Heat Function

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G. Janardhana Reddy - One of the best experts on this subject based on the ideXlab platform.

  • Bejan flow visualization of free convection in a Jeffrey fluid from a semi-infinite vertical cylinder
    Journal of Thermal Analysis and Calorimetry, 2019
    Co-Authors: Mahesh Kumar, G. Janardhana Reddy, O. Anwar Bég
    Abstract:

    This article studies the pattern of Heat lines in free convection non-Newtonian flow from a semi-infinite vertical cylinder via Bejan’s Heat Function concept. The viscoelastic Jeffrey fluid model is employed. The time-dependent, coupled, nonlinear conservation equations for momentum and energy (Heat) are solved computationally with the unconditionally stable finite difference Crank–Nicolson method. Extensive graphical results are presented for the influence of Deborah number (viscoelastic parameter) and Prandtl number (with ranges 0–0.8 and 0.68–7.2, respectively) on thermal and flow characteristics including time histories of overall skin friction and Heat transfer rate. Lower values of Deborah number indicate that the material acts in a more fluid-like manner, whereas the higher values of Deborah number correspond to the material showing characteristics more associated with a solid. The solutions indicate that the time taken for the flow-field variables to achieve the steady state is increased with higher values of Deborah number. Boundary flow visualization is presented using Heat lines, isotherms and streamlines. It is observed that as Deborah number increases the intensity of Heat lines increases and they tend to deviate from the hot cylindrical wall. Furthermore, the flow-field variables for the Newtonian fluid case exhibit a significantly different pattern from that of Jeffrey fluid.

  • Transient analysis of Casson fluid thermo-convection from a vertical cylinder embedded in a porous medium: Entropy generation and thermal energy transfer visualization
    Journal of Central South University, 2019
    Co-Authors: G. Janardhana Reddy, Kethireddy Bhaskerreddy, Kumar Mahesh
    Abstract:

    Thermal transport in porous media has stimulated substantial interest in engineering sciences due to increasing applications in filtration systems, porous bearings, porous layer insulation, biomechanics, geomechanics etc. Motivated by such applications, in this article a numerical investigation of entropy generation effects on the Heat and momentum transfer in unsteady laminar incompressible boundary layer flow of a Casson viscoplastic fluid over a uniformly Heated vertical cylinder embedded in a porous medium is presented. Darcy’s law is employed to simulate bulk drag effects at low Reynolds number for an isotropic, homogenous porous medium. Heat line visualization is also included. The mathematical model is derived and normalized using appropriate transformation variables. The resulting time-dependent non-linear coupled partial differential conservation equations with associated boundary conditions are solved with an efficient unconditionally stable implicit finite difference Crank Nicolson scheme. The time histories of average values of momentum and Heat transport coefficients, entropy generation and Bejan number, as well as the steady-state flow variables are computed for several values of non-dimensional parameters arising in the flow equations. The results indicate that entropy generation parameter and Bejan number are both elevated with increasing values of Casson fluid parameter, Darcy number, group parameter and Grashof number. To analyze the Heat transfer process in a two-dimensional domain, plotting Heat lines provides an excellent approach in addition to streamlines and isotherms. The dimensionless Heat Function values are shown to correlate closely with the overall rate of Heat transfer. Bejan’s Heat flow visualization implies that the Heat Function contours are compact in the neighbourhood of the leading edge of the boundary layer on the hot cylindrical wall. It is observed that as the Darcy number increases, the deviations of Heat lines from the hot wall are reduced. Furthermore the deviations of flow variables from the hot wall for a Casson fluid are significant compared with those computed for a Newtonian fluid and this has important implications in industrial thermal materials processing operations.

