Application of Nanofluids for Cooling Newtonian and Non-newtonian Blood Mimicking Fluids Flow in Annular Space

An experimental study performed to investigate the effect of nanofluid forced convection heat transfer and fluid flow characteristic. Three types of nanofluids {γAl2O3, CuO and ZrO2-DIW} flow under laminar or turbulent condition in inner pipe. The shear thinning behavior of blood is more accurately modeled by non-Newtonian Blood Mimic Fluids BMF. Here heat transfer and friction factor correlations developed for nonreactive Newtonian and non-Newtonian BMF fluids of (water: glycerol: xanthan gums) and heparinized bovine blood. The results show that the BMF Nussult number (Nub) increased as increasing Graetz number, and as flow index (n) decreasing. Bovine blood gives the temperatures distribution similar to (BMF6) but with lower Nusselt number by (31.2%). The BMF friction factor increases with decreasing (n), but the Bovine blood gives higher friction factor as compared with BMF6 by (25.6%). It was observed that all nanofluids types showed higher heat transfer characteristics than the base fluid DIW. It was also noted that in the γAl2O3 shows higher enhancement than the other by (82.4%) at (Renf =12670) and (ɸ=1 vol.%). Comparisons present experimental results with previously reported results it gives good agreement.


Introduction
The heat transfer characteristics in blood heat exchangers BHE used in many medical applications for cooling biofluid such as blood, where recently the most effective hypothermia method used is intravenous cooling catheters inserted in the vena cava blood vessel (IVC) and by using water as the usual cooling or warming medium. The non-Newtonian blood flows in annular space between the blood vessel wall and cooling catheter studied by [1,2]. Convective heat transfer in double pipe systems can be enhanced in several ways, by using either active or passive techniques. The active case, is to modify the fluid itself by enhancing its thermal conductivity. Various techniques have been used to increase the thermal conductivity of base fluids by introducing solid particles whose conductivity is generally higher than that of liquids. New classes of fluids called Nanofluids have recently been developed, tested and studied by Sebastien et al. [3], Choi [4], Zeinali et al. [5], Anoop et al. [6] and Zhang et al. [7]. Byung et. al. [8] Aghayari et. al., [9], Sudarmadji, [10], Mohamed et. al., [11] performed an investigation for the convective heat transfer coefficient of nanofluids made of several alumina nanoparticles and transformer oil flowing through a double pipe heat exchanger system in laminar nanofluids exhibited a considerable increase of heat transfer coefficients of alumina is much higher than that of the base fluids. Masoud et al. [12] studied the plate and concentric tube heat exchangers by using water-water and nanofluidwater streams. The ZnO/water (0.5 vol. %) nanofluid has been used as the hot stream. They results show that heat transfer rate and heat transfer coefficients of the nanofluid is higher than that of the (water). In the concentric heat exchanger the heat transfer coefficient of nanofluid at (m=10g/s) is about (14%) higher than the base fluid. Bozorgan et al. [13] used nanofluids as coolant candidate in chemical processes for water waste remediation. The inlet and outlet temperatures of hot solvent stream are equal to (40°C and 30°C), respectively. The flow rate of hot solvent stream is (0.8 kg s -1 ). The inlet temperature of nanofluid coolant is equal to (5°C). Al 2 O 3 nanoparticles dispersed in water with volume concentrations up to (2 vol. %) were selected as a coolant. The results show that the flow rate of nanofluid coolant decreases with the increase of concentration of nanoparticles in the exchanger with a given heat exchange capacity.
The study of blood flow through an axisymmetric annular tube has been the subject of many studies, due to its relevance to blood flow in a catheterized artery studied by [14, 15, 16 and 17]. Dash et. al. [18] estimated the increased flow resistance in a narrow catheterized artery using the Casson fluid model. Banerjee et al. [19] investigated the changes in flow and mean pressure gradient across a coronary artery using power law and Carreau model, a shearrate-dependent non-Newtonian fluid model. Jason [20] models two dimensional, axis-symmetric, counter flows with two domains of the catheter balloon and the vena cava blood vessel. Implemented in COMSOL program to modeling the intravenous catheter cooling system, Chose to model both the vessel and the catheter as concentric cylindrical tubes for simplicity sake. His results show that whether increasing the length of catheter and decreasing the cooling fluid temperature or decreasing the length of the catheter and increasing the cooling fluid temperature reduces the treatment time significantly. Laminar flow with pseudoplastic and dilatant fluids (power-law models) was studied experimentally by [21, 22 and 23] studied the friction factors and heat transfer with power-law fluids with flow index of 0.5 to 1.0. They showed that the friction factor increased with decrease in the flow index and he Nusselt number increased with decreasing flow indices (n) and Nusselt number increases with decreasing (n). The flow of non-Newtonian fluid in annulus also studied by [24,25]. Very little work has been done in the experimental study the flow and thermal characterizations together of BMF flows in annular space and cools by nanofluid flows in inner pipe in double-pipe heat exchanger. In this study using simulation of human blood flow in annulus between the cooling catheter wall (inner pipe) and the IVC blood vessel wall (outer pipe) of the intravascular cooling catheter, to find the temperature distribution around the catheter, using two domains of the BMF and the effect of using nanofluids instead of DIW with opposite direction flows.

