EFFECTS OF HEAT AND MASS TRANSFER FLOW OF A JEFFREY FLUID THROUGH A VERTICAL DEFORMABLE POROUS STRATUM

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1 International Journal o Mechanical Engineering and Technolog (IJMET) Volume 9, Issue, October 8, pp. 8 35, Article ID: IJMET_9 Available online at ISSN Print: and ISSN Online: IAEME Publication Scopus Indexed EFFECTS OF HEAT AND MASS TRANSFER FLOW OF A JEFFREY FLUID THROUGH A VERTICAL DEFORMABLE POROUS STRATUM M. Eswara Rao Department o Mathematics, Saveetha Institute o Medical and Technical Sciences, Chennai, Tamil Nadu, India R.L.V. Renuka Devi Department o Mathematics, Sri Venkateswara Universit, Tirupati, A.P., India N. Mahesh Babu Department o H & S, R S R Engineering College, Kadanuthala, SPSR Nellor, A.P., India M. Krishna Murth Department o Mathematics, GITAM Deemed to be Universit, Bengaluru, Karnataka, India ABSTRACT Eects o heat and mass transer low o Jere luid through a vertical deormable porous stratum are studied. The luid velocit, the displacement, the temperature and the concentration are solved numericall using ourth order Runge- Kutta method along with shooting technique. The eects o governing parameters on luid velocit, displacement, temperature and concentration are shown in graphs while the skin riction coeicient is shown in numericall. The present results have been good agreement with the existing results under some special cases. Kewords: deormable porous stratum, heat transer, Jere parameter, mass transer. Cite this Article: M. Eswara Rao, R.L.V. Renuka Devi, N. Mahesh Babu and M. Krishna Murth, Eects o Heat and Mass Transer Flow o a Jere Fluid Through a Vertical Deormable Porous Stratum, International Journal o Mechanical Engineering and Technolog, 9(), 8, pp INTRODUCTION Heat and mass transer analsis o non-newtonian luid lows are used in engineering and industrial applications such as binar gas diusion, ablation cooling, modeling o air and blood circulation in a respirator sstem. Barr et al. [] studied luid low over a thin deormable porous laer. Krishna Murth [] developed MHD Poiseuille low o a Jere luid over a deormable laer. Eect o deormable porous surace laers on the motion o a 8 editor@iaeme.com

2 Eects o Heat and Mass Transer Flow o a Jere Fluid Through a Vertical Deormable Porous Stratum sphere in a narrow clindrical tube was developed b Wen Wang et al. [3]. Free convection low o a Jere luid through a vertical deormable porous stratum was studied b Sreenadh et al. [4]. Viscous luid low in an inclined channel with deormable porous medium was reported b Sreenadh et al. [5]. Injection o luid into a laer o deormable porous medium was discussed b Barr et al. [6]. Sreenadh et al. [7] studied viscous low o Jere luid in an inclined channel through deormable porous media. MHD Couette low o a Jere luid over a deormable porous laer was investigated b Sreenadh et al. [8]. Rudraiah et al. [9] discussed Natural convection through vertical porous stratum. The present stud reveals that the eects o heat and mass transer low o a Jere luid over a deormable permeable bed. The governing equations o the luid velocit, the displacement, the heat transer and the mass transer are solved using shooting technique. While the skin riction coeicient is calculated numericall. The present results have been good agreement with the existing results under some special cases.. MATHEMATICAL FORMULATION OF THE PROBLEM Consider the stead ull developed heat and mass transer low o a Jere luid though a vertical deormable porous stratum. x - axis is taken as mid wa in the channel and - axis is taken as perpendicular to it. The walls are placed at distance b and maintained constant temperaturet, concentration C is shown in Figure. Figure The phsical model o the problem The governing equations o the velocit luid low, the displacement, the temperature and the concentration are as ollows Kv g T T a v p x () u p Kv x () T a v K v K (3) 9 editor@iaeme.com