  • Transient analysis of viscoelastic fluid past a semi-infinite vertical cylinder with respect to the Deborah and Hartmann numbers
    Journal of Thermal Analysis and Calorimetry, 2019
    Co-Authors: Mahesh Kumar, G. Janardhana Reddy, Ravi Ragoju
    Abstract:

    This article investigates the visualizations of Heatlines in a natural convection magnetohydrodynamic flow from a vertical cylinder via Heat Function concept. Fluid is electrically conducting in the existence of an applied magnetic field. The constitutive equations of time-dependent, coupled and highly nonlinear Jeffrey fluid model are evaluated mathematically by utilizing well-organized unconditionally stable finite-difference Crank–Nicolson method. Simulated results are given for several values of Deborah number and Hartmann number to present interesting aspects of the solution of the flow variables, friction factor and Heat transfer rate. Results specify that required time to achieve time-independent state rapidly rises with the boosting values of Hartmann number. Boundary-layer flow visualization has been made using Heatlines, isotherms and streamlines to perceive the understanding of Heat and fluid flow. It is noticed that Heat Function value reduces for augmenting Hartmann number and also for all smaller physical parameter values and these Heatlines become closer to the hot wall. It is also remarked that the hydromagnetic flow-field profiles concerning the Newtonian fluid show a different pattern from that of non-Newtonian Jeffrey fluid.

  • Heat flow visualization of a chemical compound isobutane (C4H10) past a vertical cylinder in the subcritical, near critical and supercritical regions
    Journal of Molecular Liquids, 2018
    Co-Authors: G. Janardhana Reddy, Hussain Basha, N.s. Venkata Narayanan
    Abstract:

    Abstract Supercritical fluids (SCF's) found to have a large number of applications in science and engineering field particularly in separation and purification, green technologies etc. The present research paper investigates the Heatline visualization of unsteady free convection supercritical fluid flow over a vertical cylinder using Bejan's Heat Function concept by using isobutane as a model compound. A new thermodynamic equation has been obtained to calculate the volumetric thermal expansion coefficient (β) based on the Redlich-Kwong equation of state (RK-EOS), in order to determine the free convection properties of isobutane in supercritical fluid (SCF) region. In this model the thermal expansion coefficient is characterized as a Function of compressibility factor, temperature and pressure. Crank-Nicolson type of implicit finite difference method is utilized to obtain the results in terms of the streamlines (ψ), isotherms (θ) and Heatlines (Π) for the different values of reduced temperature and reduced pressure in the SCF region. The numerically calculated thermal expansion coefficient values are validated with existing experimental results. Numerical simulations are performed for isobutane in three regions namely, subcritical, near critical and supercritical regions. The unsteady boundary layer flow analysis shows that the streamlines are beginning from the leading edge to the far downstream, whereas the Heatlines ends at a finite distance from the surface of cylinder. The non-dimensional values of Heat Function are closely associated with the overall Heat transfer rate. The SCF flow analysis implies that in the vicinity of the hot cylindrical surface the Heatlines are observed to be denser. Further, the deviation of streamlines, isotherms and Heatlines from the hot cylindrical surface increases as reduced temperature and reduced pressure increases.

  • Effect of Prandtl Number for Casson Fluid Flow Over a Vertical Cylinder: Heatline Approach
    International Journal of Applied and Computational Mathematics, 2018
    Co-Authors: G. Janardhana Reddy, Mahesh Kumar, Bhaskerreddy Kethireddy, H. P. Rani, Rama Subba Reddy Gorla
    Abstract:

    With the aid of Heatline visualization the current research paper investigates the Casson fluid flow over a Heated cylinder. The working partial differential equations for this physical model are time dependent non-linear coupled. They are solved numerically by the FDM which is computationally stable and second accurate in space and time. The control parameters arising in the system are varied and the corresponding flow dynamics is analyzed with respect to the velocity gradients and Heat transfer coefficients at the wall. The flow variables of Casson fluid observed to take more time to attain steady state than those of the Newtonian fluids. The Heat Function shows thicker profiles in the vicinity of surface of the cylinder. Further, the deviations from the wall between Casson fluid and the Newtonian fluid are shown.

Mahesh Kumar - One of the best experts on this subject based on the ideXlab platform.

