Caputo–Fabrizio fractional derivatives modeling of transient MHD Brinkman nanoliquid: Applications in food technology.

• The Caputo–Fabrizio derivative is applied to solve a Brinkman nanoliquid (suspension of nanomaterials in a base fluid) problem. • Studied the effect of copper nanoparticles on the MHD free convection transient motion of C 6 H 9 NaO 7 Brinkman nanoliquid lies over a vertical surface with time-dependent velocity, temperature, and concentration. • The mathematical problem is modeled for nanofluid and generalized by using the Caputo–Fabrizio fractional derivatives and solved with the Laplace transform. • The effect of different parameters has been analyzed through graphs and variations in Nusselt number, skin friction and Sherwood number are shown in tabular form. Amongst the several definitions of fractional operator (memory operator), these days the Caputo–Fabrizio operator (CF) without singular kernel is a useful extension of the classical Caputo derivative operator as the latter includes a singular mathematical expression also known as the kernel in its definition, leading to some difficulties in finding solutions to the corresponding differential equation, whereas the kernel of the former (CF) is non-singular. In this paper, the idea of CF derivative has been applied to solve a Brinkman nanoliquid (suspension of nanomaterials in a base fluid) problem. More exactly, the present article studies the effect of copper nanoparticles on the MHD free convection transient motion of C 6 H 9 NaO 7 Brinkman nanoliquid lies over a vertical surface with time-dependent velocity, temperature, and concentration. Formulation of the problem in the fractional form (CF) is done and then closed-form solution is obtained. Graphs are drawn for different embedded parameters and variations in Nusselt number, skin friction and Sherwood number are shown in tabular form. C 6 H 9 NaO 7 is a food product taken from seaweed or brown algae. C 6 H 9 NaO 7 is used in the food industry for making gel-like foods such as pimento stuffing in prepared cocktail olives. In a liquid, C 6 H 9 NaO 7 also acts as a thickener. C 6 H 9 NaO 7 Brinkman nanoliquid in this direction (food technology) using CF derivative has not been investigated yet. This study will further provide new directions to carry this research using Atangana–Baleanu fractional derivatives for other non-Newtonian C 6 H 9 NaO 7 nanoliquids used in different foods. [ABSTRACT FROM AUTHOR]