Re: Heat And Mass Transfer By Ds Kumar Pdf 11
Matt Dreher
The 17 papers included in this special issue are focused in various current topics and fundamental physics relevant to heat and mass transfer. A companion special issue is being taken out in the ASME Journal of Thermal Sciences and Engineering Applications with the papers of applications in nature and presented in the conference. The TSEA papers have also undergone the strict peer-review process of ASME standard.
The effects of chemical reaction on heat and mass transfer flow of a micropolar fluid in a permeable channel with heat generation and thermal radiation is studied. The Rosseland approximations are used to describe the radiative heat flux in the energy equation. The model contains nonlinear coupled partial differential equations which have been transformed into ordinary differential equation by using the similarity variables. The relevant nonlinear equations have been solved by Runge-Kutta-Fehlberg fourth fifth-order method with shooting technique. The physical significance of interesting parameters on the flow and heat transfer characteristics as well as the local skin friction coefficient, wall couple stress, and the heat transfer rate are thoroughly examined.
Influence of thermal radiation on flow and heat transfer study has become more important industrially. The heat transfer and temperature profile of a micropolar fluid over different geometries can be affected significantly at high temperature. Bhattacharyya et al. [26] considered thermal radiation effect on micropolar fluid flow and heat transfer over a porous shrinking sheet. Hussain et al. [27] analyzed radiation effects on the thermal boundary layer flow of a micropolar fluid towards a permeable stretching sheet. Oahimire and Olajuwon [28] investigated the influence of Hall current and thermal radiation on heat and mass transfer of a chemically reacting MHD flow of a micropolar fluid through a porous medium. Mabood et al. [29] studied effects of nonuniform heat source/sink and Soret on MHD non-Darcian convective flow past a stretching sheet in a micropolar fluid with radiation.
The effect of heat generation on heat transfer is an important issue in view of various physical problems. Ziabakhsh et al. [30] analyzed the micropolar fluid flow with heat generation. Singh and Kumar [31] considered the melting effect in stagnation-point flow of micropolar fluid towards a stretching/shrinking surface. Bakr [32] investigated the effects of chemical reaction and heat source magnetoconvection and mass transfer flow of a micropolar fluid in a rotating frame of reference. The heat generation/absorption effects on MHD flow and heat transfer of micropolar fluid through a stretching surface have been proposed by Mahmoud and Waheed [33]. Abbasi et al. [34] examined the flow of Maxwell nanofluid in the presence of heat generation/absorption. Mliki et al. [35] investigated the influence of nanoparticle Brownian motion and heat generation/absorption over linear/sinusoidally heated cavity in the presence of magnetohydrodynamic natural convection. Sheikholeslami and Ganji [36] studied three-dimensional heat and mass transfer flow of nanofluid over a rotating system. Thermal radiation effects on mixed convection flow and heat transfer of a micropolar fluid through an unsteady stretching surface with heat generation/absorption are presented by Singh and Kumar [37].
Motivated by the above studies and applications, the present work explores effects of chemical reaction on heat and mass transfer flow of a micropolar fluid over a permeable channel in the presence of radiation and heat generation. The equations of continuity, momentum, angular momentum, energy, and concentration have been reduced to a system of nonlinear ordinary differential equations by similarity transforms which are solved by Runge-Kutta-Fehlberg method with shooting technique. It is expected that the results obtained from present paper will provide important information to the audience. To the best of our knowledge, such type of study is not investigated before in the scientific literature.
The heat and mass transfer flow of a micropolar fluid in a permeable channel with chemical reaction is considered in the present work. The thermal radiation and heat source are incorporated in the energy equation. The graphical model of the problem has been given along with flow configuration and coordinate system in Figure 1. The assumptions of the problem in detail can be found in [6]. The governing equations of boundary layer are given in the following form:where and indicate the velocity components in the and directions, respectively, is the fluid density, is the dynamic viscosity, is the material parameter, is the angular or microrotation velocity, is the fluid pressure, is the microinertia density, is the microrotation viscosity, is the fluid temperature, is the specific heat at constant pressure, is the fluid concentration, is the thermal conductivity, is the radiative heat flux, is the heat generation coefficient, is the molecular diffusivity, and is the chemical reaction rate coefficient.