  • Bejan flow visualization of free convection in a Jeffrey fluid from a semi-infinite vertical cylinder
    Journal of Thermal Analysis and Calorimetry, 2019
    Co-Authors: Mahesh Kumar, G. Janardhana Reddy, O. Anwar Bég
    Abstract:

    This article studies the pattern of Heat lines in free convection non-Newtonian flow from a semi-infinite vertical cylinder via Bejan’s Heat Function concept. The viscoelastic Jeffrey fluid model is employed. The time-dependent, coupled, nonlinear conservation equations for momentum and energy (Heat) are solved computationally with the unconditionally stable finite difference Crank–Nicolson method. Extensive graphical results are presented for the influence of Deborah number (viscoelastic parameter) and Prandtl number (with ranges 0–0.8 and 0.68–7.2, respectively) on thermal and flow characteristics including time histories of overall skin friction and Heat transfer rate. Lower values of Deborah number indicate that the material acts in a more fluid-like manner, whereas the higher values of Deborah number correspond to the material showing characteristics more associated with a solid. The solutions indicate that the time taken for the flow-field variables to achieve the steady state is increased with higher values of Deborah number. Boundary flow visualization is presented using Heat lines, isotherms and streamlines. It is observed that as Deborah number increases the intensity of Heat lines increases and they tend to deviate from the hot cylindrical wall. Furthermore, the flow-field variables for the Newtonian fluid case exhibit a significantly different pattern from that of Jeffrey fluid.

  • Transient analysis of viscoelastic fluid past a semi-infinite vertical cylinder with respect to the Deborah and Hartmann numbers
    Journal of Thermal Analysis and Calorimetry, 2019
    Co-Authors: Mahesh Kumar, G. Janardhana Reddy, Ravi Ragoju
    Abstract:

    This article investigates the visualizations of Heatlines in a natural convection magnetohydrodynamic flow from a vertical cylinder via Heat Function concept. Fluid is electrically conducting in the existence of an applied magnetic field. The constitutive equations of time-dependent, coupled and highly nonlinear Jeffrey fluid model are evaluated mathematically by utilizing well-organized unconditionally stable finite-difference Crank–Nicolson method. Simulated results are given for several values of Deborah number and Hartmann number to present interesting aspects of the solution of the flow variables, friction factor and Heat transfer rate. Results specify that required time to achieve time-independent state rapidly rises with the boosting values of Hartmann number. Boundary-layer flow visualization has been made using Heatlines, isotherms and streamlines to perceive the understanding of Heat and fluid flow. It is noticed that Heat Function value reduces for augmenting Hartmann number and also for all smaller physical parameter values and these Heatlines become closer to the hot wall. It is also remarked that the hydromagnetic flow-field profiles concerning the Newtonian fluid show a different pattern from that of non-Newtonian Jeffrey fluid.

  • Effect of Prandtl Number for Casson Fluid Flow Over a Vertical Cylinder: Heatline Approach
    International Journal of Applied and Computational Mathematics, 2018
    Co-Authors: G. Janardhana Reddy, Mahesh Kumar, Bhaskerreddy Kethireddy, H. P. Rani, Rama Subba Reddy Gorla
    Abstract:

    With the aid of Heatline visualization the current research paper investigates the Casson fluid flow over a Heated cylinder. The working partial differential equations for this physical model are time dependent non-linear coupled. They are solved numerically by the FDM which is computationally stable and second accurate in space and time. The control parameters arising in the system are varied and the corresponding flow dynamics is analyzed with respect to the velocity gradients and Heat transfer coefficients at the wall. The flow variables of Casson fluid observed to take more time to attain steady state than those of the Newtonian fluids. The Heat Function shows thicker profiles in the vicinity of surface of the cylinder. Further, the deviations from the wall between Casson fluid and the Newtonian fluid are shown.

