Cattaneo–Christov flux and entropy in thermofluidics involving shrinking surface

Abstract

The paper examines radiative Casson boundary layer flow over an exponentially shrinking permeable sheet in a Cattaneo–Christov heat flux environment. The sheet is placed at the bottom of the fluid‐saturated porous medium and suction is applied normally to the sheet to contain the vorticity. The radiative heat flux in the energy equation is assumed to follow the Rosseland approximation. Similarity transformation is performed to convert the governing partial differential equations into ordinary differential equations. The resulting boundary value problem is treated numerically employing Runge–Kutta fourth‐order integration scheme along with the shooting method. The effects of pertinent parameters on quantities of interest are showcased graphically/in tabular form and are discussed. The dual profiles for velocity and temperature lead to a dual solution regime for entropy. It is found that critical mass suction rate and Nusselt number are substantially responsive to various parameters' values. Critical suction values decrease with a rise in Casson parameter β and permeability parameter K. Skin friction coefficient and Nusselt number show peculiar behavior for distinct branches of solutions.

Irreversibility analysis for Casson thermo‐fluidics inside a cone: Cattaneo–Christov heat flux

“…Then the fundamental boundary layer equations for the considered setup in Cattaneo-Christov heat flux environment read as follows 7,8,20 :…”

“…Then the fundamental boundary layer equations for the considered setup in Cattaneo–Christov heat flux environment read as follows 7,8,20 : $$${(ru)}_{r}+{(rv)}_{z}=0,$$$ $$$u{u}_{r}+v{u}_{z}=U(r)\frac{d}{dr}\{U(r)\}+{{\rm{\nu }}}_{B}{u}_{zz}\left(1+\frac{1}{\beta }\right)-\frac{{{\rm{\nu }}}_{{\rm{B}}}\phi }{{K}_{0}}\{u-U(r)\},$$$ $$$u{T}_{r}+v{T}_{z}+{\rm{\Delta }}\,\{{u}^{2}{T}_{rr}+{v}^{2}{T}_{zz}+2uv{T}_{rz}+(u{u}_{r}+v{u}_{z}){T}_{r}+(u{v}_{r}+v{v}_{z}){T}_{z}\}=\frac{\kappa }{\rho {C}_{p}}{T}_{zz}+\frac{{\mu }_{B}}{\rho {C}_{p}}\,\left(1+\frac{1}{\beta }\right){({u}_{z})}^{2}+\frac{{\nu }_{B}\phi {u}^{2}}{{K}_{0}{C}_{p}},$$$and the boundary conditions for present setup are …”

“…Realizing the potential of the field, many investigators have reported entropy analysis for a variety of fluidic systems. [18][19][20][21][22][23][24][25][26][27][28][29][30] We recall that the Fourier heat fluxlaw 31 falls short to address heat transport taking place in the waveform. Cattaneo 32 proposed a modification suggesting the inclusion of time relaxation component thermal inertia to Fourier's heat flux model.…”

“…In fact, the entropy generation analysis banking upon picking up parameters having a qualitative and quantitative impact on entropy production is pivotal in entropy minimization. Realizing the potential of the field, many investigators have reported entropy analysis for a variety of fluidic systems 18–30 …”

“…Ciarletta and Straughan 34 examined uniqueness and structural stability for the Cattaneo‐Christov equations. Straughan 35 and many investigators have resorted to the Cattaneo–Christov heat flux model in a variety of fluidic configurations such as Tassaddiq, 36 Vyas et al, 20 Reddy et al, 37–39 Khan et al, 40 Nadeem et al, 41 Ali and Sandeep, 42 Han et al 43 to name a few.…”