Endo/exothermic analysis of Casson and Maxwell quadra hybrid nanofluid flow configured by pollutant concentration with thermal and solute jump

Figures & data

Figure 1. Flow diagram with boundary constraints.

Table 1. The thermophysical attributes of the foundational fluid and nanoparticles.

Physical attributes	$\mathrm{Ag}$ (n1)	$\mathrm{Cu}$(n2)	Graphene (n3)	$\mathrm{Mo}{S}_2(n4)$	Base fluid (ethylene glycol)
$\rho$ (Density) ($\mathrm{kg}{m}^{-3}$)	10500	8933	2250	5060	1115
$C_p$ (Specific heat capacity) $JK{g}^{-1}{K}^{-1})$	235	385	2100	397.21	2430
$k$ (Thermal conductivity) ($W{m}^{-1}{K}^{-1}$)	429	401	2500	904.4	0.253
$\sigma$ (Electric conductivity) $(s{m}^{-1})$	6.30 × 10^7	59.6 × 10^6	$1\times {10}^7$	$2.09\times {10}^4$	1.10 × 10^−4

Figure 2. Impact of temperature jumps on the thermal profile.

Figure 3. Impact of temperature jump on the mass diffusion profile.

Figure 4. Impact of local pollutant source on the thermal profile.

Figure 5. Impact of local pollutant source on the mass diffusion profile.

Figure 6. Impact of solute jumps on the thermal profile.

Figure 7. Impact of solute jumps on the mass diffusion profile.

Figure 8. Impact of both endo and exothermic chemical reaction on the temperature profile.

Figure 9. Impact of both endo and exothermic chemical reaction on the concentration profile.

Table 2. Analogize findings with Wang [23] and Ishak et al. [24].

$\mathrm{Re}$	Wang [23]	Ishak et al. [24]	Present
0.5	−0.8822	−0.8827	−0.8824
1	−1.17776	−1.1781	−1.1778
2	−1.5939	−1.5941	−1.5939
5	−2.41745	−2.4175	−2.4174
10	−3.34445	−3.3445	−3.3445

Table 3. Comparison between Maxwell fluid and Maxwell Hybrid Nanofluid regarding Nusselt and Sherwood number in the context of Endothermic and Exothermic chemical reaction with and without thermal and solute jump.

		Maxwell fluid								Maxwell quadra hybrid nano fluid
		${\alpha }_3={\alpha }_4=0,{\lambda }_2=5$		${\alpha }_3={\alpha }_4=0,{\lambda }_2=-5$		${\alpha }_3={\alpha }_4=0.1,{\lambda }_2=5$		${\alpha }_3={\alpha }_4=0.1,{\lambda }_2=-5$		${\alpha }_3={\alpha }_4=0,{\lambda }_2=5$		${\alpha }_3={\alpha }_4=0,{\lambda }_2=-5$		${\alpha }_3={\alpha }_4=0.1,{\lambda }_2=5$		${\alpha }_3={\alpha }_4=0,{\lambda }_2=-5$
Parameter	Values	Nusselt	Sherwood	Nusselt	Sherwood	Nusselt	Sherwood	Nusselt	Sherwood	Nusselt	Sherwood	Nusselt	Sherwood	Nusselt	Sherwood	Nusselt	Sherwood
$n$	1	−56.5559	3.7604	27.0774	2.6749	−28.4705	2.7354	11.9645	2.0653	−60.2636	3.7949	27.5251	2.6444	−30.3923	2.7533	12.1326	2.0458
	2	−33.1945	3.4820	25.2079	2.9179	−13.9495	2.5572	10.4702	2.2237	−35.4159	3.5031	26.5111	2.6944	−14.9394	2.5667	11.0543	2.0867
	3	−15.5539	3.2990	25.0419	2.9353	−7.3169	2.4637	9.9548	2.2380	−22.4268	3.3387	26.0983	2.7272	−7.8669	2.4676	10.4037	2.1121
${\beta }_3$	0.01	−33.1945	3.4820	25.2079	2.9179	−13.9495	2.5572	10.4702	2.2237	−35.4159	3.5031	26.5111	2.6944	−14.9394	2.5667	11.0543	2.0867
	0.03	−34.9568	3.4889	25.2663	2.8822	−14.9748	2.5590	10.5080	2.1980	−37.3938	3.5140	26.6649	2.6325	−16.0860	2.5710	11.1469	2.0413
	0.05	−36.7964	3.4981	25.3248	2.8462	−16.0534	2.5626	10.5458	2.1720	−39.4556	3.5271	26.8144	2.5675	−17.2922	2.5772	11.2369	1.9933
$p$	2	−33.1945	3.4820	25.2079	2.9179	−13.9495	2.5572	10.4702	2.2237	−35.4159	3.5031	26.5111	2.6944	−14.9394	2.5667	11.0543	2.0867
	3	−30.3858	3.7125	24.8353	3.2756	−12.1268	2.6828	10.2386	2.4360	−32.4691	3.7263	26.1388	3.0496	−13.0281	2.6880	10.8196	2.3046
	4	−27.9631	3.9410	24.5052	3.6003	−10.6112	2.8039	10.0359	2.6187	−29.9070	3.9482	25.7980	3.3751	−11.4286	2.8055	10.6080	2.4939
$\delta$	0.10	−17.9031	3.2109	25.1973	2.9321	−9.9757	2.4116	11.2787	2.1354	−25.6010	3.2072	26.7601	2.7297	−10.6500	2.4125	11.4401	2.1196
	0.15	−33.1945	3.4820	25.2079	2.9179	−13.9495	2.5572	10.4702	2.2237	−35.4159	3.5031	26.5111	2.6944	−14.9394	2.5667	11.0543	2.0867
	0.20	−47.1504	3.8889	25.3265	2.9083	−19.8934	2.7593	10.2430	2.2079	−50.5772	3.9353	26.4425	2.6683	−21.3639	2.7803	10.7445	2.0596