  • Computational modeling of unsteady third-grade fluid flow over a vertical cylinder: A study of Heat transfer visualization
    Results in physics, 2017
    Co-Authors: G. Janardhana Reddy, Ashwini Hiremath, Mahesh Kumar
    Abstract:

    Abstract The present paper aims to investigate the effect of Prandtl number for unsteady third-grade fluid flow over a uniformly Heated vertical cylinder using Bejan’s Heat Function concept. The mathematical model of this problem is given by highly time-dependent non-linear coupled equations and are resolved by an efficient unconditionally stable implicit scheme. The time histories of average values of momentum and Heat transport coefficients as well as the steady-state flow variables are displayed graphically for distinct values of non-dimensional control parameters arising in the system. As the non-dimensional parameter value gets amplified, the time taken for the fluid flow variables to attain the time-independent state is decreasing. The dimensionless Heat Function values are closely associated with an overall rate of Heat transfer. Thermal energy transfer visualization implies that the Heat Function contours are compact in the neighborhood of the leading edge of the hot cylindrical wall. It is noticed that the deviations of flow-field variables from the hot wall for a non-Newtonian third-grade fluid flow are significant compared to the usual Newtonian fluid flow.

O. Anwar Bég - One of the best experts on this subject based on the ideXlab platform.

  • Bejan flow visualization of free convection in a Jeffrey fluid from a semi-infinite vertical cylinder
    Journal of Thermal Analysis and Calorimetry, 2019
    Co-Authors: Mahesh Kumar, G. Janardhana Reddy, O. Anwar Bég
    Abstract:

    This article studies the pattern of Heat lines in free convection non-Newtonian flow from a semi-infinite vertical cylinder via Bejan’s Heat Function concept. The viscoelastic Jeffrey fluid model is employed. The time-dependent, coupled, nonlinear conservation equations for momentum and energy (Heat) are solved computationally with the unconditionally stable finite difference Crank–Nicolson method. Extensive graphical results are presented for the influence of Deborah number (viscoelastic parameter) and Prandtl number (with ranges 0–0.8 and 0.68–7.2, respectively) on thermal and flow characteristics including time histories of overall skin friction and Heat transfer rate. Lower values of Deborah number indicate that the material acts in a more fluid-like manner, whereas the higher values of Deborah number correspond to the material showing characteristics more associated with a solid. The solutions indicate that the time taken for the flow-field variables to achieve the steady state is increased with higher values of Deborah number. Boundary flow visualization is presented using Heat lines, isotherms and streamlines. It is observed that as Deborah number increases the intensity of Heat lines increases and they tend to deviate from the hot cylindrical wall. Furthermore, the flow-field variables for the Newtonian fluid case exhibit a significantly different pattern from that of Jeffrey fluid.

Bhaskerreddy Kethireddy - One of the best experts on this subject based on the ideXlab platform.

  • Effect of Prandtl Number for Casson Fluid Flow Over a Vertical Cylinder: Heatline Approach
    International Journal of Applied and Computational Mathematics, 2018
    Co-Authors: G. Janardhana Reddy, Mahesh Kumar, Bhaskerreddy Kethireddy, H. P. Rani, Rama Subba Reddy Gorla
    Abstract:

    With the aid of Heatline visualization the current research paper investigates the Casson fluid flow over a Heated cylinder. The working partial differential equations for this physical model are time dependent non-linear coupled. They are solved numerically by the FDM which is computationally stable and second accurate in space and time. The control parameters arising in the system are varied and the corresponding flow dynamics is analyzed with respect to the velocity gradients and Heat transfer coefficients at the wall. The flow variables of Casson fluid observed to take more time to attain steady state than those of the Newtonian fluids. The Heat Function shows thicker profiles in the vicinity of surface of the cylinder. Further, the deviations from the wall between Casson fluid and the Newtonian fluid are shown.