Experimental Apparatus
( Figure. 1) shows the schematic diagram of experimental loop, it consists of a test section, a two centrifugal pump, condensation unit with immersion coil and a heating unit. The test section is a (1.0 m) long counter flow double-pipes heat exchanger with DIW flows inside the inner pipe while hot BMF flows in the annular space. The inner tube is made from a non-corrosive medical suitable smooth stainless steel (SS 304) with external diameters (10.05 mm) and (8.75 mm). The outer tube is made from transparent plastic diameters of (30.25 mm) and (23.45 mm). The test section is thermally isolated from its upstream and downstream section by rubber plug, and thermally isolated on the external surface of the outer tube. Seven thermocouples are mounted at different longitudinal positions on the inner pipe surface. The inlet and exit temperatures of DIW and BMF are measured using four T-type thermocouples. Two receiver tanks of (20 L) are made from glass to store the BMF and nanofluids leaving the test section. The hot BMF flow rate are controlled by a flow meter (Model LD100, MLW, Germany) was used to initially adjust the desired flow rate in each experiment, but exact measurements were obtained by weighing fluid samples collected at determined time intervals. under the laminar condition only of (1-7 l/min), it calibrated to fit work with the non-Newtonian fluid flow, for nanofluid flow under laminar and turbulent conditions using flow meters of (0.3-0.8 l/min) and (1.8-18 l/min) respectively.

BMF Sample Preparation
In the preparation process of Newtonian (BMF1 and BMF2) models using fluids content the (water: Glycerin) mixture. By adding the DIW into (5 liters) beaker, and then add the glycerin liquid, the glycerin should try to settle down because it's high viscosity and density than the DIW. Water and glycerol are easily miscible so it will dilute easily and if they mixed gently with stirring they will miscible quickly using a mechanical agitation stirring for (20 min) until the solution is reaches the homogeneous state. But preparation process of non-Newtonian (BMF3 and BMF4) and (BMF5 and BMF6) models with a high rheological properties using two polymer types, the first consist of two BMF of (water: xanthan gum), the second BMF using include two BMF of (water: Glycerin: xanthan gum), where the ternary mixture water-glycerol-xanthan simulates the non-Newtonian rheological behavior of blood. was produced by filling the beaker of (5 liters) by specified weighted ratio of the DIW and adding the polymer powder lightly sprinkled into the water and stirring continued using the mechanical agitation stirring for about (one hour) to ensure completely polymer dissolution. The prepared BMF models was kept at rest at room temperature for (24 hr) prior to conducting the measurements of rheological parameters (m) and (n) by power low of (τ=m(γ) n ) given by Brookfield DV-II+Pro coaxial rotational rheometer and using the Rheocalc software (version 3.2) for data acquisition and compared the parameters with [26,27] and give good agreements. Thermophsical properties also measured and listed shows in (Table. 1). Also was used (3.0 liters) heparinized bovine blood with a hematocrit of (35%). The blood is mixed gently every (5 minutes) to keep it homogenous. In the beginning of the first experiment, the blood is re-circulated for one minute through the primary reservoir to ensure that all components of the system work properly without loss of blood.

