Professional Experience:* Associate Professor (2016- xxxx), Chemical Engineering, IIT Roorkee* Assistant Professor (2009- 2016), Chemical Engineering, IIT Roorkee* Post-Doctoral Research Fellow (2007-2009), Chemical Phone: +91-1332-28 5304 (Office) Address: Dr. Ram Prakash Bharti
Assistant Professor
Department of Chemical Engineering
Indian Institute of Technology (IIT) Roorkee
Roorkee 247667, Uttrakhand, India
Natural convection characteristics of a partially heated open ended square cavity have been inves... more Natural convection characteristics of a partially heated open ended square cavity have been investigated numerically by using an in-house computational flow solver based on the passive scalar thermal lattice Boltzmann method (PS-TLBM) with D2Q9 (two-dimensional and nine-velocity link) lattice model. The partial part of left wall of the cavity is heated isothermally at either of the three different (bottom, middle and top) locations for the fixed heating length as half of characteristic length (H/2) while the right wall is open to the ambient conditions. The other parts of the cavity are thermally isolated. In particular, the influences of partial heating locations and Rayleigh number (10^3 ≤ Ra ≤ 10^6) in the laminar zone on the local and global natural convection characteristics (such as streamline, vorticity and isotherm contours; centerline variations of velocity and temperature; and local and average Nusselt numbers) have been presented and discussed for the fixed value of the P...
Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science
This work presents thermal lattice Boltzmann method simulation of magneto-hydrodynamic, buoyancy-... more This work presents thermal lattice Boltzmann method simulation of magneto-hydrodynamic, buoyancy-driven convection in a partially differentially heated cavity (aspect ratio = 1) subjected to a magnetic field along the vertical direction, i.e. at 90°. Lattice Boltzmann method simulations are performed for three different cooler lengths (Lc = H/4, H/2, H) placed along the middle of one vertical wall for a wide range of Rayleigh and Hartmann numbers (103 ≤ Ra ≤ 105; Ha = 0, 60, 120) at fixed Prandtl number (Pr = 0.71, air). A partial heater is placed at the center of other vertical walls and its size is kept as half of the characteristic length (H/2). The physical insights of the systems are delineated by systematic analysis of stream function and temperature contours. Heat transfer characteristics of the cavity are elucidated by using averaged values of the Nusselt number. It is noted that average Nusselt number has a proportional dependence with cooler length and Rayleigh number, whi...
The Canadian Journal of Chemical Engineering, 2016
ABSTRACT Two-dimensional unconfined flow and heat transfer across a long tapered trapezoidal bluf... more ABSTRACT Two-dimensional unconfined flow and heat transfer across a long tapered trapezoidal bluff body are investigated for the range Re = 1 to 150 (thereby covering both steady and unsteady periodic regimes) and Pr = 0.7 (air). A number of engineering parameters, e.g. drag and lift coefficients, Strouhal and Nusselt numbers, and others, is calculated for the above range of conditions. No flow separation occurs from the surface of the trapezoidal cylinder for the range Re ≤ 5; however, flow starts to separate from the rear surface of the cylinder at Re = 6. Therefore, the onset of flow separation exits between Re = 5 and 6. The critical value of the Reynolds number (i.e. transition from steady to unsteady) exists between Re = 46 and 47. The drag coefficient decreases with increasing Reynolds number in the steady regime; however, the drag increases with Reynolds number in the unsteady regime. The Strouhal number and the average Nusselt number increase with increasing value of the Reynolds number. Finally, the simple correlation for the average Nusselt number is obtained in the steady flow regime.
Electroviscous effects in steady, pressure-driven flow of a symmetric 1: 1 electrolyte in a cylin... more Electroviscous effects in steady, pressure-driven flow of a symmetric 1: 1 electrolyte in a cylindrical microfluidic 4: 1: 4 contractionexpansion at low Reynolds number are investigated numerically by solving the field equations using a finite volume method. ...