  • Flow visualization using Heat lines for unsteady radiative hydromagnetic Micropolar convection from a vertical slender hollow cylinder
    International Journal of Mechanical Sciences, 2018
    Co-Authors: G. Janardhana Reddy, Bhaskerreddy Kethireddy
    Abstract:

    The present study aims to investigate the thermal radiation Heat transfer effect on unsteady magnetohydrodynamic (MHD) flow of micropolar fluid over a uniformly Heated vertical hollow cylinder using Bejan’s Heat Function concept. The normalized conservation equations emerge as a system of time-dependent non-linear coupled partial differential equations. Under appropriate wall and free stream conditions these equations are solved with an efficient unconditionally stable implicit scheme of Crank-Nicolson type. Important thermo-physical parameters featured include the magnetic body force parameter (M), Grashof (free convection) parameter (Gr), Eringen micropolar material parameter (K), Prandtl number (Pr), conjugate Heat transfer parameter (P) and radiative-conductive Rosseland parameter (N), are analyzed on the flow-field with ranges 0-3, 105-106, 0-1.2, 0.7-7.0, 0-0.5 and 0-15, respectively. The time-histories of average values of momentum and Heat transport coefficients, as well as the steady-state flow variables are presented for selected values of these non-dimensional parameters. With elevation in magnetic parameter or radiation parameter, the time taken for the flow-field variables to attain the time-independent state increases. The dimensionless thermal radiative Heat Function values are closely correlated with the overall rate of Heat transfer on the outer hot cylindrical wall. Bejan’s Heat flow visualization implies that the thermal radiative Heat Function contours are compact in the neighbourhood of leading edge of the boundary layer on the outer hot cylindrical wall. Increasing radiation or magnetic parameter values result in an increase in the deviation of Heat lines from the hot wall. Also, the Heatlines are observed to depart slightly away from the hot wall with greater values of vortex viscosity. Furthermore, the deviations of flow variables from the hot wall for a micropolar fluid are significant compared to the Newtonian fluid (vanishing micropolar vortex viscosity).

  • Heat flow visualization for unsteady Casson fluid past a vertical slender hollow cylinder
    Thermal science and engineering, 2018
    Co-Authors: G. Janardhana Reddy, Bhaskerreddy Kethireddy, Jawali C. Umavathi, Mikhail A. Sheremet
    Abstract:

    Abstract The conjugate Heat transfer (CHT) effects have been studied on the Heat Function concept. The physical model consists of the Casson fluid flowing past a slender vertical cylinder. The inner wall of the hollow cylinder is maintained with identical temperature. The solutions of the governing equations which are coupled and non-linear are found by applying implicit scheme. The plots on the flow are depicted pictorially for all the controlling parameters. The steady-state time is extended for the Casson fluid parameter. The Bejan’s Heat flow visualization implies that the Heat Function contours are compact in the neighbourhood of leading edge at the wall of the cylinder having more temperature. The deviations of the Heatlines from the hot wall go on reducing by escalating the values of all the controlling parameters. The Casson fluid plays a significant role at the hot wall when compared to the Newtonian fluid.

  • Bejan’s Heat Flow Visualization for Unsteady Micropolar Fluid Past a Vertical Slender Hollow Cylinder with Large Grashof Number
    International Journal of Applied and Computational Mathematics, 2017
    Co-Authors: G. Janardhana Reddy, Bhaskerreddy Kethireddy, H. P. Rani
    Abstract:

    The Heat Function concept has been developed for the Heatline visualization to study the conjugate Heat transfer effects at large Grashof number. The time-dependent natural convective micropolar fluid flow past a vertical slender hollow cylinder with the inner wall kept at a uniform temperature is the physical model. The mathematical model of this problem is given by highly time reliant non-linear coupled equations and is resolved by an efficient unconditionally stable implicit scheme. The time histories of average values of momentum and Heat transport coefficients as well as the steady-state velocity, microrotation and temperature are plotted for different values of non-dimensional parameters arising in the system across the boundary layer. As the vortex viscosity parameter increases, the time taken for the flow-field variables to attain the time-independent state decreases, while the reverse trend is noticed for the conjugate Heat transfer parameter. The dimensionless Heat Function values are closely associated with the overall rate of Heat transfer. The Bejan’s Heat flow visualization implies that the Heat Function contours are compact in the neighborhood of leading edge of the hot cylindrical wall. It is observed that as the vortex viscosity parameter values get amplified, the deviations of Heatlines from the Heated wall is more. It is seen that the deviations of flow variables from the Heated wall for a micropolar fluid are significant compared to the Newtonian fluid.

