Jet Impingement Cooling of a Rotating Hot Circular Cylinder with Hybrid Nanofluid under Multiple Magnetic Field Effects

Abstract

The cooling performance of jet impinging hybrid nanofluid on a rotating hot circular cylinder was numerically assessed under the effects of multiple magnetic fields via finite element method. The numerical study was conducted for different values of Reynolds number ($100\le \mathrm{Re}\le 300$), rotational Reynolds number ($0\le \mathrm{Rew}\le 800$), lower and upper domain magnetic field strength ($0\le \mathrm{Ha}\le 20$), size of the rotating cylinder (2 w $\le r\le$ 6 w) and distance between the jets (6 w ≤ H ≤ 16 w). In the presence of rotation at the highest speed, the Nu value was increased by about 5% when Re was increased from Re = 100 to Re = 300. This value was 48.5% for the configuration with the motionless cylinder. However, the rotations of the cylinder resulted in significant heat transfer enhancements in the absence or presence of magnetic field effects in the upper domain. At Ha1 = 0, the average Nu rose by about 175%, and the value was 249% at Ha1 = 20 when cases with the cylinder rotating at the highest speed were compared to the motionless cylinder case. When magnetic field strengths of the upper and lower domains are reduced, the average Nu decreases. The size of the cylinder is influential on the flow dynamics and heat transfer when the cylinder is rotating. An optimum value of the distance between the jets was obtained at H = 14 w, where the Nu value was highest for the rotating cylinder case. A modal analysis of the heat transfer dynamics was performed with the POD technique. As diverse applications of energy system technologies with impinging jets are available, considering the rotations of the cooled surface under the combined effects of using magnetic field and nanoparticle loading in heat transfer fluid is a novel contribution. The outcomes of the present work will be helpful in the initial design and optimization studies in applications from electronic cooling to convective drying, solar power and many other systems.

1. Introduction

Jet impinging heat transfer (j-imp HT) applications arise in different thermal engineering systems. Some examples include drying, solar power, electronic cooling, textiles and turbine blade cooling. In solar power applications, photovoltaic panel thermal management can be achieved by using impinging jets. Locally higher HT coefficients can be achieved. The coupled interactions among the established recirculations, pressure gradients and thermal field within the system make the system’s performance analysis very complex in the presence of complex geometries. Effects of different geometric factors and operating parameters on the j-imp HT characteristics were analyzed for single and multiple jets Garimella [1]. Many review works have been devoted to analyzing the convective HT with impinging jets: j-imp HT in the turbulent regime for a single circular j-imp [2], air j-imp HT in food processing [3] and j-imp in solar power [4].

The effectiveness of using liquid jets can be enhanced by introducing nano-sized particles in HT fluid, forming nanojets. In thermal energy systems, nanofluids (N-F) are widely used in different applications, such as solar, refrigeration and thermal management in diverse HT systems [5,6,7,8,9,10]. The potential benefits of using N-Fs in those systems have been shown. In j-imp HT, N-Fs have been used, and improved HT characteristics were reported in many studies [11,12,13,14,15]. In a review Mohammadpour and Lee [16], the effects of using N-Fs on the HT improvements for conventional and swirl type impinging jets were analyzed. Some challenges, such as nanoparticle agglomeration and pressure drop, were mentioned with future trends and applications. In the experimental work of Teamah et al. [17], an up to 62% increment in the HT coefficient was obtained with nanofluid as compared to water for j-imp on a flat surface. Using CuO nanoparticles delivered the best performance. Naphon and Wiriyasart [18] experimentally analyzed the nano j-imp HT in a micro channel heat sink by using TiO₂ nanoparticles. They observed convective HT incrementation by about 18.56% at a nanofluid concentration of 0.015%, and no additional pressure drop was obtained. Some other aspects of j-imp HT with nanofluids have been considered, such as moving surface [19], flow pulsation [20,21], boiling HT [22,23] and surface corrugation [24,25]. The form of the target surface is also very important in j-imp HT [26,27]. Rotating objects have been considered in several convective HT applications. Size, rotational speed and the location of the object were found to be effective in altering the flow dynamics and HT characteristics [28,29,30]. Some studies considered the rotations of the surface with impinging jets [31,32,33,34].