ABSTRACT Electroviscous effects in steady, pressure-driven flow of a Carreau shear-thinning liqui... more ABSTRACT Electroviscous effects in steady, pressure-driven flow of a Carreau shear-thinning liquid in a cylindrical microfluidic 4:1:4 contraction-expansion at low Reynolds number are investigated numerically by solving the equations governing the flow, the electric field, and ion transport, using a finite volume method. The channel wall is considered to have a uniform surface charge density and the liquid is assumed to be a symmetric 1:1 electrolyte solution. Predictions are presented for a range of values of the shear-thinning parameters in the Car-reau model for various surface charge densities and Debye lengths. The aim is to examine the effect of shear-thinning on the apparent viscosity due to the electroviscous effect. The appar-ent/physical viscosity ratio (Y) is shown to increase as the degree of shear-thinning increases. Thus the electroviscous effect is stronger in shear-thinning liquids than it is when the liquid is Newtonian. The trend holds true regardless of the choice of surface charge density or De-bye length, although the sensitivity of the trend decreases as the surface charge density and/or the Debye length is reduced. For thick enough EDLs, the factor is found to be lower for flow through the expansion-contraction geometry than it is in corresponding uniform pipe flow, except when the amount of shear-thinning and the surface charge density are greatest.
In this work, numerical simulation of natural convection in a square cavity with one vertical wal... more In this work, numerical simulation of natural convection in a square cavity with one vertical wall subjected to both hot and cold conditions and other vertical wall maintained at cold is car-ried out for laminar range of Rayleigh numbers (10 3 ≤ Ra ≤ 10 6) and constant Prandtl number (Pr = 0.71). The lattice Boltz-mann method with D2Q9 lattice model is used as numerical tool for solving equations governing heat and fluid flow. The investi-gation of flow and thermal fields is done by evaluation of stream function and isotherms, respectively. The rate of heat transfer is calculated by using average Nusselt number (Nu). The av-erage Nusselt numbers (Nu) for both walls shown proportional increase with Rayleigh number (Ra). At Ra = 10 5 , same level of heat transfer rate is achieved which is explained by nearly same values of average Nusselt number (Nu) of both vertical walls. Further the overall Nusselt number is obtained to elucidate the overall heat transfer in the cavity. The results...
ABSTRACT Natural convection heat transfer in an square enclosure, consisting of partially heated ... more ABSTRACT Natural convection heat transfer in an square enclosure, consisting of partially heated west wall with east end open to ambient, is investigated numerically by using in-house computational fluid dynamics solver based on thermal lattice Boltzmann method. In particular, the influences of Rayleigh number (10 3 − 10 6), heating location (bottom, middle and top) on west wall and di-mensionless heating length (0.25 − 0.75) on momentum and heat transfer characteristics of air are presented and discussed. The streamline patterns show bifurcation at lowest Rayleigh number for bottom and middle heating whereas at highest Rayleigh number, all heating positions yields bifurcation and elongation of flow patterns with secondary vortex near the lower side of open end. The middle and bottom heating locations show linear increase in Nusselt number with heater size whereas inverse dependence is seen for top heating. The maximum heat transfer is observed in case of middle heating. As expected, average Nusselt number increased with increasing Rayleigh number. Finally, the functional dependence of average Nusselt number on flow governing param-eters (Rayleigh number and heating length) for different heating locations is presented as a simple predictive empirical relationship.
ABSTRACT In this paper, study of natural convection in an enclosure containing heated solid body ... more ABSTRACT In this paper, study of natural convection in an enclosure containing heated solid body is presented. Passive scalar approach is used for solving temperature equation. Top and bottom walls of an enclosure are thermally insulated, while side walls are maintained at non-dimensional temperature Tc=0.0. Heated square body is placed at geometric center of enclosure and it is kept at non-dimensional temperature of TH=1.0. The aim of the study is to investigate the temperature distribution across an enclosure at three different Prandtl numbers (Pr=0.71, 5.0 and 8.0) and Rayleigh numbers (Ra=1e+4, 1e+5 and 1e+6) for geometric aspect ratio (AR=L/H) of 1.0.