H. P. Rani - One of the best experts on this subject based on the ideXlab platform.

  • Effect of Prandtl Number for Casson Fluid Flow Over a Vertical Cylinder: Heatline Approach
    International Journal of Applied and Computational Mathematics, 2018
    Co-Authors: G. Janardhana Reddy, Mahesh Kumar, Bhaskerreddy Kethireddy, H. P. Rani, Rama Subba Reddy Gorla
    Abstract:

    With the aid of Heatline visualization the current research paper investigates the Casson fluid flow over a Heated cylinder. The working partial differential equations for this physical model are time dependent non-linear coupled. They are solved numerically by the FDM which is computationally stable and second accurate in space and time. The control parameters arising in the system are varied and the corresponding flow dynamics is analyzed with respect to the velocity gradients and Heat transfer coefficients at the wall. The flow variables of Casson fluid observed to take more time to attain steady state than those of the Newtonian fluids. The Heat Function shows thicker profiles in the vicinity of surface of the cylinder. Further, the deviations from the wall between Casson fluid and the Newtonian fluid are shown.

  • Bejan’s Heat Flow Visualization for Unsteady Micropolar Fluid Past a Vertical Slender Hollow Cylinder with Large Grashof Number
    International Journal of Applied and Computational Mathematics, 2017
    Co-Authors: G. Janardhana Reddy, Bhaskerreddy Kethireddy, H. P. Rani
    Abstract:

    The Heat Function concept has been developed for the Heatline visualization to study the conjugate Heat transfer effects at large Grashof number. The time-dependent natural convective micropolar fluid flow past a vertical slender hollow cylinder with the inner wall kept at a uniform temperature is the physical model. The mathematical model of this problem is given by highly time reliant non-linear coupled equations and is resolved by an efficient unconditionally stable implicit scheme. The time histories of average values of momentum and Heat transport coefficients as well as the steady-state velocity, microrotation and temperature are plotted for different values of non-dimensional parameters arising in the system across the boundary layer. As the vortex viscosity parameter increases, the time taken for the flow-field variables to attain the time-independent state decreases, while the reverse trend is noticed for the conjugate Heat transfer parameter. The dimensionless Heat Function values are closely associated with the overall rate of Heat transfer. The Bejan’s Heat flow visualization implies that the Heat Function contours are compact in the neighborhood of leading edge of the hot cylindrical wall. It is observed that as the vortex viscosity parameter values get amplified, the deviations of Heatlines from the Heated wall is more. It is seen that the deviations of flow variables from the Heated wall for a micropolar fluid are significant compared to the Newtonian fluid.

  • Heatline visualization for conjugate Heat transfer of a couple stress fluid from a vertical slender hollow cylinder
    International Communications in Heat and Mass Transfer, 2013
    Co-Authors: H. P. Rani, G. Janardhana Reddy
    Abstract:

    Abstract The flow visualization has been made using the Heat Function concept for the conjugate Heat transfer effects on the transient free convective couple stress fluid flow over a vertical slender hollow circular cylinder with the inner surface kept at a constant temperature. The governing non-linear equations are solved numerically by using an unconditionally stable implicit method. Numerical results show that the deviations of flow variables of couple stress fluid from those of the Newtonian fluid turn out to be considerable. Boundary layer flow visualization indicates that the streamlines exist starting from the leading edge to the far downstream, while the Heatlines terminate at a finite distance from the cylinder wall. It is noticed that the steady-state values of average skin-friction and Heat transfer rate decrease as the conjugate-conduction parameter increases.