Table 4. Comparison between Casson fluid and Casson Hybrid Nanofluid regarding Nusselt and Sherwood number in the context of Endothermic and Exothermic chemical reaction with and without thermal and solute jump.

		Casson fluid								Casson quadra hybrid nano fluid
		${\alpha }_3={\alpha }_4=0,{\lambda }_2=5$		${\alpha }_3={\alpha }_4=0,{\lambda }_2=-5$		${\alpha }_3={\alpha }_4=0.1,{\lambda }_2=5$		${\alpha }_3={\alpha }_4=0.1,{\lambda }_2=-5$		${\alpha }_3={\alpha }_4=0,{\lambda }_2=5$		${\alpha }_3={\alpha }_4=0,{\lambda }_2=-5$		${\alpha }_3={\alpha }_4=0.1,{\lambda }_2=5$		${\alpha }_3={\alpha }_4=0.1,{\lambda }_2=-5$
Parameter	Values	Nusselt	Sherwood	Nusselt	Sherwood	Nusselt	Sherwood	Nusselt	Sherwood	Nusselt	Sherwood	Nusselt	Sherwood	Nusselt	Sherwood	Nusselt	Sherwood
$n$	2	−23.0732	3.4118	25.1953	2.9357	−9.1104	2.5295	10.4264	2.2355	−23.9134	3.4142	25.5294	2.9229	−9.4662	2.5302	10.5293	2.2278
	3	−14.6577	3.3171	24.9929	2.9556	−4.5280	2.4697	9.8973	2.2511	−15.1755	3.3158	25.3113	2.9435	−4.7200	2.4683	9.9882	2.2439
	4	−9.3580	3.2611	25.0585	2.9689	−1.9489	2.4352	9.5581	2.2614	−9.7057	3.2577	25.3680	2.9572	−2.0634	2.4328	9.6408	2.2545
${\beta }_3$	0.01	−23.0732	3.4118	25.1953	2.9357	−9.1104	2.5295	10.4264	2.2355	−23.9134	3.4142	25.5294	2.9229	−9.4662	2.5302	10.5293	2.2278
	0.03	−23.7647	3.3952	25.2888	2.8923	−9.5362	2.5170	10.4836	2.2043	−24.6569	3.3987	25.6261	2.8787	−9.9199	2.5183	10.5881	2.1960
	0.05	−24.4843	3.3798	25.3819	2.8478	−9.9792	2.5053	10.5405	2.1722	−25.4311	3.3844	25.7222	2.8333	−10.3924	2.5072	10.6466	2.1632
$p$	2	−23.0732	3.4118	25.1953	2.9357	−9.1104	2.5295	10.4264	2.2355	−23.9134	3.4142	25.5294	2.9229	−9.4662	2.5302	10.5293	2.2278
	3	−21.0007	3.6981	24.8045	3.3091	−7.7459	2.6859	10.1859	2.4559	−21.7678	3.6973	25.1367	3.2955	−8.0596	2.6848	10.2880	2.4482
	4	−19.3043	3.9727	24.4581	3.6467	−6.6586	2.8300	9.9759	2.6446	−20.0079	3.9692	24.7880	3.6326	−6.9369	2.8278	10.0770	2.6369
$\delta$	0.10	−17.3571	3.2352	25.1759	2.9519	−6.5769	2.4348	10.6939	2.2553	−17.9382	3.2321	25.5241	2.9401	−6.8244	2.4327	10.8055	2.2482
	0.15	−23.0732	3.4118	25.1953	2.9357	−9.1104	2.5295	10.4264	2.2355	−23.9134	3.4142	25.5294	2.9229	−9.4662	2.5302	10.5293	2.2278
	0.20	−31.5456	3.6674	25.3195	2.9242	−12.8276	2.6617	10.2065	2.2188	−32.8399	3.6797	25.6444	2.9106	−13.3632	2.6668	10.3025	2.2106

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Data availability statement

No datasets were analysed or generated during the present study.