Electroviscous effects in steady, pressure-driven flow of a Carreau shear-thinning liquid in a cy... more Electroviscous effects in steady, pressure-driven flow of a Carreau shear-thinning liquid in a cylindrical microfluidic 4: 1: 4 contractionexpansion at low Reynolds number are investigated numerically by solving the equations governing the flow, the electric field, and ...
Lattice Boltzmann analysis of natural convection in a partially heated open ended enclosure for d... more Lattice Boltzmann analysis of natural convection in a partially heated open ended enclosure for different fluids by Krunal M. Gangawane , Ram P. Bharti, and Surendra Kumar
his work presents the lattice Boltzmann simulation of natural convection in an open ended square cavity subjected to partial heating. The size of heater is half of characteristic length and placed at middle location of one vertical wall. Numerical simulations are performed for three different fluids of industrial, scientific as well as domestic field, viz., air (Pr = 0.71), dichloro-difluoro-methane (Pr = 4.5) and water (Pr = 7). The influence of the partial heater on heat and hydrodynamic characteristics of an open ended cavity have been elucidated. It is observed that isotherms become more confined toward the partially heated portion of wall with the increase in Prandtl number. The heat transfer rate shows linear increase with the Prandtl number, i.e., enclosure containing water shows higher heat transfer rate followed by R-12 refrigerant and air. The numerical results are summarized by the empirical correlation relating Nusselt number with Rayleigh and Prandtl numbers.
Two-dimensional lattice Boltzmann simulation of natural convection in differentially heated squar... more Two-dimensional lattice Boltzmann simulation of natural convection in differentially heated square cavity: Effect of Prandtl and Rayleigh numbers by Krunal M. Gangawane, Ram P. Bharti and Surendra Kumar
A thermal lattice Boltzmann method is utilized for the numerical simulation of the natural convection heat transfer phenomena inside a differentially heated square cavity. Numerical simulations are performed to elucidate the combined effects of Prandtl number (0.71 ≤ Pr ≤ 100) and Rayleigh number (104 ≤ Ra ≤ 106) on heat transfer and fluid flow characteristics inside the cavity. Detailed insights are gained by the evaluation of isotherms, stream functions and vorticity profiles. For higher Prandtl and Rayleigh numbers, streamlines become more confined to hot wall with the loss of symmetry. Similarly, isotherms patterns become more stratified towards the hot wall. The centre-line velocity and temperature profiles are also analyzed. Further, the heat transfer rate is estimated in terms of average Nusselt number. It suggests a proportional increase in the average Nusselt number with the increasing values of Prandtl number for considered range of Rayleigh numbers. Finally, the numerical data for the average Nusselt number are presented in the form of a correlation for their best utilization in design and engineering practices.
This work presents an extension of the Deforming-Spatial-Domain/Stabilized Space–Time (DSD/SST) m... more This work presents an extension of the Deforming-Spatial-Domain/Stabilized Space–Time (DSD/SST) method to non-Newtonian fluid flow and heat transfer with moving boundaries. In this method, the variational formulation is written over the space–time domain. Three sets of stabilization parameters are used for the continuity, momentum and thermal energy equations. The more efficient solution for highly non-linear problems is achieved by using the Newton–Raphson iterative method for non-linear terms and the generalized minimal residual method for algebraic equations. This work makes the computations feasible with third-order accuracy in time, which is higher then most versions of the FEM. To validate this method, it is used to solve the well-known benchmark problems such as channel-confined flow, lid-driven cavity, flow around a cylinder, and flow in channel with wavy wall, where the non-Newtonian fluid rheological behaviour is incorporated. In particular, the results in terms of the Nusselt number, wall shear stress (WSS), vorticity fields and streamlines are discussed. It shows that the flow and heat transfer characteristics are quite different if the moving boundaries are taken into account. In summary, this work provides an effective extension of the DSD/SST method to hydrodynamics and heat transfer problems involving complex fluids and moving boundaries.
