S. Roy

Bio: S. Roy is an academic researcher from Indian Institute of Technology Madras. The author has contributed to research in topics: Heat transfer & Nusselt number. The author has an hindex of 34, co-authored 130 publications receiving 3832 citations. Previous affiliations of S. Roy include Indian Institute of Science & Indian Institutes of Technology.

Effects of thermal boundary conditions on natural convection flows within a square cavity

Abstract: A numerical study to investigate the steady laminar natural convection flow in a square cavity with uniformly and non-uniformly heated bottom wall, and adiabatic top wall maintaining constant temperature of cold vertical walls has been performed. A penalty finite element method with bi-quadratic rectangular elements has been used to solve the governing mass, momentum and energy equations. The numerical procedure adopted in the present study yields consistent performance over a wide range of parameters (Rayleigh number Ra, 103 ⩽ Ra ⩽ 105 and Prandtl number Pr, 0.7 ⩽ Pr ⩽ 10) with respect to continuous and discontinuous Dirichlet boundary conditions. Non-uniform heating of the bottom wall produces greater heat transfer rates at the center of the bottom wall than the uniform heating case for all Rayleigh numbers; however, average Nusselt numbers show overall lower heat transfer rates for the non-uniform heating case. Critical Rayleigh numbers for conduction dominant heat transfer cases have been obtained and for convection dominated regimes, power law correlations between average Nusselt number and Rayleigh numbers are presented.

Natural convection in a square cavity filled with a porous medium: Effects of various thermal boundary conditions

Abstract: Natural convection flows in a square cavity filled with a porous matrix has been studied numerically using penalty finite element method for uniformly and non-uniformly heated bottom wall, and adiabatic top wall maintaining constant temperature of cold vertical walls. Darcy–Forchheimer model is used to simulate the momentum transfer in the porous medium. The numerical procedure is adopted in the present study yields consistent performance over a wide range of parameters (Rayleigh number Ra , 10 3 ⩽ Ra ⩽ 10 6 , Darcy number Da , 10 −5 ⩽ Da ⩽ 10 −3 , and Prandtl number Pr , 0.71 ⩽ Pr ⩽ 10) with respect to continuous and discontinuous thermal boundary conditions. Numerical results are presented in terms of stream functions, temperature profiles and Nusselt numbers. Non-uniform heating of the bottom wall produces greater heat transfer rate at the center of the bottom wall than uniform heating case for all Rayleigh numbers but average Nusselt number shows overall lower heat transfer rate for non-uniform heating case. It has been found that the heat transfer is primarily due to conduction for Da ⩽ 10 −5 irrespective of Ra and Pr . The conductive heat transfer regime as a function of Ra has also been reported for Da ⩾ 10 −4 . Critical Rayleigh numbers for conduction dominant heat transfer cases have been obtained and for convection dominated regimes the power law correlations between average Nusselt number and Rayleigh numbers are presented.

Finite element analysis of natural convection flows in a square cavity with non-uniformly heated wall(s)

Abstract: A penalty finite element analysis with bi-quadratic rectangular elements is performed to investigate the influence of uniform and non-uniform heating of wall(s) on natural convection flows in a square cavity. In the present investigation, one vertical wall and the bottom wall are uniformly and non-uniformly heated while the other vertical wall is maintained at constant cold temperature and the top wall is well insulated. Parametric study for a wide range of Rayleigh number ( Ra ), 10 3 ⩽ Ra ⩽ 10 6 and Prandtl number ( Pr ), 0.2 ⩽ Pr ⩽ 100 shows consistent performance of the present numerical approach to obtain the solutions as stream functions and temperature profiles. Heat transfer rates at the heated walls are presented in terms of local Nusselt number.

Analysis of mixed convection flows within a square cavity with uniform and non-uniform heating of bottom wall

