Mixed convection flow in vertical channel with boundary conditions of third kind in presence of heat source/sink

The effects of viscous dissipation and heat source/sink on fully developed mixed convection for the laminar flow in a parallel-plate vertical channel are investigated. The plate exchanges heat with an external fluid. Both conditions of equal and different reference temperatures of the external fluid are considered. First, the simple cases of the negligible Brinkman number or the negligible Grashof number are solved analytically. Then, the combined effects of buoyancy forces and viscous dissipation in the presence of heat source/sink are analyzed by a perturbation series method valid for small values of the perturbation parameter. To relax the conditions on the perturbation parameter, the velocity and temperature fields are solved by using the Runge-Kutta fourth-order method with the shooting technique. The velocity, temperature, skin friction, and Nusselt num- bers at the plates are discussed numerically and presented through graphs.

Flow and heat transfer of composite porous medium saturated with nanofluid

The present article is concerned with the heat transfer of nanofluid saturated with porous medium sandwiched between clear viscous fluid filled in a vertical channel.The model is developed to analyze the behavior of nanofluids taking into account the solid volume fraction.The governing equations are obtained based on the Darcy's law for the porous medium and Tiwari and Das model to define the nanofluid.The viscous and Darcy dissipation terms are included in the energy equation.The transformed dimensionless governing equations are solved analytically using regular perturbation.Investigations are carried out on the flow characteristics for different values of Grashof number,Brinkman number,solid volume fraction and porous parameter using water as base fluid and copper as nanoparticle.Flow and heat transfer are also observed using five different types of nanoparticles.It is found that the maximum value of Nusselt number is obtained for silver nanoparticle.

Flow characteristics in a parallel-plate porous channel under convective boundary conditions and triple diffusion for the non-Darcy porous matrix

This article inspects the effect of triple diffusion in a vertical conduit encapsulated with porous matrix and subjected to third kind boundary conditions.Third kind boundary condition is a combination of Dirichlet and Neumann boundary conditions which specifies a linear combination of function and its derivative values on the boundary.Homogeneous chemical reaction along with viscous and Darcy dissipation effects are included.Adapting the Boussinesq approximation,the soultal buoyancy effects due to concentration gradients of the dispersed components are taken into account.Applying suitable transformations,the conservation equations are reduced into dimensionless form and the dimensionless parameters evolved are thermal Grashof number (0≤Λ_(1)≤20),solutal Grashof number(for species 1 and 2,0≤Λ_(2);Λ_(3)≤20),porous (2≤σ≤8) and inertial parameters (0≤Ι≤6),Biot numbers(at the left and right walls,1≤Bi_(1);Bi_(2)≤10),Brinkman number (0≤Br≤1),Schmidt numbers (0≤Sc_(1);Sc_(2)≤6),Soret numbers (Sr_(1) =Sr_(2) =1) and temperature difference ratio (R_(T) = 1).Adopting perturbation technique,the analytical solutions which are applicable only when the Brinkman number is less than one is appraised.However for any values of the Brinkman number,Runge-Kutta shooting method is operated.The impact of selected parameters on the momentum,heat and dual species concentration fields are presented in the form of pictures.The solutions computed by numerical method are justified by comparing with the analytical method.The numerical and analytical solutions are equal in the absence of Darcy and viscous dissipations and the discrepancy advances as the Brinkman number expands.Further the solutions obtained are also justified by comparing the results with Zanchini[1]in the absence of chemical reaction for clear fluid.The thermal field is augmented with the Brinkman number for symmetric and asymmetric Biot numbers.However the profiles are highly distinct at the cold plate for unequal Biot numbers in comparison with equal Biot numbers.The conclusions are admissible to materials processing and chemical transport phenomena.