The application of a magnetic field (MaF) in engineering is encountered in diverse applications, such as in geothermal energy, coolers of nuclear reactors, micro pumps, continuous casting processes and many others [35,36]. Finite element method (FEM) simulations of configurations with MaF effects have been proposed in diverse studies [37,38,39,40], and extensive literature on the electromagnetic forward problem computation via the FEM is available [41,42,43]. In convective HT, applications have also been considered with imposed external MaF for thermal management and flow control [44,45,46,47,48,49]. The effectiveness of using MaF was further elaborated by using nano-sized particles in HT fluid [50,51,52,53]. In j-imp HT, MaF effects were considered in several studies [54,55] and with nanojets [56,57]. In those studies, reduction in the convective HT was achieved, and adding nanoparticles improved the HT. The suppression of the vortices and potential of the HT entrancement can be achieved with MaF effects depending upon the geometry of the configuration, such as flow over step, or in cavity flows [58,59,60]. As different geometries and various corrugation levels of the impinging surfaces are available with impinging jets, there is potential for MaF to improve the convective HT.

The present study deals with the confined slot j-imp HT and flow features for a rotating surface located in between the domains that are under the effects of MaF of different strengthens. Two opposing cold jets were used for cooling the hot rotating cylinder, and MaFs in different domains were uniform and inclined. A hybrid nanofluid was used, as the HT fluid and the experimental data were available for the effective viscosity and thermal conductivity of the nanofluid. As there are many applications of impinging jets in different energy system technologies, the use of multiple MaF effects for a jet impinging on a hot rotating surface is a novel contribution. The MaF effects can be available within systems such as continuous casting systems for molten metals and nuclear reactor cooling, or they can be imposed as external sources for flow and HT control. The use of nanofluids in a jet configuration with accurate descriptions of nanofluid property relations improves the HT performance and gives more flexibility for convective HT control of the thermo-fluid system. In this study, modal analysis was used for exploring the heat transfer dynamics of the j-imp system under multiple MaF effects, and the details are explained in the following subsection of the manuscript.

2. Mathematical Model

Jet impingement (j-imp) cooling performance with hybrid nanofluid (N-F) is explored for a rotating hot cylinder exposed to jets in opposite directions, as shown in Figure 1. A hot rotating cylinder (R-C) with radius r is used, with a rotational speed of $\omega$. Single confined jets emerging from nozzles with width w are considered. The R-C is in the middle of the computational domain, and the upper and lower parts are exposed to uniform MaF with strengths of ${\overrightarrow{B}}_1$ and ${\overrightarrow{B}}_2$. The inclinations of the MaF are denoted by ${\gamma }_1$ and ${\gamma }_2$. The hot cylinder is maintained at a constant temperature of $T_h$; the cold fluid streams at temperature $T_c$ and velocity $u_c$ enter the domains. The distance of jet inlets to the interface is H, and the lengths of the upper and lower plates, which are adiabatic, is L.

As the HT fluid, hybrid N-F is used. It is 40% ethylene glycol and contains TiO${}_2$-Al${}_2$O${}_3$ binary nanoparticles. Experimental data were used to derive viscosity (${\mu }_{nf}$) and thermal conductivity ($k_{nf}$) correlations for nanoparticle concentrations from 0.02 to 0.1% [61]. They are given by the following expressions [61]:

$${\mu }_{nf}=7.1074+3.65\varphi -0.14097T+0.05176\varphi T+0.907\varphi \varphi +0.00092T^2,$$

(1)

$$k_{nf}=0.386e^{(2.27\varphi +0.002939T)}.$$

(2)