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The electroviscous flow at low Reynolds number through a two-dimensional slit contraction with el... more The electroviscous flow at low Reynolds number through a two-dimensional slit contraction with electric double-layer overlap is investigated numerically for cases where the permittivity of the wall material is significant in comparison with the permittivity of the liquid. The liquid-solid interface is assumed to have uniform surface-charge density. It is demonstrated that a finite wall permittivity has a marked effect on the distribution of ions in and around the contraction, with a significant build-up of counter-ions observed at the back-step. The development length of the flow increases substantially as the wall permittivity becomes significant, meaning that the electric double-layers require a longer distance to develop within the contraction. Consequently, there is a corresponding decrease in the hydrodynamic and electro-potential resistance caused by the contraction. The effect of wall-region width on the flow characteristics is also quantified, demonstrating that the development length increases with increasing wall-region width for widths up to 5 channel widths.
The forced convective heat transfer characteristics for incompressible power-law fluids past a bu... more The forced convective heat transfer characteristics for incompressible power-law fluids past a bundle of circular cylinders have been investigated numerically. The cylinder-to-cylinder hydrodynamic interactions have been approximated via a simple cell model. The momentum and energy equations have been solved using a finite difference based numerical method for a range of physical and kinematic conditions. The role of the two commonly used thermal boundary conditions, namely, constant temperature or constant heat flux, on heat transfer characteristics has also been studied. Extensive numerical results elucidating the effect of shear-thinning viscosity on the values of Nusselt number have been obtained for Peclet numbers ranging from 1 to 5000, Reynolds number in the range 1–500, flow behaviour index 1greater-or-equal, slantedngreater-or-equal, slanted0.5 and three values of voidages, namely, 0.4, 0.5 and 0.6, typical of tubular heat exchangers and tube banks. Under all conditions, varying levels of enhancement in Nusselt number are observed due to shear-thinning behaviour. The surface averaged Nusselt number shows strong dependence on the values of voidage, power-law index, Reynolds and Peclet numbers. The paper is concluded by presenting comparisons with the scant experimental results available in the literature.
Natural convection characteristics of a partially heated open ended square cavity have been inves... more Natural convection characteristics of a partially heated open ended square cavity have been investigated numerically by using an in-house computational flow solver based on the passive scalar thermal lattice Boltzmann method (PS-TLBM) with D2Q9 (two-dimensional and nine-velocity link) lattice model. The partial part of left wall of the cavity is heated isothermally at either of the three different (bottom, middle and top) locations for the fixed heating length as half of characteristic length (H/2) while the right wall is open to the ambient conditions. The other parts of the cavity are thermally isolated. In particular, the influences of partial heating locations and Rayleigh number (10^3 ≤ Ra ≤ 10^6) in the laminar zone on the local and global natural convection characteristics (such as streamline, vorticity and isotherm contours; centerline variations of velocity and temperature; and local and average Nusselt numbers) have been presented and discussed for the fixed value of the P...
Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science
This work presents thermal lattice Boltzmann method simulation of magneto-hydrodynamic, buoyancy-... more This work presents thermal lattice Boltzmann method simulation of magneto-hydrodynamic, buoyancy-driven convection in a partially differentially heated cavity (aspect ratio = 1) subjected to a magnetic field along the vertical direction, i.e. at 90°. Lattice Boltzmann method simulations are performed for three different cooler lengths (Lc = H/4, H/2, H) placed along the middle of one vertical wall for a wide range of Rayleigh and Hartmann numbers (103 ≤ Ra ≤ 105; Ha = 0, 60, 120) at fixed Prandtl number (Pr = 0.71, air). A partial heater is placed at the center of other vertical walls and its size is kept as half of the characteristic length (H/2). The physical insights of the systems are delineated by systematic analysis of stream function and temperature contours. Heat transfer characteristics of the cavity are elucidated by using averaged values of the Nusselt number. It is noted that average Nusselt number has a proportional dependence with cooler length and Rayleigh number, whi...