Preparation of Nanofluid
Three types of nanoparticles of (Alumina Al 2 O 3 , Copper Oxide CuO and Zirconia ZrO 2 ) are used in this research. All thermophysical properties for the three types of the nanoparticle and the base fluid are given in (Table. 2). The Two-steps method is used for preparation of nanofluid. By using the electronic gram scale, to get the desired mass of nanopowder, the dispersant weighed powder (Al 2 O 3 , CuO or ZrO 2 ) nanoparticles were dissolved in the DIW. The volume of mixture (water/nanoparticles) was set at (3.0 liters). This mixture was mixed slowly in the sonicator that can be timed for a maximum of (15-20 minutes) to break up any particle aggregates. All the suspensions, that had an ink-like appearance, were stored at ambient temperature and checked periodically for visual changes. In this research during the experiments five volume concentrations (0.02, 0.06, 0.2, 0.6 and 1.0 vol. %) for (Al 2 O 3 and CuO and ZrO 2 ). All thermophysical properties of these nanofluids employed are measured experimentally by using certificated instruments. (Figure. 2) show samples of (ZrO 2 -DIW, CuO-DIW, γAl 2 O 3 -DIW) nanofluids

BMF Calculations
The heat transfer coefficients and pressure drop of BMF can be calculated from the following equations: The heat transfer rate into the BMF is defined as: The heat transfer rate into the DIW is defined as: The average heat transfer rate is defined as follows: The experimental local heat transfer coefficient and Nusselt number of the BMF are computed from the following equations.
The convection BMF heat flux can be represented by: where A i is the heat transfer area given by: The BMF local heat transfer coefficient can be obtained as: And the BMF local Nusselt number can be obtained as: Where hydraulic diameter of annular space calculate as: The experimental average heat transfer coefficient and Nusselt number of the BMF are computed from the following equation: The BMF average heat transfer coefficient can be obtained as: Then the BMF average Nusselt number can be obtained as: Similarly to the heat transfer coefficient, the friction factor of the BMF is calculated from: where (fb) is the friction factor of the BMF, (∆P b ) is the measured pressure drop of the BMF.
All BMFs employed in this study exhibit the power-law rheological behavior expressed by the following equation [28]: In this work, the non-Newtonian fluids are based on a power-law equation (Eq.11). Values of (n < 1) are shearthinning fluids and with (n > 1) are shear-thickening fluids. For Newtonian fluids have (n=1). The shear stress is proportional with the fluid viscosity (µ) and shear strain(< ).
For power-law shear-thinning fluids the wall shear rate is: [29] γ > ?? = The effective viscosity at the wall shear rate is: [29] F = (γ > ?? ) $B For purely viscous non-Newtonian fluid, Wickramasinghe et al. [30] define a generalized Reynolds, Re b for power law as follows (14) where u b is the average velocity of the shear-thinning fluid, which may be related to the average velocity of a Newtonian fluid by: And modified Prandtl number is given by [31]: The Graetz number is defined by: The Péclet number is given by:

Coolant Calculations
Using (Eq.2) to find the convection heat flux of nanofluid can be represented by: The nanofluid local heat transfer coefficient can be obtained as: And the nanofluid local Nusselt number can be obtained as: Where hydraulic diameter of inner pipe calculate as: Dh=di For Newtonian nanofluid, the Reynolds number is defined as: The Darcy friction factor (f) of the nanofluid flowing through inner pipe is defined as:

Results and Discussion
The experimental conditions used in this study are:

Temperature Distribution
The variation curves of inner pipe wall temperatures (T wx ) have the general shape plotted in (Figure. 3a, b) in the case of using the nanofluid to cooling (BMF2 and BMF6) under the laminar condition. It shows that the (T wx ) increases gradually from (pipe inlet x=0.0 m), along the inner pipe until to attains a maximum value at (pipe exit x=1.0 m). (Figure. 4) shows the variation of (T wx ) for nanofluid laminar and turbulent flow to cool the Bovine blood (H=35%) and BMF6 models it shows that the using BMF6 gives the nearest values of (T wx ). Due to approach between the non-Newtonian fluid behavior BMF6 and Bovine blood in the rheological behavior index (n) of the two fluids.     The effect of the inner Reynolds number (nanofluid) can be found in (Figure. 6 a, b) for the case of using (Al 2 O 3 -DIW) at concentration of the nanoparticles (ϕ=0.2). It shows that the Reynolds number will be changed from case to another according to the types of the nanofluid and according to the concentration of the nanoparticles (ϕ) due to the differences in the thermo phsical properties for various concentrations.    Figure. 8 a, b) shows the effect of nanoparticles concentration in the case of using types of coolants (DIW, Al 2 O 3 , CuO and ZrO 2 ) on the experimental (T wx ) to cool the (BMF2). Zero concentration of the nanoparticles (ϕ=0.0) for (DIW), clearly show that increasing the concentration of the nanoparticles (ϕ) in the nanofluid decrease the (T wx ), in Al 2 O 3 ( Figure. 8 a). Increasing the concentration of the nanoparticles ϕ (from 0.0 to 1.0 vol. %) causes a decrease in the (T wx ) by (8.1%). due to increasing of the thermal conductivity of the base fluid DIW for all types of nanofluid. (Figure. 8b) compares between coolant types (DIW, Al 2 O 3 , CuO and ZrO 2 ). It shows that using Al 2 O 3 gives the lowest (T wx ) and DIW gives the highest with decreasing percent of (12.1%).

Convective Heat Transfer
Effect of using Bovine blood compared with BMF6 suggested in this study on the annular Nusselt number (Nu b ) with Greatz number at the same experimental conditions showed in (Figure. 9). The results show the Bovine blood gives decreasing in (Nu b ) by (19.4%) compared with non-Newtonian BMF6 but gives maximum increasing of (Nu b ) if compared with Newtonian BMF2 by (14.6%) at (Gz=500). The effect of the annular Reynolds number of the BMF2 and BMF6 on the annular Nusselt number (Nu b ) is illustrated in (Figure. 10 a, b) for laminar DIW. The (Nu b ) began at high value at (pipe exit x=1.0 m) and dropped gradually forward to the (pipe inlet x=0.0 m) due to counter flow. And the overall behavior of (Nu b ) seems as straight line for the folly developing region in the test section. This shows that the annular Reynolds numbers different according to the BMF models type because of the difference in the thermophysical properties and rheological behavior especially on the flow behavior index (n) between these fluids. It is observed that the (Nu b ) increases with annular Reynolds number. The Newtonian type (BMF1) in ( Figure. 10a) gives maximum increasing of (51%) when increasing the Re b from 500 to 1260.