They are valid for an 80:20 mixture ratio of TiO${}_2$-Al${}_2$O${}_3$ in 40% EG. The valid temperature range is between 30 and 80 °C and concentration is between 0.02% and 0.1%. N-F behaves as Newtonian [61]. In the modeling with MaF, Joule heating, induced MaF effects and displacement currents are not considered. The viscous dissipation and natural convection effects are also ignored. The conservation equations are given as:

$$\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}=0,$$

(3)

$$u\frac{\partial u}{\partial x}+v\frac{\partial u}{\partial y}=-\frac{1}{{\rho }_{nf}}\frac{\partial p}{\partial x}+{\nu }_{nf}\left(\frac{{\partial }^{2}u}{\partial x^2}+\frac{{\partial }^{2}u}{\partial y^2}\right)+\frac{{\sigma }_{nf}{B}_i^2}{{\rho }_{nf}}\left(vcos{\gamma }_{i}sin{\gamma }_i-u{sin}^2{\gamma }_i\right),$$

(4)

$$u\frac{\partial v}{\partial x}+v\frac{\partial v}{\partial y}=-\frac{1}{{\rho }_{nf}}\frac{\partial p}{\partial y}+{\nu }_{nf}\left(\frac{{\partial }^{2}v}{\partial x^2}+\frac{{\partial }^{2}v}{\partial y^2}\right)+\frac{{\sigma }_{nf}{B}_i^2}{{\rho }_{nf}}\left(\begin{array}{c}\hfill ucos{\gamma }_i\end{array}sin{\gamma }_i-v{cos}^2{\gamma }_i\right),$$

(5)

$$u\frac{\partial T}{\partial x}+v\frac{\partial T}{\partial y}={\alpha }_{nf}\left(\frac{{\partial }^{2}T}{\partial x^2}+\frac{{\partial }^{2}T}{\partial y^2}\right).$$

(6)

In the above representations, $B_i$ and ${\gamma }_i$ denote MaF strength and inclinations for upper $i=1$ and lower $i=2$ domains, respectively. Here, ${\sigma }_{nf}$ and ${\alpha }_{nf}$ are the electrical conductivity and diffusivity of the nanofluid.

The boundary conditions in dimensional form are written as:

• At the inlet,
  $u=0,v=u_c,T=T_c$.
• At the exit:
  $\frac{\partial u}{\partial x}=0,\frac{\partial v}{\partial x}=0,\frac{\partial T}{\partial x}=0$
• Top and bottom plate are adiabatic and stationary:
  $u=v=0,\frac{\partial T}{\partial y}=0$
• On the rotating cylinder surface:
  $u=-\omega (y-y_c),v=\omega (x-x_c),T=T_h$
• At the interface between the upper and lower domains:
  $u_1=u_2,v_1=v_2,{\left(\frac{\partial T}{\partial n}\right)}_1={\left(\frac{\partial T}{\partial n}\right)}_2$

At the exit of the channels, pressure outlet boundary conditions are utilized.

The following physical, non-dimensional parameters are relevant:

$$\mathrm{Re}=\frac{\rho u_c{D}_h}{\mu },\mathrm{Pr}=\frac{\nu }{\alpha },{\mathrm{Ha}}_i=B_i{D}_h\sqrt{\frac{\sigma }{\mu }}$$

(7)

where $\rho ,\nu ,\alpha ,\mu$ and $\sigma$ denote the density, kinematic viscosity, thermal diffusivity, dynamic viscosity and electrical conductivity of the nanofluid. The characteristic length based on the slot width is given by $D_h$ = 2 w.

As the solver, the Galerkin weighted residual FEM is used. In the formulation, residual R is obtained after using the approximated field variables in the equations. Different ordered Lagrange FEMs are utilized for approximations of field variable (F):

$$F=\sum _{r=1}^{N^s}{\Phi }_r^s{G}_k.$$

(8)

where ${\Phi }^r$ is the shape function and G denotes the nodal value. The residual is forced to be zero in an average manner as:

$${\int }_{V}WRdV=0,$$

(9)

where W represents the weight function, and R is the residual. Artificial diffusion with the streamline upwind Petrov–Galerkin method (SUPG) is used in the solver to handle local numerical instabilities. The biconjugate gradient stabilized iterative method solver (BICGStab) is used for fluid flow and heat transfer modules of code. The convergence criterion of 10${}^{-7}$ was assumed when converged solution results were achieved.