Equations (2), (3), (4), (6), and (8) can be transformed into a set of nonlinear ordinary differential equations by using the following similarity transformations:where and , with and as constants. The stream function is defined asThe coupled system of transformed nonlinear ordinary differential equations isBoundary conditions in nondimensional form arewhere is the coupling number, is the spin-gradient viscosity parameter, is the micropolar material constant, is the local Eckert number, is the heat generation parameter, and are the Peclet numbers for the diffusion of heat and the diffusion of mass, is the Reynolds number, is the thermal radiation parameter, is the Grashof number, is the Prandtl number, is the Schmidt number, and is the chemical reaction parameter.
The other parameters of physical interest are the local Nusselt and Sherwood numbers, which are defined as follows:where and are the local heat flux and mass flux, respectively, which are defined asNow using (10) and (15) in (14), we get
In order to study, the effects of various governing physical parameters on the flow, heat, and mass transfer numerical computations are carried out for , , , , , , and while the Eckert number is fixed. A critical analysis with previously published work is done in Table 1 and these results are found to be in very good agreement.
Figures 15 and 16 displayed the variation of the Sherwood number or mass transfer rate for different parameters. Figures 15 and 16 depict the behavior of the mass transfer rate against Reynolds number with different values of Peclet number and chemical reaction parameter . The mass transfer rate rises with increasing values of the Peclet number and chemical reaction parameter . It is also clear from these figures that there is no change in mass transfer rate with rise in Reynolds number values.
The present paper deals with numerical analysis of chemical reaction effects on heat and mass transfer flow of a micropolar fluid over a permeable channel in the presence of radiation and heat generation. The system of nonlinear partial differential equations was converted to a system of ordinary differential equations and then is solved numerically using the Runge-Kutta-Fehlberg method along with shooting method. From the above discussion, the important results are summarized as follows:(i)Velocity and Reynolds number are inversely proportional to each other at lower channel wall, while velocity and Reynolds number are proportional to each other at upper channel wall.(ii)Microrotation decreases with increase in the value of coupling number, micropolar material constant, and Reynolds number, but it increases with increase in the value of spin-gradient viscosity parameter.(iii)Temperature increases with heat generation parameter and and are the Peclet numbers for the diffusion of heat and the diffusion of mass, and temperature decreases with thermal radiation parameter.(iv)Concentration is inversely proportional to the Peclet number for the diffusion of mass and chemical reaction parameter.(v)The rate of heat transfer increases with thermal radiation parameter and rate of heat transfer decreases with Peclet number and heat generation parameter.(vi)The rate of mass transfer rises with increase Peclet number and chemical reaction parameter.
This paper discusses the effect of Chemical reaction, Radiation and MHD on laminar mixed convection boundary layer flow and heat and mass transfer on continuously moving vertical surface. The fluid viscosity is assumed to vary as an inverse linear function of temperature and local similarity solutions are obtained for the boundary layer equations subject to isothermally moving vertical surface with uniform speed. The system of non-linear partial differential equations developed in the process is finally transformed into a set of ordinary differential equations with the help of similarity transformations involved in the problem. This set of equations is for different values of the various parameters. The results showing the effect of physical parameters on velocity, temperature and concentration have been computed and presented graphically to discuss their in details.
The heat transfer and flow performance of the plate fin heat sink in a horizontal rectangular channel with dimples and protrusions on the fin surfaces has been experimentally investigated in forced convection. The Nusselt number and friction factor are obtained by varying the system parameters as depth and pitch of the dimples for inline and staggered arrangements. The Reynolds number is considered in the range of 6800 to 15,200. The effect of depth and pitch of dimples are examined under constant heat flux while keeping the constant diameter of dimples. Experimental results indicate that the heat transfer and flow performance of fin array are significantly influenced by increasing the depth of dimples. The heat transfer from fin array is enhanced and the flow resistance is increased by decreasing the pitch ratio (s/d) and increasing the depth ratio (D/d). The maximum fin performance of dimpled fin heat sink corresponds to the staggered arrangement of dimpled heat sink with dimple pitch ratio (s/d) of 2.5 and dimple depth ratio (D/d) of 0.5.
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