The Canadian Journal of Chemical Engineering, 2016
ABSTRACT Two-dimensional unconfined flow and heat transfer across a long tapered trapezoidal bluf... more ABSTRACT Two-dimensional unconfined flow and heat transfer across a long tapered trapezoidal bluff body are investigated for the range Re = 1 to 150 (thereby covering both steady and unsteady periodic regimes) and Pr = 0.7 (air). A number of engineering parameters, e.g. drag and lift coefficients, Strouhal and Nusselt numbers, and others, is calculated for the above range of conditions. No flow separation occurs from the surface of the trapezoidal cylinder for the range Re ≤ 5; however, flow starts to separate from the rear surface of the cylinder at Re = 6. Therefore, the onset of flow separation exits between Re = 5 and 6. The critical value of the Reynolds number (i.e. transition from steady to unsteady) exists between Re = 46 and 47. The drag coefficient decreases with increasing Reynolds number in the steady regime; however, the drag increases with Reynolds number in the unsteady regime. The Strouhal number and the average Nusselt number increase with increasing value of the Reynolds number. Finally, the simple correlation for the average Nusselt number is obtained in the steady flow regime.
Electroviscous effects in steady, pressure-driven flow of a symmetric 1: 1 electrolyte in a cylin... more Electroviscous effects in steady, pressure-driven flow of a symmetric 1: 1 electrolyte in a cylindrical microfluidic 4: 1: 4 contractionexpansion at low Reynolds number are investigated numerically by solving the field equations using a finite volume method. ...
ABSTRACT Electroviscous effects in steady, pressure-driven flow of a Carreau shear-thinning liqui... more ABSTRACT Electroviscous effects in steady, pressure-driven flow of a Carreau shear-thinning liquid in a cylindrical microfluidic 4:1:4 contraction-expansion at low Reynolds number are investigated numerically by solving the equations governing the flow, the electric field, and ion transport, using a finite volume method. The channel wall is considered to have a uniform surface charge density and the liquid is assumed to be a symmetric 1:1 electrolyte solution. Predictions are presented for a range of values of the shear-thinning parameters in the Car-reau model for various surface charge densities and Debye lengths. The aim is to examine the effect of shear-thinning on the apparent viscosity due to the electroviscous effect. The appar-ent/physical viscosity ratio (Y) is shown to increase as the degree of shear-thinning increases. Thus the electroviscous effect is stronger in shear-thinning liquids than it is when the liquid is Newtonian. The trend holds true regardless of the choice of surface charge density or De-bye length, although the sensitivity of the trend decreases as the surface charge density and/or the Debye length is reduced. For thick enough EDLs, the factor is found to be lower for flow through the expansion-contraction geometry than it is in corresponding uniform pipe flow, except when the amount of shear-thinning and the surface charge density are greatest.
In this work, numerical simulation of natural convection in a square cavity with one vertical wal... more In this work, numerical simulation of natural convection in a square cavity with one vertical wall subjected to both hot and cold conditions and other vertical wall maintained at cold is car-ried out for laminar range of Rayleigh numbers (10 3 ≤ Ra ≤ 10 6) and constant Prandtl number (Pr = 0.71). The lattice Boltz-mann method with D2Q9 lattice model is used as numerical tool for solving equations governing heat and fluid flow. The investi-gation of flow and thermal fields is done by evaluation of stream function and isotherms, respectively. The rate of heat transfer is calculated by using average Nusselt number (Nu). The av-erage Nusselt numbers (Nu) for both walls shown proportional increase with Rayleigh number (Ra). At Ra = 10 5 , same level of heat transfer rate is achieved which is explained by nearly same values of average Nusselt number (Nu) of both vertical walls. Further the overall Nusselt number is obtained to elucidate the overall heat transfer in the cavity. The results...
