MHD Flow of Thermally Radiative Maxwell Fluid Past a Heated Stretching Sheet with Cattaneo–Christov Dual Diffusion

Research and Development Wing, Live4Research, Tiruppur-638106, Tamilnadu, India Department of Mathematical Sciences, Faculty of Science, Princess Nourah Bint Abdulrahman University, Riyadh, Saudi Arabia Department of Humanities and Management, Jigme Namgyel Engineering College, Royal University of Bhutan, Dewathang, Bhutan Department of Electronics and Communication Engineering, Aditya College of Engineering and Technology, Surampalem 533 437, Andhra Pradesh, India


Introduction
Many industrial processes depend on fluids especially, non-Newtonian fluids. Few examples are plastic sheet extrusion, paper production, spinning of metals, glass fiber, etc. Maxwell is one of the non-Newtonian models, and he predicts the stress relaxation. e primary principle of MHD is that forces are produced in the fluid when the magnetic field induces a current through a moving conducting fluid. Magnetohydrodynamics has diverse engineering applications. Sandeep et al. [1] examined the stretching surface flows of Oldroyd-B, Jeffrey, and Maxwell fluids with nonuniform heat source/sink impacts along with radiation effects. ey found that Oldroyd-B and Maxwell fluids have lesser effects compared to the Jeffrey fluid. Farooq et al. [2] analyzed the exponentially stretching sheet flow of a Maxwell-type nanomaterial. e Buongiorno model was used in this study to construct the physical model. Fetecau et al. [3] discussed the porous channel flow of the upper-convected Maxwell (UCM). Also, steady-state transient components have an appearance of oscillatory motion. Wang et al. [4] and Sun et al. [5] established the incompressible Maxwell fluid passed through a tube through a triangular cross section (rectangular or isosceles). Analytical approaches are implemented for steady-state solutions of two oscillatory motions. Few other studies about the Maxwell fluid types have been implemented by Qi and Xu [6], Wenchang et al. [7], and Qi and Liu [8].
Heat transfer is a natural phenomenon of heat owing between the object or within the object in the order of the temperature difference. is phenomenon has a wide application in enormous fields such as semiconductors, cooling devices, and power generation. In earlier days, heat transfer is characterized by the Fourier law of heat conduction [9]. However, this law fails to explain the heat transfer effect, and in nature, no material will satisfy this law. So, Catteneo [10] extended the work of Fourier by including the thermal relaxation time. Later, Christov [11] upgraded Catteneo's work with the help of Oldroyd's upper-convected derivatives and thermal relaxation time for efficient performance. Saleem et al. [12] investigated the 3D combined convective Maxwell fluid with mass and heat Catteneo-Christov heat flux models with heat generation. Loganathan et al. [13] presented the second-order slip phenomenon of Oldroyd-B fluid with cross diffusion, radiation, and Catteneo-Christov heat flux impacts. Magento-free convection of nanoliquid flow towards a vertical cone, vertical wedge, and a vertical plate with Catteneo-Christov heat flux was studied by Jayachandra et al. [14]. Some other cutting edge research reports in this area can be found in [15][16][17][18][19][20][21][22]. e emission of electromagnetic waves from a material with a temperature greater than zero is known as thermal radiation. Solar radiation from the Sun and the infrared radiation emitted by the household products are examples of thermal radiation. e study of thermally radiative flow over a stretchy plate plays a vital role in many engineering applications, such as disposals of nuclear waste, drying the food products, film cooling, radial diffusers, gas turbines, and power plants. Ali et al. [23] investigated the thermal radiation properties of Newtonian-type nanofluid with stagnation point, combined convection, Joule heating, and stratification. Pal and Mandal [24] evaluated the porous medium flow of radiative nanoliquid with viscous dissipation and combined convection. ey find double solutions for the shrinking case. Haroun et al. [25] presented the new process named spectral relaxation method (SRM) to solute the problem of MHD nanofluid flow with mixed convection. e fluid flow with thermal radiation over different geometries and situations is reported [26][27][28][29][30].
e authors examine the impression of Cattaneo-Christov dual diffusion of a non-Newtonian Maxwell fluid with the magnetic field, heat generation, and thermal radiation past a heated surface. e homotopy analysis method (HAM) [31][32][33][34][35][36] is employed to solute the physical system. Visualization of physical parameters reported and discussed in detail.

Formulation of Physical Problem
We analyze the 2D flow of a MHD Maxwell fluid over an extended sheet. Energy and mass determinations are calculated with Cattaneo-Christov dual diffusion. Let T ∞ and C ∞ be the free stream fluid temperature and fluid concentration which is lower than the fluid temperature and fluid concentration T w and C w , respectively. e lowermost part of the plate was heated with hot fluid T f . Figure 1 shows the physical representation of the flow problem. e governing mathematical models with the above assumptions are Consider the following similarity transformations: Apply the above transformations: e nondimensional variables are declared as e engineering quantities are stated as

HAM Solution
Several numerical schemes are available for solute the nonlinearity problems. e efficient semianalytic process HAM was employed to solute these current nonlinearity problems. is method presents the independence to select the primary assumptions of the solutions.

Journal of Mathematics
Generally, the HAM solution depends on the auxiliary parameters h f , h θ , and h ϕ , and these parameters control the convergence. e range value of h f , h θ , and h ϕ are We fix h f � − 0.8 and h θ � h ϕ � − 1 for better convergence (see Figure 2). Table 1 provides the order of HAM, and we found that 15 th order is adequate for all profiles. Table 2

Result and Discussion
In this section, we focus on the importance of physical parameters of fluid velocity, fluid temperature, fluid concentration, skin friction coefficient, local Nusselt number, and local Sherwood number for viscous fluid   concentration for "c c , fw, and Sc" for both fluids. It is noted that the fluid concentration is a nondecreasing function of injection, and the reverse trends were obtained in "c c > � 0, fw, and Sc" for both fluids. It is also noted that the concentration boundary layer is high in Maxwell fluid compared to viscous fluid. e skin friction coefficient for different combination of "fw, M, and λ" was shown in Figures 6(a) and 6(b). It is concluded that the surface shear stress declines with increasing values of "fw, M, and λ" . Figures 7(a) and 7(b) explain the local Nusselt number for different combinations of "Bi, lambda, R, and c." It is found that the heat transfer gradient raises with escalating the values of "Bi, c, and R," and it decreases with heightening the values of "λ." e local Sherwood number for different combinations of "c c , M, λ, and Sc" are presented in Figures 8(a) and 8(b). We noted that the mass transfer gradient becomes small with rising the values of "M and λ" and it is high for the presence of "c c and Sc."

Data Availability
e raw data supporting the conclusions of this article will be made available by the authors without undue reservation.

Conflicts of Interest
e authors declare that they have no conflicts of interest.