Figure 10. Effect of BMF types on the variation of annular Nusselt number, at various annular Reynolds number.
The types of BMF flow in the annulus, are given in (Figure. 11 a, b) for laminar and turbulent DIW flow conditions (Rew=830 and 5070) with various Greatz number (Gz =RePr). The results show that the (Nub) increases by (51.6%) with increasing Gz from 500 to 1260 for using BMF1, and by (46.2%) when using BMF6 but the BMF4 gives the high (Nub). ( Figure. 12 a, b) presents the effect of inner nanofluid Reynolds number in the condition of turbulent flow, using (Al 2 O 3 -DIW) at (ɸ=0.2 %) as a coolant to cooling (BMF2 and BMF6). It is noted that the local inner Nusselt number (Nu nf ) increased with increasing nanofluid Reynolds number by (82.4%) if Re w increased from (5070 to 12670). Non-Newtonian Blood Mimicking Fluids Flow in Annular Space

Friction Factor
Pressure drop results for the BMF models are presented in (Figure. 14 a, b). It shows the effect of the BMF types and flow index (n) of Newtonian and non-Newtonian (BMF) on the annular friction factor. It basically shows that the four non-Newtonian fluid BMF models have the highest values of friction factor as compared with the two Newtonian fluids BMF models due to increasing the fluid viscosity and rheological properties. (Figure. 14 a) shows that the (f b ) increases by (34.6%) at Re= 360 between the BMF1 and BMF2. ( Figure. 15) shows the effect of using Bovine blood and BMF6 on the experimental annular friction factor with the annular Greatz number. It shows that the real bovine blood gives a maximum annular friction factor by (21.3%) compared with BMF6. The behavior of friction factor for the types of coolant at laminar and turbulent flow in ( Figure. 16 a, b) shows that the inner friction factor decreases with increasing Reynolds number for all types. But when using (Al 2 O 3 -DIW) gives the highest friction factor by (40.2%) for laminar condition at Re nf =1630 due to the smallest nanoparticles diameter of (20 nm) lead to increasing the nanofluid viscosity and then increased pressure drop. But (Al 2 O 3 -DIW) shows the highest values for turbulent flow condition by (36.6%) at (Re=10080) as compared with the DIW. Effect of the concentration of (Al 2 O 3 -DIW) on friction factor for laminar and turbulent flows presented in ( Figure.  17 a, b). The inner friction factor for all nanofluids increases with increasing the nanoparticles concentrations by (33.2 %) when ɸ increased (from 0.0 to 1.0 vol. %) for laminar Re w =1630 and by about (36.3%) for turbulent Re w =10050. The rise in friction factor is due to rise in viscosity of the nanofluids when the nanoparticles are adding to the DIW.

Performance Evaluation Criterion (PEC)
Performance evaluation criterion: is defined as the ratio of heat transferred to the required pumping power in the BMF section [32]: (22) ( Figure. 18 a, b) shows the PEC was decreased with increasing inner Reynolds number due to increasing pressure drop across the inner pipe for all types of nanofluid at concentration (ϕ=0.2 vol. %). The DIW and ZrO 2 -DIW give low values and the CuO-DIW gives an increasing PEC by (52%) and Al 2 O 3 -DIW gives increasing by (57%) for laminar condition of (Re=1200) than the using DIW. But for the case of turbulent flow, it can be observed that the value of PEC is very low compared with the laminar condition due to the higher value of pressure drop. The ZrO 2 -DIW gives an increasing in the PEC by (11%), for CuO-DIW by (34%) and for Al 2 O 3 -DIW about (56%) at turbulent condition of (Re=7500).

Validation Results with Proposed Correlations
To compared the experimental annular Nusselt number (Nub) for Newtonian and non-Newtonian BMF using ( Figure. 19a, b) as comparison the experimental Results of (Nub) flow with the Newtonian and non-Newtonian Leveque Eq. [33] general equation (Eq. 23), and obtained on the acceptable agreements with deviation about (15.4%) for the Newtonian BMF2 and about (9.7%) for the non-Newtonian BMF6.
, (23)  In general, Nusselt numbers and friction factor of the working fluids related with parameters listed in (Table.3). The equation for predicting the heat transfer performance and friction factor of DIW, Al 2 O 3 -DIW nanofluid and (BMF2, BMF6) was formed and is proposed in (Table. 4