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An Analysis of Heat Transfer and the Impact of Gold and Silver
Nanoparticles on Blood Flow Within Arterial Stenosis
Tejpal Singh, Prof., P. K. shukla
K. G. K. College Moradabad, MJPRU Bareilly, India
DOI: https://dx.doi.org/10.51584/IJRIAS.2025.1010000050
Received: 07 October 2025; Accepted: 16 October 2025; Published: 03 November 2025
ABSTRACT
The current study's simulation made use of COMSOL Multiphysics' CFD. Blood was used as the basic fluid in
this simulation. Blood was considered to be a laminar, unstable, and incompressible Newtonian fluid, and its
Newtonian nature is tolerable at high shear rates. The behavior of blood flow was investigated to ascertain the
effects of temperature, velocity, and pressure through vascular stenosis. Gold (Au) and silver (Ag)
nanoparticles were the two types utilized in this investigation. The mass, momentum, and energy equations
were solved using the CFD method.
A fine element size mesh was made using COMSOL. The analysis's conclusions show that the artery's
velocity fluctuates over constrained sections, falling both before and after the stenotic zone and being higher in
a diseased location. The heat transfer feature's upper and lower boundary temperatures were selected to be
24.85°C and 27.35°C, respectively. The nanoparticles affected the density, specific heat, dynamic viscosity,
and thermal conductivity of blood. The use of gold and silver nanoparticles prevented overheating since they
both have high thermal conductivity, which is essential for quickly dispersing heat. Nusselt number variations
were also calculated, and the results show that the curve decreases inside the stenosis. At t = 0.7 s and 1 s,
recirculation occurs right after the stenosed area, and it is possible to infer that the streamlines behave
abnormally. These discoveries will have a significant impact on the treatment of stenosed arteries.
Keywords: Newtonian fluid, blood flow, unsteady, CFD, nanoparticles (gold and silver), stenosed , artery.
INTRODUCTION
Nanoparticles aid in the successful treatment of cardiovascular disorders as well as other diagnostic
applications. Better treatment approaches are made possible by the physical characteristics of nanoparticles,
such as changes to their size, shape, and surface, and these characteristics are primarily responsible for the
delivery of nanoparticles into the arteries.
T. Hayat and S. Nadeem [1] investigated how adding copper oxide and silver nanoparticles to water, the base
fluid, could improve heat transfer. Single wall carbon nanotubes in blood flow through numerous stenoses
were investigated by S. Nadeem and S. Ijaz [2] while taking varying viscosity into account. [3,4] have
examined three-dimensional flow models with the addition of nanoparticles and under various impacts. Prandt
l magnetoh ydrodynamic nanofluid flow via arterial stenoses was examined by S. Nadeem et al. [5]. One
significant and distinct application of nanoparticles is in the contemporary field of medicine. The most
influential material in nanoscience and nanomedicine is gold nanoparticles. They are employed as medication
transporters, contrast agents, photovoltaic agents, and radioinfection agents. Gold and silver nanoparticles also
have a lot of qualities that make them appealing for use in biological diagnosis and treatment. Nanoparticle
therapy is still being developed for vascular disorders. In their investigation of blood flow via stenosed vessels,
T. Elnaqeeb et al. [6] provided findings for several flow parameters.
They also compared their findings to Cu and TiO2 models and came to the conclusion that adding gold
nanoparticles enhances blood velocity. Numerous researchers [7–10] have focused on the study of vascular
disorders using various approaches. Crucial elements of the circulatory system are blood vessels. Transporting
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vital nutrients and oxygen to the body's active tissues while eliminating waste is the main goal of the
circulatory system. Blood flow patterns are crucial to the development and progression of cardiovascular
disorders.
Causes
Symptoms
Complications
Rheumatic fever, radiation
therapy, calcium accumulation, and
birth abnormalities.
palpitations, swelling ankles or
feet, chest pain, and trouble
walking short distances.
arrhythmias, endocarditis, blood
clots, cardiac failure, and stroke.
In recent years, the computational fluid dynamics (CFD) technique has gained utility for problems involving
physiological fluxes. CFD's primary goal is to use computational power to numerically simulate fluid motion
and heat transport. Using COMSOL, J. Liu et al. [11] investigated numerical solutions to equation-governing
issues. The maximum and minimum values for temperature, pressure, and velocity were determined by A.
