P. Rajesh Kanna

CONJUGATE HEAT TRANSFER STUDY OF TWO-DIMENSIONAL LAMINAR INCOMPRESSIBLE OFFSET JET FLOWS

ABSTRACT Steady-state conjugate heat transfer study of a slab and fluid is carried out for a two-dimensional laminar incompressible offset jet. The unsteady stream function–vorticity formulation is used to solve the governing equations. The energy equation in the fluid and the conduction equation in the solid are solved simultaneously. The conjugate heat transfer characteristics are studied with four parameters, Re, Pr, S/h, and k. The fluid properties affect the heat transfer in the solid slab. The conjugate interface temperature is decreased up to the recirculation region and further increased to a developed condition. As the k is increased, its effect on Nu is reduced. Variation of local Nusselt number and average Nu are reported in detail.

Heat Transfer Study of Two-Dimensional Laminar Incompressible Wall Jet over Backward-Facing Step

A steady-state heat transfer study is carried out for a two-dimensional, laminar, incompressible, plane wall jet over a backward-facing step. An unsteady stream function–vorticity formulation is used to solve the governing equations. The heat transfer characteristics of the jet as functions of Reynolds number (Re), Prandtl number (Pr), and step geometry (step length l and step height s) are reported in detail. Results are presented in the form of isotherm, Nusselt number, and average Nusselt number. In some cases, the computed results are compared with the results when the step length is zero.

Application of an ADI scheme for steady and periodic solutions in a lid‐driven cavity problem

Purpose – The purpose of the paper is to study the steady and periodic solution of a lid‐driven cavity flow problem with the gradual increase of Reynolds number (Re) up to 10,000.Design/methodology/approach – The problem is solved by unsteady stream function‐vorticity formulation using the clustered grids. The alternating direction implicit (ADI) method and the central difference scheme have been used for discretization of the governing equations. Total vorticity error and the total kinetic energy have been considered for ensuring the state of flow condition. The midplane velocity distribution and the top wall vortex distribution are compared with the results of other authors and found to show good agreement.Findings – Kinetic energy variation with time is studied for large time computation. Below 7,500, it becomes constant signifying the flow to be in steady‐state. At Re=10,000, the fluid flow has an oscillating nature. The dimensionless period of oscillation is found to be 1.63. It is demonstrated that ...

Conjugate Heat Transfer Study of a Two-Dimensional Laminar Incompressible Wall Jet Over a Backward-Facing Step

Steady-state conjugate heat transfer study of a slab and a fluid is carried out for a two-dimensional laminar incompressible wall jet over a backward-facing step. Unsteady stream function-vorticity formulation is used to solve the governing equation in the fluid region. An explicit expression has been derived for the conjugate interface boundary. The energy equation in the fluid, interface boundary and the conduction equation in the solid are solved simultaneously. The conjugate heat transfer characteristics, Nus- selt number are studied with flow property (Re), fluid property (Pr), and solid to fluid conductivity ratio k. Average Nusselt number is compared with that of the nonconjugate case. As k is increased, average Nusselt number is increased, asymptotically approaching the non-conjugate value. DOI: 10.1115/1.2424235 have solved for a variable starting length of the heated section at a constant wall temperature. The solution was derived with the plate and the jet regimes as nonconjugated. The experimental study on the laminar plane wall jet is presented in Bajura and Szewczyk 3. Based on jet exit Reynolds number, they have re- ported the laminar wall jet results up to Re=770. Angirasa 4 has studied the laminar buoyant wall jet and re- ported the effect of velocity and the width of the jet during con- vective heat transfer from the vertical surface. Seidel 5 has done a numerical work to find the effect of high amplitude forcing on the laminar and the turbulent wall jet over a heated flat plate. Seidel has used DNS for the laminar case and RANS for the turbulent wall jet. Recently, Bhattacharjee and Loth 6 have simulated the laminar and transitional cold wall jets. They have investigated the significance of three different inlet profiles viz. parabolic, uniform, and ramp. They have presented the detailed results of a time-averaged wall jet thickness and temperature dis- tribution with RANS approach for higher Reynolds number and DNS approach for a three-dimensional wall jet. They have re- ported that the early transition begins at about Re=700 for the plane wall jet. Recently Kanna and Das 7 have studied the conjugate heat transfer of plane wall jet flow and reported a closed-form solu- tions for the conjugate interface temperature, the local Nusselt number distribution and the average Nusselt number. In another study, Kanna and Das 8 have investigated the conjugate heat transfer from a plane laminar offset jet. The bottom of the slab is maintained at a constant higher temperature. Effect of the varia- tions of offset geometry, Re, Pr, and slab geometry have been presented in details. The flow emanating from a two-dimensional plane wall jet over

Effect of Geometry on the Conjugate Heat Transfer of Wall Jet Flow Over a Backward-Facing Step

Conjugate heat transfer study of a backward-facing step cooled by a two-dimensional laminar incompressible wall jet has been carried out. The study is performed to find the isotherm patterns, conjugate interface temperature, local Nusselt number and average Nusselt number by varying the geometry of the solid slab. Different step length, step height, and slab thickness are considered for conjugate heat transfer study.