The cooling performance can be represented in terms of Nusselt number (Nu). Local and average Nu are given as:

$${\mathrm{Nu}}_s=\frac{h_s{D}_h}{k_{nf}}=-\frac{D_h}{T_h-T_c}{\frac{\partial T}{\partial s}}_w,{\mathrm{Nu}}_m=\frac{1}{S_{}}{\int }_0^{S_{}}{\mathrm{Nu}}_{s}ds.$$

(10)

where $h_s$ and S denote the local heat transfer coefficient and total length along the circumferential of the hot cylinder; $D_h$ is the hydraulic diameter.

Numerical simulations were checked for grid independency. Numerical tests were conducted for different grid sizes, and results are given in Figure 2a for the variations of the average Nu at two different MaF strengths of the upper domain. Grid system Gr4 with 115,534 elements was selected, and the distribution of the grid near the R-C is presented in Figure 2b.

The numerical code was validated by using different studies available in the literature. In the first study, numerical results from the work of Sahoo and Sharif [62] for j-imp cooling of a surface held at constant heat flux were used. Figure 3a presents the comparison results of average Nu for two different aspect ratios (AR) at Re = 500. The deviations are 0.6% and 1.3% from the reference solution at AR = 4 and AR = 10. Another validation was performed by using the confined slot j-imp cooling results available in [63,64].

Table 1. Stagnation Nu comparisons for confined slot j-imp at Re = 300.

Reference Study	Re = 300
Present study	9.81
Ref. [63]	9.85
Ref. [64]	9.66

presents the stagnation point Nu at Re = 300. The highest deviation was 1.55%, from the results of [64]. Finally, the effect of using MF in convective HT was considered within a cavity by using the results of [65]. Comparison of average Nu for different MF strengths is shown in Figure 3b at Gr = $2\times {10}^5$. The highest difference was found to be below 5% when the present solver results were compared. The results showed that the present code is capable of simulating the effects of MF in convective HT and j-imp HT.

3. Results and Discussion

Coupled interactions between the multiple MaF effects, rotational surface and forced convection of hybrid N-F on the cooling performance were examined for j-imp on a hot rotating cylinder. The upper and lower domains of the were exposed to uniform MaF of different strengths while double jets of hybrid N-F were used for different parts of the rotating cylinder. The nanoparticle concentration was taken as between 0.02 to 0.1%; the nanofluid behaved as a Newtonian fluid. The Reynolds number was between 100 and 300, and the unsteady flow effects were ignored. The MaF strengths and rotational Reynolds numbers were taken as $0\le \mathrm{Ha}\le 20$ and $0\le \mathrm{Rew}\le 800$. Modal analysis was used for the heat transfer dynamics.

3.1. Computational Fluid Dynamics Simulation Results

Flow patterns are shown for different Re numbers in the absence (Figure 4a–c) and presence of (Figure 4d–f) rotational surface effects. When rotations were not active, due to confinement and entrainment, vortices were established near the inlet zones. As the Re was increased, vortex size enlarged. As the rotational surface effects were considered, the vortices near the inlet region were distorted due to the rotations of the cylinder, and additional recirculation zones were observed near the hot cylinder. Effects of Rew on the flow pattern distributions in the absence and presence of MaF in the upper domain are shown in Figure 4g–l. When there were no MaF effects present, recirculation zones near the inlet and and secondary vortices at the interface on the upper part were observed. When rotations were introduced, on the top wall of the upper domain, multi-recirculation regions were established. At Rew = 800, three vortices are shown adjacent to the upper domain top wall. As the MaF was imposed at the highest strength, suppression of the vortices in the upper region is shown for all Rew. Impacts of Re on the average Nu were weaker when rotational surface effects were considered at the highest speed, as shown in Figure 4m. For the case with a motionless cylinder, the average Nu rose by about 48.5%, but this amount was only 5% when rotational surface effects were dominant. The rotations of the cylinder brought significant enhancement of the average Nu as compared to the motionless cylinder configuration in the absence and presence of MaF effects. The enhancements were 175% and 249% when rotational effects at the highest speed were compared with the cases of stationary cylinder at Ha1 = 0 and Ha1 = 20, respectively (Figure 4n).