Hussainetal [12] in his study of the heat transfer consequences for laminar and unsteady fluid flow through
several elliptic cylinders. This article examines the dynamics of blood flow via a stenosed area. The Newtonian
characteristics of blood in big cavities, veins, and arteries led us to infer that blood is a Newtonian fluid. CFD
was used to determine the velocity, temperature, and pressure of the blood flow inside the affected area after
the law of conservation of mass, momentum, and energy was solved using COMSOL Multiphysics software.
In order to find out how hybrid nanoparticles (NPs) can improve blood flow, this article presents the
mathematical analysis of adding gold and silver nanoparticles to blood passing through a stenosed area.
Materials and Procedures :
Blood was considered to be an incompressible, unstable Newtonian fluid passing through an artery
constriction in this study. Figure 1 depicts a sketch of the arterial stenosis blood flow problem. The coordinate
system was chosen so that the blood flow was along the z-axis and r was interpreted as perpendicular to the
flow.
Figure 1. The geometry of arterial stenosis
The two-dimensional artery's coordinate locations were r = 0.1 and z = 0, and its breadth and height were 1.1
and 0.8 meters, respectively. The "add physics" function in COMSOL 5.4 was used to incorporate the physics
of laminar blood flow and heat transfer. The entrance and exit locations were chosen, and the velocity was zero
at the boundary wall.
19.85 °C was chosen as the reference temperature for the laminar flow and heat transfer. Temperature 1 at the
upper boundary was determined to be 24.85 °C, whereas temperature 2 at the lower boundary was 27.35 °C.
The initial temperature in the heat transfer was −73.15 °C. Blood's material qualities, or thermophysical
qualities, were added. The time-dependent model governing equations, which include the mass, momentum,
and heat transfer equations [13, 14], were then included.
Continuty Equation :
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In COMSOL, the equation of continuity that described the blood mass transport was expressed as:
where u and w are the velocities of the nanofluid denoted in r and z
directions, respectively.
Equation of Motion :
The momentum equation model in COMSOL was displayed as follows:
whre
,
and P are the density, viscoity and pressure of the nanofluid, respectively.
Energy Equation :
In COMSOL, the governing heat transfer equation was
where q =
is the thickness of the fluid, which is equal to 1 m, Q is the heat source, Q
vd
is viscous dissipation heat
source. T shows the tempetrature gradient, C
p,nf
shows the heat capacitance of the fluid and k
nf
is specific
heat. The considered initial values are :
and P = 0. (9)
The thermophysical properties of the hybrid nanofluids were defined as follows (15)
:
Boundary Conditions :
Inlet, outflow, wall, and thermal insulation were all part of the boundary conditions.
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The Inlet : At the artery's inlet, the velocity, or blood flow rate, was simulated. The area of the inflow cross-
section and the velocity at the intake could be used to regulate the blood volume. The model's inlet definition is
depicted in Figure 2.
Figure 2. The geometry of the inlet.
The inlet boundary condition was :
(11)
where U
o
is the normal inflow velocity, which is equal to 0.5.
The Outlet : To give the simulation a more genuine feel, we introduced the blood flow model's pressure at the
outlet. The exit, where the blood poured out, is shown in Figure 3. It was located on the other side of the
entrance.
Figure 3. The geometry of the outlet.
In COMSOL, the equation at the outlet was given as :
(12)
where n = (n
r
, n
z
) is the pointing normal outflow velocity and the absolute pressure is P
0
= 0 Pa.
At the Wall : Because blood is viscous, it adheres to the wall and cannot pass through it. Consequently, the
boundary conditions at the wall were :
(13) and no slip condition was considered. Figure 4 represent the wall of
arterial stenosis.
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Figure 4. The wall of arterial stenosis.
Thermal Insulation :
The insulated boundaries in the COMSOL heat transfer feature are shown in Figure 5.
Figure 5. The thermal insulated boundaries of the problem.