ABSTRACT Natural convection heat transfer in an square enclosure, consisting of partially heated ... more ABSTRACT Natural convection heat transfer in an square enclosure, consisting of partially heated west wall with east end open to ambient, is investigated numerically by using in-house computational fluid dynamics solver based on thermal lattice Boltzmann method. In particular, the influences of Rayleigh number (10 3 − 10 6), heating location (bottom, middle and top) on west wall and di-mensionless heating length (0.25 − 0.75) on momentum and heat transfer characteristics of air are presented and discussed. The streamline patterns show bifurcation at lowest Rayleigh number for bottom and middle heating whereas at highest Rayleigh number, all heating positions yields bifurcation and elongation of flow patterns with secondary vortex near the lower side of open end. The middle and bottom heating locations show linear increase in Nusselt number with heater size whereas inverse dependence is seen for top heating. The maximum heat transfer is observed in case of middle heating. As expected, average Nusselt number increased with increasing Rayleigh number. Finally, the functional dependence of average Nusselt number on flow governing param-eters (Rayleigh number and heating length) for different heating locations is presented as a simple predictive empirical relationship.
ABSTRACT In this paper, study of natural convection in an enclosure containing heated solid body ... more ABSTRACT In this paper, study of natural convection in an enclosure containing heated solid body is presented. Passive scalar approach is used for solving temperature equation. Top and bottom walls of an enclosure are thermally insulated, while side walls are maintained at non-dimensional temperature Tc=0.0. Heated square body is placed at geometric center of enclosure and it is kept at non-dimensional temperature of TH=1.0. The aim of the study is to investigate the temperature distribution across an enclosure at three different Prandtl numbers (Pr=0.71, 5.0 and 8.0) and Rayleigh numbers (Ra=1e+4, 1e+5 and 1e+6) for geometric aspect ratio (AR=L/H) of 1.0.
Electroviscous effects in steady, pressure-driven flow of a Carreau shear-thinning liquid in a cy... more Electroviscous effects in steady, pressure-driven flow of a Carreau shear-thinning liquid in a cylindrical microfluidic 4: 1: 4 contractionexpansion at low Reynolds number are investigated numerically by solving the equations governing the flow, the electric field, and ...
Lattice Boltzmann analysis of natural convection in a partially heated open ended enclosure for d... more Lattice Boltzmann analysis of natural convection in a partially heated open ended enclosure for different fluids by Krunal M. Gangawane , Ram P. Bharti, and Surendra Kumar
his work presents the lattice Boltzmann simulation of natural convection in an open ended square cavity subjected to partial heating. The size of heater is half of characteristic length and placed at middle location of one vertical wall. Numerical simulations are performed for three different fluids of industrial, scientific as well as domestic field, viz., air (Pr = 0.71), dichloro-difluoro-methane (Pr = 4.5) and water (Pr = 7). The influence of the partial heater on heat and hydrodynamic characteristics of an open ended cavity have been elucidated. It is observed that isotherms become more confined toward the partially heated portion of wall with the increase in Prandtl number. The heat transfer rate shows linear increase with the Prandtl number, i.e., enclosure containing water shows higher heat transfer rate followed by R-12 refrigerant and air. The numerical results are summarized by the empirical correlation relating Nusselt number with Rayleigh and Prandtl numbers.