The suppression of the vortices within different domains by imposing MaF of various strengths is shown in Figure 5a–f for different (Ha1, Ha2) combinations. The computational domain is characterized by multiple recirculations near the inlet zones and interface boundaries when no MaF is present in the system. As is shown in Figure 5a–c, the upper zone recirculation regions were suppressed as Ha1 increased. The vortex size and its number can be adjusted by changing the MaF strengths of the upper and lower domains. The impacts of MaF on the average Nu variation are shown in Figure 5g for different combinations of upper and lower domain MaF strengths. The average Nu decreased with higher Ha1 or Ha2 values. As the MaF strength increased, the suppression of the vortices was observed within the domains, but the flow field was retarded and convective heat transfer was reduced. The trends in the average Nu-Ha1 curves are similar for different Ha2 values. When cases in the absence ((Ha1, Ha2) = (0, 0)) and presence of MaF effects at the highest strength ((Ha1, Ha2) = (20, 20)) are compared, reductions in average Nu by 54.5% are obtained. Reductions in the convective heat transfer with MaF have been shown in various studies for impinging jets. However, in this work, multiple domains were under the effects of MaF with different strengths for impinging jet cooling.

The size of the cylinder and distance between the opposite jets were expected to be influential on the convective heat transfer performance. The flow pattern variations for different sizes (H = 8 w) and different jet spacing (r = 4 w) are shown in Figure 6a–f and Figure 6g–l. For larger cylinder sizes, the distance between the inlet port and impinging surface was reduced; and the vortex size near the inlet regions was affected when rotational surface effects were considered. However, the effects on the flow patterns variations became significant at the largest cylinder size. The distance effects between the opposite jets on the flow patterns are shown in Figure 6 without rotations (g–i) and with rotational surface effects (j–l). At the highest distance, the recirculation regions near the inlet extended toward the cylinder while vortex size was increased. When rotations were considered, small vortices near the hot cylinder surface were established, while the impinging effects became weaker. For the flow dynamics and heat transfer, the size of the cylinder became influential when rotational surface effects were considered. The increment in the average Nu was 23.5% when varying the size from r = 2 w to r = 6 w at the highest rotational speed, and this value was only 1.5% without rotational effects (Figure 7a). The trends in the average Nu while varying the opposite jet distances were different up to H = 14 w, whether the rotations were active or not. As the rotations were present, the average Nu rose up to H = 14 w and then decreased from H = 14 w to H = 16 w (Figure 7b). This is attributed to the weakening of the impinging jet effects at the highest distance where flow field at the inlet zones was directed away from the hot surface of the cylinder. The optimum value of the distance between the jets was attained at H = 14 w, where the average Nu value achieved its highest value for the case with a rotating cylinder—the highest cylinder. In this case, the increment in the average Nu was obtained as 54.5% when jet spacing at the smallest value was compared. There was a 30% reduction in the average Nu when cases at H = 6 w and H = 14 w were compared in the absence of rotational surface effects.

3.2. Modal Approach for Analyzing the Heat Transfer Dynamics

The cooling performance was represented with average Nu from the hot rotating cylinder. Local values of Nu along the circumferential of the cylinder were collected, and modal analysis was performed. The proper orthogonal decomposition (POD) technique was used. The method was used for flow control, identification of flow dynamics, model order reduction and the parametric estimation of various thermo-fluid system performance factors [66,67,68,69]. The dataset for the local Nu along the R-C was collected for different values of Re, Rew and Ha. They are stated in terms of modal representation with POD modes multiplied by coefficients as:

$$\mathrm{Nu}=\overline{Nu}+\sum _{k=1}^N{c}_k(\mathrm{Re},\mathrm{Rew},\mathrm{Ha})\Psi (x,y),$$

(11)

where N is the number of modes and $\Psi$ denotes the POD mode. Here, $c_k$ denotes the modal coefficient. The modes were obtained after solving the following integral eigenvalue problem:

$${\int }_V〈K^{\prime }\left(\mathbf{x}\right)\otimes {\mathbf{K}}^{\prime }\left({\mathbf{x}}^{\prime }\right)〉\Psi \left({\mathbf{x}}^{\prime }\right){\mathbf{d}}^{\prime }=\Lambda \Psi \left(\mathbf{x}\right),$$

