.

  4. Ethical approval: The conducted research is not related to either human or animal use.

  5. Data availability statement: The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

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Received: 2024-11-18
Revised: 2024-12-13
Accepted: 2024-12-21
Published Online: 2025-01-21

© 2025 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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https://doi.org/10.1515/arh-2024-0028
Keywords for this article
variable thermal conductivity; hybrid nanofluid; DTM, Runge; Kutta; Fehlberg; convergent/divergent channel
Creative Commons
BY 4.0

Articles in the same Issue

  1. Research Articles
  2. Lie symmetry analysis of bio-nano-slip flow in a conical gap between a rotating disk and cone with Stefan blowing
  3. Mathematical modelling of MHD hybrid nanofluid flow in a convergent and divergent channel under variable thermal conductivity effect
  4. Advanced ANN computational procedure for thermal transport prediction in polymer-based ternary radiative Carreau nanofluid with extreme shear rates over bullet surface
  5. Effects of Ca(OH)2 on mechanical damage and energy evolution characteristics of limestone adsorbed with H2S
  6. Effect of plasticizer content on the rheological behavior of LTCC casting slurry under large amplitude oscillating shear
  7. Studying the role of fine materials characteristics on the packing density and rheological properties of blended cement pastes
  8. Deep learning-based image analysis for confirming segregation in fresh self-consolidating concrete
  9. MHD Casson nanofluid flow over a three-dimensional exponentially stretching surface with waste discharge concentration: A revised Buongiorno’s model
  10. Rheological behavior of fire-fighting foams during their application – a new experimental set-up and protocol for foam performance qualification
  11. Viscoelastic characterization of corn starch paste: (II) The first normal stress difference of a cross-linked waxy corn starch paste
  12. An innovative rheometric tool to study chemorheology
  13. Effect of polymer modification on bitumen rheology: A comparative study of bitumens obtained from different sources
  14. Rheological and irreversibility analysis of ternary nanofluid flow over an inclined radiative MHD cylinder with porous media and couple stress
  15. Rheological analysis of saliva samples in the context of phonation in ectodermal dysplasia
  16. Analytical study of the hybrid nanofluid for the porosity flowing through an accelerated plate: Laplace transform for the rheological behavior
  17. Brief Report
  18. Correlations for friction factor of Carreau fluids in a laminar tube flow
  19. Special Issue on the Rheological Properties of Low-carbon Cementitious Materials for Conventional and 3D Printing Applications
  20. Rheological and mechanical properties of self-compacting concrete with recycled coarse aggregate from the demolition of large panel system buildings
  21. Effect of the combined use of polyacrylamide and accelerators on the static yield stress evolution of cement paste and its mechanisms
  22. Special Issue on The rheological test, modeling and numerical simulation of rock material - Part II
  23. Revealing the interfacial dynamics of Escherichia coli growth and biofilm formation with integrated micro- and macro-scale approaches
  24. Construction of a model for predicting sensory attributes of cosmetic creams using instrumental parameters based on machine learning
  25. Effect of flaw inclination angle and crack arrest holes on mechanical behavior and failure mechanism of pre-cracked granite under uniaxial compression
  26. Special Issue on The rheology of emerging plant-based food systems
  27. Rheological properties of pea protein melts used for producing meat analogues
  28. Understanding the large deformation response of paste-like 3D food printing inks
  29. Seeing the unseen: Laser speckles as a tool for coagulation tracking
  30. Composition, structure, and interfacial rheological properties of walnut glutelin
  31. Microstructure and rheology of heated foams stabilized by faba bean isolate and their comparison to egg white foams
  32. Rheological analysis of swelling food soils for optimized cleaning in plant-based food production
  33. Multiscale monitoring of oleogels during thermal transition
  34. Influence of pea protein on alginate gelation behaviour: Implications for plant-based inks in 3D printing
  35. Observations from capillary and closed cavity rheometry on the apparent flow behavior of a soy protein isolate dough used in meat analogues
  36. Special Issue on Hydromechanical coupling and rheological mechanism of geomaterials
  37. Rheological behavior of geopolymer dope solution activated by alkaline activator at different temperature
  38. Special Issue on Rheology of Petroleum, Bitumen, and Building Materials
  39. Rheological investigation and optimization of crumb rubber-modified bitumen production conditions in the plant and laboratory
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