Two-dimensional lattice Boltzmann simulation of natural convection in differentially heated squar... more Two-dimensional lattice Boltzmann simulation of natural convection in differentially heated square cavity: Effect of Prandtl and Rayleigh numbers by Krunal M. Gangawane, Ram P. Bharti and Surendra Kumar
A thermal lattice Boltzmann method is utilized for the numerical simulation of the natural convection heat transfer phenomena inside a differentially heated square cavity. Numerical simulations are performed to elucidate the combined effects of Prandtl number (0.71 ≤ Pr ≤ 100) and Rayleigh number (104 ≤ Ra ≤ 106) on heat transfer and fluid flow characteristics inside the cavity. Detailed insights are gained by the evaluation of isotherms, stream functions and vorticity profiles. For higher Prandtl and Rayleigh numbers, streamlines become more confined to hot wall with the loss of symmetry. Similarly, isotherms patterns become more stratified towards the hot wall. The centre-line velocity and temperature profiles are also analyzed. Further, the heat transfer rate is estimated in terms of average Nusselt number. It suggests a proportional increase in the average Nusselt number with the increasing values of Prandtl number for considered range of Rayleigh numbers. Finally, the numerical data for the average Nusselt number are presented in the form of a correlation for their best utilization in design and engineering practices.
This work presents an extension of the Deforming-Spatial-Domain/Stabilized Space–Time (DSD/SST) m... more This work presents an extension of the Deforming-Spatial-Domain/Stabilized Space–Time (DSD/SST) method to non-Newtonian fluid flow and heat transfer with moving boundaries. In this method, the variational formulation is written over the space–time domain. Three sets of stabilization parameters are used for the continuity, momentum and thermal energy equations. The more efficient solution for highly non-linear problems is achieved by using the Newton–Raphson iterative method for non-linear terms and the generalized minimal residual method for algebraic equations. This work makes the computations feasible with third-order accuracy in time, which is higher then most versions of the FEM. To validate this method, it is used to solve the well-known benchmark problems such as channel-confined flow, lid-driven cavity, flow around a cylinder, and flow in channel with wavy wall, where the non-Newtonian fluid rheological behaviour is incorporated. In particular, the results in terms of the Nusselt number, wall shear stress (WSS), vorticity fields and streamlines are discussed. It shows that the flow and heat transfer characteristics are quite different if the moving boundaries are taken into account. In summary, this work provides an effective extension of the DSD/SST method to hydrodynamics and heat transfer problems involving complex fluids and moving boundaries.
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The electroviscous flow at low Reynolds number through a two-dimensional slit contraction with el... more The electroviscous flow at low Reynolds number through a two-dimensional slit contraction with electric double-layer overlap is investigated numerically for cases where the permittivity of the wall material is significant in comparison with the permittivity of the liquid. The liquid-solid interface is assumed to have uniform surface-charge density. It is demonstrated that a finite wall permittivity has a marked effect on the distribution of ions in and around the contraction, with a significant build-up of counter-ions observed at the back-step. The development length of the flow increases substantially as the wall permittivity becomes significant, meaning that the electric double-layers require a longer distance to develop within the contraction. Consequently, there is a corresponding decrease in the hydrodynamic and electro-potential resistance caused by the contraction. The effect of wall-region width on the flow characteristics is also quantified, demonstrating that the development length increases with increasing wall-region width for widths up to 5 channel widths.
The forced convective heat transfer characteristics for incompressible power-law fluids past a bu... more The forced convective heat transfer characteristics for incompressible power-law fluids past a bundle of circular cylinders have been investigated numerically. The cylinder-to-cylinder hydrodynamic interactions have been approximated via a simple cell model. The momentum and energy equations have been solved using a finite difference based numerical method for a range of physical and kinematic conditions. The role of the two commonly used thermal boundary conditions, namely, constant temperature or constant heat flux, on heat transfer characteristics has also been studied. Extensive numerical results elucidating the effect of shear-thinning viscosity on the values of Nusselt number have been obtained for Peclet numbers ranging from 1 to 5000, Reynolds number in the range 1–500, flow behaviour index 1greater-or-equal, slantedngreater-or-equal, slanted0.5 and three values of voidages, namely, 0.4, 0.5 and 0.6, typical of tubular heat exchangers and tube banks. Under all conditions, varying levels of enhancement in Nusselt number are observed due to shear-thinning behaviour. The surface averaged Nusselt number shows strong dependence on the values of voidage, power-law index, Reynolds and Peclet numbers. The paper is concluded by presenting comparisons with the scant experimental results available in the literature.