Numerical Simulation of Mixed Convection in a Two-Dimensional Laminar Plane Wall Jet Flow

A two-dimensional, laminar, incompressible mixed convection with plane wall jet is simulated numerically using the stream function–vorticity method. The buoyancy is assisting the main flow. The flow and heat transfer study is carried out for Rexa0=xa0300–600, Grxa0=xa0103–107, and Prxa0=xa00.01–15. The streamlines, isotherm contours, similarity profiles, vorticity at the walls, and the local and average Nu values are presented and analyzed. In some cases, similarity behaviour is observed. The vorticity profile at the wall is similar to boundary-layer-type flow. However, for high Gr, the wall vorticity increases in the downstream direction. The average Nusselt number increases when Re, Gr, and Pr are increased.A two-dimensional, laminar, incompressible mixed convection with plane wall jet is simulated numerically using the stream function–vorticity method. The buoyancy is assisting the main flow. The flow and heat transfer study is carried out for Re = 300–600, Gr = 103–107, and Pr = 0.01–15. The streamlines, isotherm contours, similarity profiles, vorticity at the walls, and the local and average Nu values are presented and analyzed. In some cases, similarity behaviour is observed. The vorticity profile at the wall is similar to boundary-layer-type flow. However, for high Gr, the wall vorticity increases in the downstream direction. The average Nusselt number increases when Re, Gr, and Pr are increased.

Numerical Simulation of Two-Dimensional Laminar Incompressible Wall Jet Flow Under Backward-Facing Step

Two-dimensional laminar incompressible wall jet flow over a backward-facing step is solved numerically to gain insight into the expansion and recirculation of flow processes. Transient streamfunction vorticity formulation of the Navier-Stokes equation is solved with clustered grids on the physical domain. The behavior of the jet has been studied for different step geometry (step length, l, step height, s) and Reynolds number (Re). It is found that the presence of a step in the wall jet flow creates recirculation and the reattachment length follows an almost linear trend within the range considered for both parameters Re and step geometry. Simulations are made to show the effect of entrainment on recirculation eddy. Detailed study of u velocity decay is reported. The velocity profile in the wall jet region shows good agreement with experimental as well as similarity results. The distance where the similarity profile forms is reduced by increasing the step geometry whereas an increment in Re increases this distance. The effects of Re, step length, and step height on wall vorticity are presented. The parametric study is helpful to predict the reattachment location for wall jet flows over step.

Conjugate Heat Transfer from Sudden Expansion Using Nanofluid

Conjugate heat transfer from sudden expansion using nanofluid is studied numerically. The governing equations are solved using unsteady stream function-vorticity formulation method. Results are compared with zero nanoparticle fluid to exhibit the role of nanoparticle. The effect of volume fraction of nanoparticles and type of nanoparticles on heat transfer are examined and found to have a significant impact. Local Nusselt number and average Nusselt number are reported in connection with various nanoparticle, volume fraction, and Reynolds number for expansion ratio 2. Two dimensionality is more pronounced in the solid wall up to recirculation length. Local Nusselt number reaches peak values near the reattachment point and reaches asymptotic value in the downstream. Bottom wall eddy and volume fraction show significant impact on average Nusselt number. The wall thickness causes larger temperature gradient at the conjugate interface boundary, which leads to larger average Nusselt number.

Numerical investigation of flow and heat transfer from a block placed in a cavity subject to different inlet conditions

Numerical simulation is carried out for steady-state, two-dimensional, incompressible, laminar fluid flow and forced convective heat transfer over a square solid block (0.1 L × 0.1 L) placed in a square cavity (L × L). The square block is placed inside the geometric centre of square cavity and maintained at a fixed temperature higher than the inlet fluid temperature. The simulation is carried out for different positions of the inlet and the results are reported in terms of streamline contours and Nusselt number distributions. The governing equations are solved by finite volume method-based commercial Fluent software. The simulations are carried out for a Reynolds number of 100 and Prandtl number of 0.7. For the considered cases, the maximum average block Nusselt number is observed to occur when the lower edge of the inlet boundary with a height of 0.1 L is placed at a distance of 0.6 L from the of the lower edge of the cavity.