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Endothermic and exothermic chemical reaction on MHD ternary (Fe2O4–TiO2–Ag/H2O) nanofluid flow over a variable thickness surface

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Abstract

Recently, there has been an increasing recognition of the crucial significance of waste management and the need for environmental preservation. Moreover, the impact of endothermic and exothermic reactions on heat transfer and the behavior of liquids on surfaces of variable thicknesses has significant implications for improving diverse operations, such as temperature exchange systems, commercial power plants, and waste administration facilities. In view of these applications, the current study investigates the endothermic and exothermic chemical reactions and waste discharge concentration over variable thickness surface. The governing equations are transformed into ordinary differential equations and solved using Runge–Kutta–Fehlberg 45 method. The results are visually presented using graphs and then analyzed. The results claim that the heat transfer rate is significant in the presence of wall thickness parameter and exothermic reaction. Elevated concentrations are observed when the external source parameter is augmented, and higher rate concentrations are commonly observed when the wall thickness parameter is present. This study explores the complex interaction of these responses and their consequences, providing insight into how they might be used to enhance these crucial processes. Further, it also focuses mainly on the concentration of waste discharge. It aims to provide significant insights into the impact of these processes on waste treatment operations, pollution control, and the effective disposal of industrial waste. The outcomes offer a strong basis for making well-informed decisions in companies and environmental sectors that rely on efficient waste management and sustainable practices.

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Abbreviations

a :

Stretching rate

b :

Shift constant

B 0 :

Magnetic field (kg0.5Ω0.5s−0.5m−1)

Cp:

Specific heat (J kg−1 K−1)

C*:

Concentration

\(C_{\infty } *\) :

Ambient concentration

\(C_{{\text{w}}} *\) :

Wall concentration

Cf:

Skin friction

D :

Diffusivity (m2 s−1)

Ea:

Activation energy (kg m2 s−2)

E :

Activation energy parameter

k :

Thermal conductivity (kg ms−3 K−1)

\(k_{{\text{r}}}^{2}\) :

Reaction rate (s−1)

K :

Boltzmann constant (kg m2 s−2 K−1)

m :

Power index of the velocity

ml :

Fitted rate constant

\(M^{*}\) :

Magnetic parameter

Nu:

Nusselt number

Pr:

Prandtl number

P E :

Parameter related to local pollutant external source

P In :

External pollutant source variation parameter

Re:

Local Reynolds number

\(S\left( {C*} \right)\) :

External pollutant source function

Sh:

Sherwood number

Sc:

Schmidt number

T*:

Temperature (K)

\(T_{\infty } *\) :

Ambient temperature (K)

\(T_{{\text{w}}} *\) :

Wall temperature (K)

\(u_{{\text{w}}} *\) :

Uniform velocity (ms−1)

(u*,v*):

Velocity components (ms−1)

(x*,y*):

Coordinates (m)

\(\nu\) :

Kinematic viscosity (m2s−1)

\(\alpha\) :

Wall thickness parameter

\(\delta_{C}\) :

Reaction rate parameter

\(\rho\) :

Density (kgm−3)

\(\varphi_{1} ,\varphi_{2} ,\varphi_{3}\) :

Solid volume fraction

\(\sigma\) :

Electrical conductivity (Ω−1m−1)

\(\lambda^{*}\) :

Endo\exothermic parameter

\(\beta\) :

Endo/exothermic factor

\(\delta\) :

Temperature difference parameter

Thnf:

Ternary hybrid nanofluid

Nf:

Nanofluid

Hnf:

Hybrid nanofluid

f:

Fluid

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Authors and Affiliations

  1. Department of Mathematics, K.L.E. Society’s J.T. College, Gadag, Karnataka, 582101, India

    G. K. Ramesh

  2. Department of Mathematics, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Bengaluru, India

    J. K. Madhukesh

  3. Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt

    Emad H. Aly

  4. Department of PG Studies and Research in Mathematics, Kuvempu University, Shankaraghatta, Shivamogga, Karnataka, 577451, India

    B. J. Gireesha

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Contributions

JKM and GKR were involved in conceptualization, methodology, software, formal analysis, writing—original draft, resources, data curation, investigation, visualization, and validation. EHA and BJG participated in conceptualization, project administration, writing—review and editing, supervision, and resources. JKM helped with validation, investigation, writing—review and editing, formal analysis, validation, and resources.

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Correspondence to G. K. Ramesh.

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Ramesh, G.K., Madhukesh, J.K., Aly, E.H. et al. Endothermic and exothermic chemical reaction on MHD ternary (Fe2O4–TiO2–Ag/H2O) nanofluid flow over a variable thickness surface. J Therm Anal Calorim (2024). https://doi.org/10.1007/s10973-024-13013-x

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