Abstract
In blood flow and fluid mechanics, Jeffrey fluid has a vital role because of its viscoelastic characteristics. The application of Caputo-Fabrizio time-fractional derivatives for dusty-type Jeffrey fluid is discussed in this article. The concept of free convection flow of dusty Jeffrey fluid between infinite vertical parallel static plates is generalized. Free convection and buoyant force produce the flow. Furthermore, the fluid contains homogeneous dispersion of all spherical dust particles. Heat transmission is therefore taken into account for free convection. Nondimensional variables are used to write the dusty Jeffrey fluid classical model in dimensionless form. Also, the dimensionless model is transformed into a generalized dusty Jeffrey fluid model via a fractional derivative. Using the finite sine and Laplace method, the governing equations of the generalized dusty Jeffrey fluid model have been solved exactly. Numerical computation is used to study the physics of velocity and temperature profiles for a variety of embedded parameters. The collected results are discussed in detail and are shown graphically in this report. Mathcad-15 is used to plot the graphical outcomes for Jeffrey fluid, dust particle, and temperature profiles. Furthermore, skin friction and the Nusselt number are calculated. Table demonstrates how the rate of heat transmission reduces as the Peclet number's value rises. Similarly, Table demonstrates that skin friction increases as the fractional parameter rises. By increasing the dusty Jeffrey fluid parameter lambda, both velocity profiles are retarded.