3 M. Eswara Rao, R.L.V. Renuka Devi, N. Mahesh Babu and M. Krishna Murth C DB R C C (4) The boundar conditions on the velocit, the displacement, the temperature and the concentration are v u T T C C at b,,, dv du dt dc,,, at d d d d (5) Where a the apparent viscosit o the luid in the porous material, is the Jere parameter, is the volume raction component o the luid phase, p is the pressure, K drag coeicient, is the luid densit, g is the acceleration due to gravit, is the coeicient o linear thermal expansion o the luid, T is the temperature, T is the constant temperature at the walls, T is the ambient temperature, is lame constant, u is the solid displacement, v is the luid velocit, K is the thermal conductivit, the concentration, Cis the constant concentration at the walls, the chemical reaction. The ollowing non-dimensional quantities are * * * *, a,, DB is the thermo diusion coeicient, C is C ambient concentration, R is u x v u x b g b T T g b T T b T T C C * p,, p T T C C gbt T (6) Using equation (6) in equations ()-(5) the ollowing non-dimensional equations are o the orm as d du dv Gv Gv d (7) (8) d N dv N v d d (9) d d Sc The ollowing boundar conditions are () v, u,, at dv du d d,,, at d d d d () 3 editor@iaeme.com

4 Eects o Heat and Mass Transer Flow o a Jere Fluid Through a Vertical Deormable Porous Stratum Kb Where is the viscous drag coeicient, is the bulk luid viscosit to the apparent luid viscosit in the porous laer, parameter, Sc D B a g b T T N 4 Ka dp is the Schmidt number, G is the pressure gradient, dx is the buoanc Rb is the chemical reaction parameter, is the Jere parameter and is the volume raction s component o the luid phase. The phsical quantities o interest are the skin riction coeicient, the rate o heat transer and the Sherwood number are as ollows dv d, d Nu d and d Sh d 3. RESULTS ANDDISCUSSION The present stud investigates eects o heat and mass transer low o Jere luid though a vertical deormable porous stratum. The governing equations o the luid velocit, the displacement, the temperature and the concentration are solved numericall using shooting technique. The eects o governing parameters on the luid velocit, the displacement, the temperature and the concentration are shown in graphicall while the skin riction coeicient and the rate o heat transer are calculated numericall it is shown in Table and Table. The inluence o non-newtonian Jere parameter on the velocit temperature distribution v and the is shown in Figures and 3. We observed that the velocit and the temperature decrease or higher values o Jere parameter. The impact o volume raction component on the solid displacement u and the velocit v is displaed in Figures 4 and 5. We have seen that the solid displacement velocit increases with increase in volume raction component and the opposite nature in the luid velocit. The variation o v, the displacement u and the temperature or dierent values o velocit pressure gradient G is presented in Figures 6, 7 and 8. We report that the velocit, displacement and the temperature decreases with increase in pressure gradient G. The inluences o viscous drag coeicient and the apparent viscosit on the luid velocit, the temperature and the solid displacement u are shown in Figures 9-4. We noticed that the luid velocit, the temperature reduces with increase in, and the opposite behaviors in the solid displacement are reported. This reduction causes or higher values o viscosit parameter gives rise to increasing in velocit and temperature. The variation o the temperature distribution or distinct values o buoanc parameter N is displaed in Figure 5. We reveal that the temperature reduces or enhancing in buoanc parameter N. From Figure 6 and 7 that the inluence o Schmidt number Sc and Chemical reaction parameter on the concentration distribution is displaed. We noticed that the concentration reduces or higher values o Schmidt number Sc and Chemical reaction. The magnitude o skin riction coeicient at the wall is calculated numericall or distinct values o buoanc parameter N and is shown in Table. We noticed that the skin riction coeicient increases with increasing N the same nature we observed that or undeormable vertical 3 editor@iaeme.com

5 M. Eswara Rao, R.L.V. Renuka Devi, N. Mahesh Babu and M. Krishna Murth porous channel Rudraiah et al. [9]. The skin riction coeicient is more or non-newtonian luid when comparing with Newtonian luid and is represented in Table. The present results have been good agreement with the existing result Sreenadh et al. [4] =.,.,.,.3 =.,.,.,.3.3. v ().5..5 ().5..5 =.5, G =., =, =, N =, Sc =.6, = Figure The Velocit or distinct values o =.5, =, G =., =, N =, Sc =.6, = Figure 3 The temperature or distinct values o =.5,.6,.7,.8.35 =.4,.5,.6, u ().8 v() G =., =., =, =, N =, Sc =.6, = Figure 4 The displacement or distinct values o.5 =., G =., =, =, N =, Sc =.6, = Figure 5 The Velocit or distinct values o G =.,.,.3, v () u ().6.4 G =.,.,.3,.4.5 =.5, =., =, =, N =, Sc =.6, = Figure 6 The velocit or distinct values o G. =.5, =., =, =, N =, Sc =.6, = Figure 7 The displacement or distinct values o G 3 editor@iaeme.com

