Melting rheology in thermally stratified graphene-mineral oil reservoir (third-grade nanofluid) with slip condition

More effective and lengthy energy storage systems have been highly desired by researchers. Waste heat recovery, renewable energy, and combined heating and power reactors all utilize energy storage technologies. There are three techniques that are more effective for storing thermal energy: Latent heat storage is one type of energy storage, along with sensible heat storage and chemical heat storage. Latent thermal energy storage is far more efficient and affordable with these methods. A method of storing heat energy in a substance is melting. The substance is frozen to release the heat energy it had been storing. A ground-based pump's heat exchanger coils around the soil freezing, tundra melting, magma solidification, and semiconducting processes are examples of melting phenomenon. Due to the above importance, the present study scrutinizes the behavior of third-grade nanofluid in a stagnation point deformed by the Riga plate. The Riga plate, an electromagnetic actuator, is made up of alternating electrodes and a permanent magnet that is positioned on a flat surface. Graphene nanoparticles are put in the base fluid (Mineral oil) to make a homogenous mixture. Mathematical modeling is acquired in the presence of melting phenomenon, quadratic stratification, viscous dissipation, and slippage velocity. Suitable transformations are utilized to get the highly non-linear system of ODEs. The remedy of temperature and velocity is acquired via the homotopic approach. Graphical sketches of various pertinent parameters are obtained through Mathematica software. The range of various pertinent parameters is 1 ≤ B 1 ≤ 4, B 2 = 1, 3, 5, 7, B 3 = 0.1, 0.5, 0.9, 1.3, 0.8 ≤ A ≤ 1.2, Re = 1, 3, 5, 7, S 1 = 1, 3, 5, 7, M 1 = 1, 6, 11, 16, 0.1 ≤ I ≤ 0.4, 0.1 ≤ Q ≤ 0.4, Ec = 1, 3, 5, 7, 0.1 ≤ S ≤ 0.4 and Nr = 1, 6, 11, 16 1\le {B}_{1}\le 4,\hspace{.5em}{B}_{2}=1,3,5,7,{B}_{3}=0.1,0.5,0.9,1.3,\hspace{.5em}0.8\le A\le 1.2,\mathrm{Re}=1,3,5,7,\hspace{.2em}{S}_{1}=1,3,5,7,\hspace{.5em}{M}_{1}=1,6,11,16,\hspace{.25em}0.1\le {\vartheta }\le 0.4,\hspace{.33em}0.1\le Q\le 0.4,\text{Ec}=1,3,5,7,\hspace{.5em}0.1\le S\le 0.4\hspace{.65em}\text{and}\hspace{.65em}\text{Nr}=1,6,11,16. Skin friction (drag forces) and Nusselt number (rate of heat transfer) are explained via graphs. The velocity is enhancing the function against melting parameter while temperature is the decelerating function as melting factor is amplified. The temperature field reduces with the accelerating estimations of stratified parameter. The energy and velocity profiles de-escalate with intensifying values of volume fraction parameter.