The thermal insulation equation used in COMSOL was :
(14)
2.5.Computational Mesh : One of the key components of computational fluid dynamics is mesh. The mesh
quality can be used to determine the accuracy of the solution and the pace of convergence. Mesh is
automatically created by COMSOL's "physics controlled mesh" function. Meshes with finer element sizes
perform better and yield more accurate results than those with larger elements. The "normal" and "fine"
element size meshes are depicted in Figures 6 and 7. It was found that the mesh was less refined when it was
far from the stenosis and more refined in the stenosed area.
Figure 6. Normal element size mesh
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Figure-7. Find element size mesh.
3. Validation : The results produced by adding a hybrid nanoparticle were compared to those of [15] in
order to assess the problem's correctness. The starting velocities of 0.1 and 0.05 were chosen. We used
a starting velocity of 0.5 in our simulation. The findings of our simulation show that adding
nanoparticles enhanced the velocity outcome, even if the other circumstances remained the same. There
is good agreement between the current results and [15].
4. Results : An important and difficult subject is the mathematical analysis of blood flow in the arteries.
Arterial stenosis, the contraction and hardening of blood channel walls, is the most prevalent illness in
the arterial system. When hybrid nanoparticles are added to arteries with stenosis, a mathematical
model to determine the blood's velocity, temperature, and pressure was examined. The simulation
findings changed when hybrid nanoparticles were included because they altered the physical
characteristics of blood, including its density, specific heat, dynamic viscosity, and thermal
conductivity. Nusselt number variation was examined in order to observe the heat transport
phenomenon. The problem's two-dimensional drawing is displayed in Figure 1. The blood flow's
entrance point is shown in Figure 2, and this boundary condition also determined the fluid's velocity.
The fluid flowed out of the outlet point, which is depicted in Figure 3. The problem's wall and thermal
insulation borders are depicted in Figures 4 and 5, respectively. The boundary conditions for thermal
insulation suggested that the simulation's heat source had no effect on the circumstances. We examined
the effects of normal and fine element size meshes on the outcomes, which are displayed in Figures 6
and 7. There were 1529 elements in total, with the mesh vertices of the normal element size being 948,
the total triangles being 1315, the quad entities being 214, the highest element size being 0.0737, and
the minimum being 3.3 × 10-
4.
The resolution of the narrow region was 1, the minimum element size
was 8 × 10-
4
, the maximum element size was 0.028, the total number of elements was 1981, the mesh
vertices of the fine element size were 1195, the total triangles were 1747, the quad entities were 234,
and the vertex elements were 8. The temporal variations for velocity, pressure, temperature, isothermal
contours, and streamlines for t = 0.1 s, 0.7 s, and 1 s are shown in Figures 8–21. Figures 8–10 illustrate
the velocity profile's effects. At t = 0.1 s, the velocity in Figure 8 is 1.59 m/s. The top speed in Figure 9
is 1.57 m/s at 0.7 s. The top speed in Figure 10 is 1.58 m/s at 1 s. The findings indicate that t = 0.1 s, or
1.59 m/s, was the maximum velocity. As can be observed, the inlet's flow pattern was smooth.
Additionally, compared to both before and after the stenosis, the sick region had a higher velocity.This
was expected as the narrow zone should have a higher velocity according to the results of Bernoulli's
equation. The temperature profiles for heat transport are displayed in Figures 11–13. While the
temperature fluctuated over time, the upper and lower temperature limits stayed constant at 26.85 0C
and -73.15 0C, respectively. The findings demonstrate that the heat transfer ratio was successfully
increased by the use of nanoparticles.The pressure profiles are displayed in Figures 14–16. At t = 1 s,
the pressure reached its highest and minimum values. The pressure was at its lowest toward the end of
the stenosis, while it was at its highest right before the stenosed area. The isothermal contours for the
temperature profiles are displayed in Figures 17–19. The isothermal contours' minimum contours were
discovered at t = 0.1 s, while their maximum range stayed constant. The contour pattern dispersed and
moved out of the confined area. The streamlines that recirculated following the stenosis are shown in
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Figures 20–22. The Nusselt number (Nu) was used to analyze the overall heat transfer. Figure 23 shows
how the Nuav number changes over time in the current problem. It is evident that as the fluid flow
reached the stenosis borders, the Nusselt number decreased, and that the average Nusselt number rose
before and after that point at different periods. The current model is validated in Figure 24.