6 Eects o Heat and Mass Transer Flow o a Jere Fluid Through a Vertical Deormable Porous Stratum G =.,.,.3,.4.4 =.5,.,.5,. () v ().3.. =.5, =., =, =, N =, Sc =.6, = Figure 8 The temperature or distinct values o G. =.5, =., G =., =, N =, Sc =.6, = Figure 9 The velocit or distinct values o =.,.5,.,.5. =.,.5,.,.5 ().8.5 u () =.5, =., G =., =, N =, Sc =.6, = Figure The temperature or distinct values o Figure The displacement or distinct values o.5 =.5, =., G =., =, N =, Sc =.6, = v (). =.,.5,.,.5.. ().8 =.,.5,., =.5, =., G =., =, N =, Sc =.6, = Figure The velocit or distinct values o. =.5, =., G =., =, N =, Sc =.6, = Figure 3 The temperature or distinct values o 33 editor@iaeme.com

7 M. Eswara Rao, R.L.V. Renuka Devi, N. Mahesh Babu and M. Krishna Murth.5.4. =.,.5,., N =.,.5,., u () () =.5, =., G =., =, N =, Sc =.6, = Figure 4 The displacement or distinct values o..5 =.5, =., =, =, G =., Sc =.6, = Figure 5 The temperature or distinct values o N.995 Sc =.,.6,.78, =.,.,.3, ().975 () =.5, =, G =., =. =, N =, = Figure 6 The Concentration or distinct values o Sc.9 =.5, =, G =.,Sc =.6 =, N =, Sc =.6, = Figure 7 The Concentration or distinct values o Table The Skin riction coeicient or distinct values o N S. No. N N N 3 Rudraiah et al. [9] (undeormable porous laer) Sreenadh et al.[4] (deormable porous laer with ) 3 Present results (deormable porous laer with ) Table The Skin riction coeicient or distinct values o Sreenadh et al.[4] Present results editor@iaeme.com

8 Eects o Heat and Mass Transer Flow o a Jere Fluid Through a Vertical Deormable Porous Stratum REFERENCES [] Barr SI, Parker K H, Aldis GK, Fluid low over a thin deormable Porous laer, J. Appl.Maths. Phs 99; 4: [] Krishna Murth M, MHD Poiseuille low o a Jere luid over a deormable laer, Chem. Proc. Eng. Res 5; 38: 8-4. [3] Wen Wang Kimh. Parker, Eect o deormable porous surace laers on the motion o a sphere in a narrow clindrical tube, J. Appl. Fluid. Mech 995; 83: [4] Sreenadh S, Rashidi MM, Kumara swam naidu K, Parandhama A, Free convection low o a Jere luid through a vertical deormable porous stratum, J. Appl. Fuid Mech 6; 9: [5] Sreenadh S, Gopi krishna G,Manoj kumar uppuluri V, Srinivas ANS, Viscous luid low in an inclined channel with deormable porous medium, Int. J. Mech. Engg. Tech 8; 9: [6] Barr S, Aldis G, Mercer G, Injection o luid into a laer o deormable porous medium, Appl. Mech. Reviews 995; 48: [7] Selvi PD, Sreenadh S, Kesava redd E, Gopi krishna G, Viscous low o Jere luid in an inclined channel through deormable porous media, W. Appl. Sci. J 7; 35: [8] Sreenadh S, Prasad KV, Vaida H, Sudhakara E, Gopi krishna G, Krishna Murth M, MHD Couette low o a Jere luid over a deormable porous laer, Int. J. Appl. Comp. Math 7; 3: [9] Rudraiah N, Nagaraj ST, Natural convection through vertical porous stratum, Int. J. Eng. Sci. 977; 5: editor@iaeme.com