(12)

where the first term of the integral is the cross-correlation tensor, and $\Lambda$ denotes the eigenvalues. Singular value decomposition may also be used to get the modes. The largest energy content was captured with the first mode, and it is distributed in a hierarchical manner. Mode coefficients can be obtained after the projection of the dataset onto modes due to the orthogonality features of the modes. The number of spatial points in the dataset is 1032. Parametric variations of Nu with different Re (eight values), Rew (eight values) and Ha (eight values) were considered. The number of snapshots was 8 × 8 × 8 = 512. The cumulative contribution (CC) of the modes was considered to determine the number of modes retained in the modal representation. For one, three and ten modes, the CC values were 0.681, 0.860 and 0.974, respectively. In the present work, a twenty mode approximation was considered where the CC value was 0.995. The modal coefficients are dependent upon the Re, Rew and Ha. The variations of several mode coefficients with varying Rew and Ha are presented in Figure 8a,b. The modal coefficients are sensitive to the variations in Rew and Ha. The reconstruction of the average Nu which denotes the cooling performance was achieved by superposing all of the modal coefficients multiplied by the corresponding modes. The modes were functions of spatial coordinates which were obtained with SVD. For any parameter of interest within the interval of Re, Rew and Ha, interpolation among the modal coefficients could be utilized to determine the cooling performance at the specified parameter. Polynomials, splines and neural network-based approximations for the modal coefficients can be considered. Variations in the average Nu from the R-C with different numbers of modes are presented in Figure 8c–e.

Table 2. Comparisons of modal approximations of average Nu from the hot rotating cylinder with varying Re, Ha and Rew considering different numbers of modes.

Re	Ha	Rew	Nm (CFD)	Nm (Pm = 20)	Nm (Pm = 10)	Nm (Pm = 5)	Nm (Pm = 1)
100.0000	0	0	6.2497	6.4462	9.5632	57.3214	545.8495
100.0000	0	50.0000	6.8237	7.1213	11.9184	17.3907	462.4441
100.0000	0	400.0000	14.6884	14.9741	18.6315	28.1527	80.9423
100.0000	0	800.0000	24.5434	25.5128	31.3278	79.0200	200.1170
100.0000	10.0000	0	5.6470	5.9361	7.1699	49.7720	493.4111
100.0000	10.0000	100.0000	6.8706	6.9632	10.2770	7.4057	308.0403
100.0000	10.0000	200.0000	8.8338	8.8570	8.9427	44.0794	179.6151
100.0000	10.0000	800.0000	23.9908	24.1325	29.1065	83.9645	259.1009
100.0000	20.0000	0	5.4673	5.5938	5.9929	54.9489	477.0083
100.0000	20.0000	50.0000	6.0726	6.2576	7.0391	12.4069	391.0110
100.0000	20.0000	100.0000	6.8875	6.9375	8.2319	15.3442	308.9107
100.0000	20.0000	200.0000	8.7475	8.8960	8.7819	49.1804	167.7980
100.0000	20.0000	400.0000	12.6457	12.9282	17.9019	22.0853	122.6875
100.0000	20.0000	800.0000	21.6047	21.9554	32.6789	65.2207	469.4697
200.0000	0	0	7.8387	7.9967	10.6971	74.6170	687.7526
200.0000	0	50.0000	8.2268	8.4720	11.9520	9.6814	591.5352
200.0000	0	100.0000	9.1310	9.2616	12.1394	29.0391	511.3187
200.0000	0	200.0000	11.0642	11.3022	11.2247	30.8318	359.0287
200.0000	0	800.0000	26.6669	26.6894	30.3759	30.5815	46.3589
200.0000	10.0000	0	6.5669	6.8824	9.7931	44.4367	576.1642
200.0000	10.0000	200.0000	10.0864	10.2961	10.6333	29.5709	272.8990
200.0000	10.0000	400.0000	14.2078	14.3630	20.9316	43.2918	19.1135
200.0000	10.0000	800.0000	24.1272	24.3464	30.2456	50.9392	265.3572
200.0000	20.0000	0	6.2107	6.4886	7.4037	51.6364	544.8552
200.0000	20.0000	50.0000	6.7583	6.9124	6.8784	7.2988	453.0497
200.0000	20.0000	100.0000	7.6583	7.7101	8.7380	18.4243	374.5025
200.0000	20.0000	800.0000	22.6811	22.2298	28.6700	32.9669	409.4980
300.0000	0	0	9.7896	9.8251	15.7833	81.4567	862.7452
300.0000	0	50.0000	9.9599	10.072	15.3358	18.1471	755.0554
300.0000	0	100.0000	10.8957	11.1617	14.1908	51.4394	675.1634
300.0000	0	200.0000	13.0772	13.2291	18.3195	83.1912	545.4293
300.0000	0	400.0000	17.2439	17.5309	18.8414	71.4711	263.1526
300.0000	0	800.0000	26.8919	27.1330	27.4019	66.5719	50.5082
300.0000	10.0000	0	7.8904	7.9299	11.7347	38.9112	694.0833
300.0000	10.0000	50.0000	8.1642	8.26032	16.6721	48.1251	584.9435
300.0000	10.0000	100.0000	9.2769	9.43595	10.6890	61.3910	526.4681
300.0000	10.0000	200.0000	11.7848	11.9949	14.8063	77.0788	427.1771
300.0000	10.0000	400.0000	16.1658	16.1997	17.3894	61.7393	169.3253
300.0000	10.0000	800.0000	25.5614	25.8692	29.0225	73.8450	180.4926
300.0000	20.0000	0	6.9272	6.9962	8.6297	44.9572	609.7692
300.0000	20.0000	50.0000	7.4184	7.5229	7.8931	20.1793	514.5291
300.0000	20.0000	100.0000	8.3501	8.4897	8.8413	37.1866	438.6225
300.0000	20.0000	200.0000	10.5743	10.8618	13.3447	46.6147	313.8373
300.0000	20.0000	400.0000	14.8214	14.98553	16.2357	66.1440	57.5720
300.0000	20.0000	800.0000	24.1676	24.3551	30.1478	81.6907	308.1989