Figure 8. The velocity profile at t = 0.1 s.
Figure 9. The velocity profile at t = 0.7 s.
Figure 10. The velocity profile at t = 1 s.
Figure. 11. The temperature profile at t = 0.1 s.
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Figure. 12. The temperature profile at t = 0.7 s.
Figure. 13. The temperature profile at t = 1 s.
Figure 14. The pressure profile at t = 0.1 s.
Figure 15. The pressure profile at t = 0.7 s.
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Figure 16. The pressure profile at t = 1 s.
Figure 17. The isothermal contour profile at t = 0.1 s.
Figure 18. The isothermal contour profile at t = 0.7 s.
Figure 19. The isothermal contour profile at t = 1 s.
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Figure 20. The streamlines at t = 0.1 s.
Figure 21. The streamlines at t = 0.7 s.
Figure 22. The streamlines at t = 1 s.
Figure 23. The Nusselt number variation with time.
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The calculated mesh element size and area in m
2
for the normal and fine settings are shown in Table 1. For
improved performance and more accurate results, we utilized the fine element size mesh. The mesh statistics
for the mesh elements, mesh area, mesh quality, total number of triangular and quadrilateral entities, and total
number of elements are described in Table 2. The stenosed artery's mesh size, including its maximum and
minimum mesh element sizes, narrow region resolution, maximum element growth rate, geometric entity level,
and curvature factor, is displayed in Table 3.
A key component of the simulation is the mesh pieces' quality and resolution. The dynamic viscosity, thermal
conductivity, heat capacity, and density of the blood were all impacted by the characteristics of the blood base
fluid and the gold and silver nanoparticles used to determine the solution in Table 4.
Table 1. The mesh elements computed using COMSOL.
Elements
Element Size
Mesh Area
Mesh 1
Normal
0.5949 m
2
Present study
Mesh 2
Fine
0.5948 m
2
Figure 24. The validation figures with [17] and our obtained results.
Table 2. A description of the mesh statistics.
Property
Value
Mesh vertices
1195
Edge elements
173
Quadrilateral entities
234
Triangles
1747
Vertex elements
8
Average element quality
0.8291
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Minimum element quality
0.3539
Mesh area
0.5948 m
2
Total no. of elements
1981
Ratio area of element
0.06767
Table 3. A description of the mesh sizes.
Property
Value
Maximum element growth rate
1.13
Maximum element size
0.028
Minimum element size
8 x 10
-4
Curvature factor
0.3
Resolution of narrow region
1
Geometric entity level
Entire geometry
Table 4. The thermophysical properties of the blood fluid and the silver and gold nanoparticles [16].
Property
Variable
Blood
Gold
Silver
Unit
Dynamic viscosity
0.003
0.00464
0.005
Pa. s
Heat capacity
3746
129
235
J/(kg. K)
Thermal conductiry
K
0.52
310
429
W/(m. K)
Density
1063
19,300
10,500
Kg/m
2
CONCLUSIONS
We looked into how utilizing hybrid nanoparticles affected the flow of blood through an artery that was
damaged. This study's primary goal was to report the CFD results for the pressure, temperature, and velocity
across the artery's narrow section. The results show that the inclusion of silver and gold nanoparticles inhibited
the maximum velocity and prevented overheating. Hemodynamics could be better understood by using our
simulations. Among the primary findings were:
• The laminar flow investigation demonstrated that arterial plaque causes variations in the blood flow velocity
throughout the model.
The maximum velocity of the blood flow was 1.59 m/s at t = 0.1 s;
• The isothermal contours clearly showed the results on colored surfaces at t = 0.1, 0.7, and 1 s;
• The temperature and Nusselt number curves varied for slight variations of time; • The pressure profiles also
showed clear patterns near the stenosed region;
• The streamlines displayed abnormal behavior near the stenosis area and that recirculation occurred as the
intensity of the stenosis increased; the flow was normal when nanoparticles were added;
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• We can further study the physical characteristics, such as skin friction coefficient, and also analyze the
problem using radiation and magnetohydrodynamic effects to understand the causes of stenosis, which may aid
in the treatment of arterial stenosis.
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