Abstract: A penalty finite element analysis with bi-quadratic elements is performed to investigate the influence of uniform and non-uniform heating of bottom wall on mixed convection lid driven flows in a square cavity In the present investigation, bottom wall is uniformly and non-uniformly heated while the two vertical walls are maintained at constant cold temperature and the top wall is well insulated and moving with uniform velocity A complete study on the effect of Gr shows that the strength of circulation increases with the increase in the value of Gr irrespective of Re and Pr As the value of Gr increases, there occurs a transition from conduction to convection dominated flow at Gr=5×103 and Re=1 for Pr=07 A detailed analysis of flow pattern shows that the natural or forced convection is based on both the parameters Ri (GrRe2) and Pr As the value of Re increases from 1 to 102, there occurs a transition from natural convection to forced convection depending on the value of Gr irrespective of Pr Particularly for higher value of Grashof number (Gr=105), the effect of natural convection is dominant upto Re=10 and thereafter the forced convection is dominant with further increase in Re As Pr increases from 0015 to 10 for a fixed Re and Gr (Gr=103), the inertial force gradually becomes stronger and the intensity of secondary circulation gradually weakens The local Nusselt number (Nub) plot shows that the heat transfer rate is very high at the edges of the bottom wall and then decreases at the center of the bottom wall for the uniform heating and that contrasts lower heat transfer rate at the edges for the non-uniform heating of the bottom wall It is also observed that Nul shows non-monotonic behavior with both uniform and non-uniform heating cases for Re=10 at higher value of Pr The average Nusselt number plot for the left or right wall shows a kink or inflexion at Gr=104 for highest value of Pr Thus the overall power law correlation for average Nusselt number may not be obtained for mixed convection effects at higher Pr

Heat flow analysis for natural convection within trapezoidal enclosures based on heatline concept

Abstract: Heat flow patterns in the presence of natural convection within trapezoidal enclosures have been analyzed with heatlines concept. In the present study, natural convection within a trapezoidal enclosure for uniformly and non-uniformly heated bottom wall, insulated top wall and isothermal side walls with inclination angle φ have been investigated. Momentum and energy transfer are characterized by streamfunctions and heatfunctions, respectively, such that streamfunctions and heatfunctions satisfy the dimensionless forms of momentum and energy balance equations, respectively. Finite element method has been used to solve the velocity and thermal fields and the method has also been found robust to obtain the streamfunction and heatfunction accurately. The unique solution of heatfunctions for situations in differential heating is a strong function of Dirichlet boundary condition which has been obtained from average Nusselt numbers for hot or cold regimes. Parametric study for the wide range of Rayleigh number ( Ra ) , 10 3 ⩽ Ra ⩽ 10 5 and Prandtl number ( Pr ) , 0.026 ⩽ Pr ⩽ 1000 with various tilt angles φ = 45 ° , 30 ° and 0 ° (square) have been carried out. Heatlines are found to be continuous lines connecting the cold and hot walls and the lines are perpendicular to the isothermal wall for the conduction dominant heat transfer. The enhanced thermal mixing near the core for larger Ra is explained with dense heatlines and convective loop of heatlines. The formation of boundary layer on the walls has a direct consequence based on heatlines. The local Nusselt numbers have also been shown for side and bottom walls and variation of local Nusselt numbers with distance have also been explained based on heatlines. It is found that average heat transfer rate does not vary significantly with φ for non-uniform heating of bottom wall.

I and i

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

Boundary Layer Theory

Abstract: The boundary layer equations for plane, incompressible, and steady flow are $$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Introduction to the Finite Element Method

Abstract: This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems. Although we discuss the main points in the application of the finite element method to electromagnetic design, including formulation and implementation, those who seek deeper understanding of the finite element method should consult some of the works listed in the bibliography section.

Matrix iterative analysis (2nd edn), by Richard S. Varga. Springer Series in Computational Mathematics 27. Pp. 358. £55. 2000. ISBN 3 540 66321 5 (Springer Verlag).

Abstract: a 'sleeper', receiving only modest attention for 50 years before emerging as a cornerstone of communications engineering in more recent times. Roughly one in six of Walsh's 281 publications are included, photographically reproduced. Reproduction is excellent except for one paper from 1918. The book also reproduces three brief papers about Walsh and his work, by W. E. Sewell, D. V. Widder and Morris Marden. The first two were written for a special issue of the SIAM Journal celebrating Walsh's 70th birthday; the third is an obituary.

Convection Heat Transfer

Abstract: Geometry: shape, size, aspect ratio and orientation Flow Type: forced, natural, laminar, turbulent, internal, external Boundary: isothermal (Tw = constant) or isoflux (q̇w = constant) Fluid Type: viscous oil, water, gases or liquid metals Properties: all properties determined at film temperature Tf = (Tw + T∞)/2 Note: ρ and ν ∝ 1/Patm ⇒ see Q12-40 density: ρ ((kg/m) specific heat: Cp (J/kg ·K) dynamic viscosity: μ, (N · s/m) kinematic viscosity: ν ≡ μ/ρ (m/s) thermal conductivity: k, (W/m ·K) thermal diffusivity: α, ≡ k/(ρ · Cp) (m/s) Prandtl number: Pr, ≡ ν/α (−−) volumetric compressibility: β, (1/K)