presents the comparison results for the average Nu variations with different parametric combinations of (Re, Ha, Rew) considering different numbers of modes. A 20-mode approximation of the Nu gave satisfactory results and captured the variations in Re, Rew and Ha as compared to CFD.

4. Conclusions

In the current study, convective HT performance for impinging jets onto a rotating hot circular cylinder was numerically assessed under multiple MaF effects. Binary nanoparticles were used in the HT fluid, and different strengths of MaF were considered in the opposing jet domains. The following conclusions were drawn from the numerical simulation results:

• The coupled interactions between the rotating hot body, forced flow of hybrid nanofluid and multiple magnetic field effects determine the flow recirculations with the systems and heat transfer enhancement amounts.
• When the rotational surface effects are dominant, the impacts of Re on the average Nu increase become weak as compared to motionless cylinder case. When the lowest and highest Re cases were compared, a 5% rise of average Nu was seen at Rew = 800, and it was 48.5% at Rew = 0.
• Impacts of rotation on the HT enhancement are significant when MaF effects are present in the system. The average Nu rose by about 249% at Ha1 = 0, and it was only 175% at Ha1 = 0.
• When the configuration in the presence of MaF effects at the highest strength is compared with the case in the absence of MaF in both domains, a 54.5% reduction in the average Nu was obtained.
• When cases with the smallest and highest cylinder sizes were compared at the highest rotational speeds, the increment in the average Nu was observed as 23.5%.
• The optimum value of distance between the opposing jets was obtained at H = 14 w for the maximum HT, where a 54.5% rise in the average Nu was attained as compared to the case at the smallest spacing.
• A modal analysis of the local Nu was proposed with 20-modes, with varying Re, Rew and Ha parameters.

The present work may be extended to include unsteady flow effects, different thermal boundary conditions, multiple rotating cylinder configurations, non-uniform magnetic field effects and different nanoparticle types. A multi-domain POD approach may also be utilized where different numbers of modes for the lower and upper domains may be considered. Efficient interpolation methods may also be used among the modal coefficients which are dependent upon the parameters to predict the cooling performance of the system. These will increase the applicability of the present configuration to diverse energy system technologies.