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his work presents the lattice Boltzmann simulation of natural convection in an open ended square cavity subjected to partial heating. The size of heater is half of characteristic length and placed at middle location of one vertical wall. Numerical simulations are performed for three different fluids of industrial, scientific as well as domestic field, viz., air (Pr = 0.71), dichloro-difluoro-methane (Pr = 4.5) and water (Pr = 7). The influence of the partial heater on heat and hydrodynamic characteristics of an open ended cavity have been elucidated. It is observed that isotherms become more confined toward the partially heated portion of wall with the increase in Prandtl number. The heat transfer rate shows linear increase with the Prandtl number, i.e., enclosure containing water shows higher heat transfer rate followed by R-12 refrigerant and air. The numerical results are summarized by the empirical correlation relating Nusselt number with Rayleigh and Prandtl numbers.
Krunal M. Gangawane, Ram P. Bharti and Surendra Kumar
A thermal lattice Boltzmann method is utilized for the numerical simulation of the natural convection heat transfer phenomena inside a differentially heated square cavity. Numerical simulations are performed to elucidate the combined effects of Prandtl number (0.71 ≤ Pr ≤ 100) and Rayleigh number (104 ≤ Ra ≤ 106) on heat transfer and fluid flow characteristics inside the cavity. Detailed insights are gained by the evaluation of isotherms, stream functions and vorticity profiles. For higher Prandtl and Rayleigh numbers, streamlines become more confined to hot wall with the loss of symmetry. Similarly, isotherms patterns become more stratified towards the hot wall. The centre-line velocity and temperature profiles are also analyzed. Further, the heat transfer rate is estimated in terms of average Nusselt number. It suggests a proportional increase in the average Nusselt number with the increasing values of Prandtl number for considered range of Rayleigh numbers. Finally, the numerical data for the average Nusselt number are presented in the form of a correlation for their best utilization in design and engineering practices.
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his work presents the lattice Boltzmann simulation of natural convection in an open ended square cavity subjected to partial heating. The size of heater is half of characteristic length and placed at middle location of one vertical wall. Numerical simulations are performed for three different fluids of industrial, scientific as well as domestic field, viz., air (Pr = 0.71), dichloro-difluoro-methane (Pr = 4.5) and water (Pr = 7). The influence of the partial heater on heat and hydrodynamic characteristics of an open ended cavity have been elucidated. It is observed that isotherms become more confined toward the partially heated portion of wall with the increase in Prandtl number. The heat transfer rate shows linear increase with the Prandtl number, i.e., enclosure containing water shows higher heat transfer rate followed by R-12 refrigerant and air. The numerical results are summarized by the empirical correlation relating Nusselt number with Rayleigh and Prandtl numbers.
Krunal M. Gangawane, Ram P. Bharti and Surendra Kumar
A thermal lattice Boltzmann method is utilized for the numerical simulation of the natural convection heat transfer phenomena inside a differentially heated square cavity. Numerical simulations are performed to elucidate the combined effects of Prandtl number (0.71 ≤ Pr ≤ 100) and Rayleigh number (104 ≤ Ra ≤ 106) on heat transfer and fluid flow characteristics inside the cavity. Detailed insights are gained by the evaluation of isotherms, stream functions and vorticity profiles. For higher Prandtl and Rayleigh numbers, streamlines become more confined to hot wall with the loss of symmetry. Similarly, isotherms patterns become more stratified towards the hot wall. The centre-line velocity and temperature profiles are also analyzed. Further, the heat transfer rate is estimated in terms of average Nusselt number. It suggests a proportional increase in the average Nusselt number with the increasing values of Prandtl number for considered range of Rayleigh numbers. Finally, the numerical data for the average Nusselt number are presented in the form of a correlation for their best utilization in design and engineering practices.
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