Kedar shukla - Academia.edu (original) (raw)

Prof. Kedar N Shukla received his Ph.D. (1973) from the Banaras Hindu University, Varanasi, India on Heat and Mass Diffusion. In 1974 he joined the Vikram Sarabhai Space Center (VSSC), Trivandrum as a Scientist and continued in various capacities till his superannuation in July, 2005. In september 2005 he joined as a Professor in the School of Mechanical Sciences of the Karunya University, Coimbatore and continued till May 2009. He again joined the Gurgaon College of Engineering, Gurgaon as a Director in July 2009. In 1978, he was awarded Alexander von Humboldt Fellowship to carry out post doctoral research on Variable Conductance Heat Pipe at the Institute for Nuclear Energy and Energy systems of the University of Stuttgart, Germany. He further visited the Technical University of Munich in 1985, University of Stuttgart in 1997, Technical University of Darmstadt in Germany in 2006, university of Stuttgart in 2010 and University of Erlangen, Germany on the invitation from the Alexander von Humboldt Foundation.

He was offered Visiting Professor at the University of Applied Sciences, Rosenheim, in Germany for the summer semester in 2011 by the German Academic Exchange Office where he delivered courses on the Electronics Cooling and the Discrete Events Modeling and Simulation for the postgraduate students.

Prof. Shukla research has centered on Mathematioal Modelling, Analysis and Simulation of Aerospace Systems, Fluid Dynamics and Heat Transfer, Diffusion and Reaction, Nanofluids and Numerical Methods. He has guided PhD thesis of Kerala University on Numerical Characterization and computer simulation of Heat transfer in solid rocket nozzles, Department of Mathematics, and several M Tech thesis of the technical University of Munich and Kerala University. He taught Systems Modeling and Simulation, Computational Mathematics, Finite Element Analysis and Computational Fluid Dynamics for postgraduate students in Engineering in Karunya University and heat transfer for under graduate students in Gurgaon college of Engineering.

Prof. Shukla authored Mathematical Principles of Heat Transfer, Begell House Inc. (2005) and Diffusion Processes during Drying of solids, World Scientific, (1990) and has 70 papers published in archival journals and conference proceedings.
Phone: +91124117329
Address: B-303, Prerana Apartments
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Papers by Kedar shukla

Research paper thumbnail of The Linear Indeterminate Equation - a Brief Historical Account

Revista brasileira de história da matemática (RBHM), 2020

The paper presents in brief the contribution of Aryabhata in developing general solution of indet... more The paper presents in brief the contribution of Aryabhata in developing general solution of indeterminate equation of the type ax + c = by, where a, b, c are the integers. Also the contributions of Bhaskara and Brahmagupta in developing the solution of the indeterminate equations are discussed. Finally an example of Paramesvara is illustrated to solve coupled linear indeterminate equations which may be adopted to find the multiplicative inverse in a group that is of interest in cryptology, signal processing, coding and computer design.

Research paper thumbnail of The Linear Indeterminate Equation - a Brief Historical Account

Revista brasileira de história da matemática, 2015

The paper presents in brief the contribution of Aryabhata in developing general solution of indet... more The paper presents in brief the contribution of Aryabhata in developing general solution of indeterminate equation of the type ax + c = by, where a, b, c are the integers. Also the contributions of Bhaskara and Brahmagupta in developing the solution of the indeterminate equations are discussed. Finally an example of Paramesvara is illustrated to solve coupled linear indeterminate equations which may be adopted to find the multiplicative inverse in a group that is of interest in cryptology, signal processing, coding and computer design.

Research paper thumbnail of Overview of World ATW (Air to Water) Heat Pump Market and Opportunities with Respect to the Air-Conditioning Industry

Prabandhan: Indian Journal of Management, 2015

A heat pump is a device that transfers heat energy from a heat source to a heat sink against a te... more A heat pump is a device that transfers heat energy from a heat source to a heat sink against a temperature gradient. Heat pumps are designed to move thermal energy opposite to the direction of spontaneous heat flow. A heat pump uses some amount of external high-grade energy to accomplish the desired transfer of thermal energy from heat source to a heat sink. While compressor-driven air conditioners and freezers are familiar examples of heat pumps, the term "heat pump" is more general and applies to Heating Ventilation and Air Conditioning (HVAC, hereafter) devices used for space heating or space cooling. When a heat pump is used for heating, it employs the same basic refrigeration-type cycle used by an air conditioner or a refrigerator but in the opposite direction, releasing heat into the conditioned space rather than the surrounding environment. There are two types of heat pump technology, geothermal and aerothermal. Geothermal types include ground to water and water to water type heatpumps, while aerothermal heatpump technology is broadly used by the air-conditioning industry. Among the two types of aerothermal heat pumps, these are (a) Air to Air (ATA) and (b) Air to Water (ATW). Though ATA heat pumps were widely used so far in the air-conditioning industry, predominantly, there is a sudden and significant growth observed in the ATW heat pump market due to their energy efficient performance; and hence, the market is observing a technology shift. The present paper attempted to study the market segmentation of the heat pump industry with special focus on technical detailing and applications of ATW heat pumps. The research paper further described the key competitive players competing in the world market of ATW heat pump business. Secondary data analysis and review of global market for the last one decade (2004 to 2012) was carried out with a focus on leading countries or subcontinents' performance like that of Japan, China , Europe, Australia, United States, and some other small markets to draw the 'opportunities and challenges' roadmap for the ATW heat pump industry.

Research paper thumbnail of Thermal Performance of Vapor Chamber with Nanofluids

Frontiers in Heat Pipes, 2013

The paper describes experimental studies on the heat transfer performance of a wickless vapor cha... more The paper describes experimental studies on the heat transfer performance of a wickless vapor chamber with a heat sink. A vapor chamber of 78 mm length and 64 mm width was fabricated with a thickness of 5 mm and tested for two different working fluids, copper-water and aluminium-water nanofluids with the filling ratio of 30% of the vapor chamber volume. As a baseline comparison de-ionized (DI) water is considered as a working fluid. The vapor chamber was tested for heat inputs ranging from 90-150 W. The effects of heat input and metal concentration in the working fluids and the effect of particle deposition on the performance of the vapor chamber are presented. The thermal resistance of vapor chamber was decresed with the increase of the heat input for copper-water nanofluids while it remained constant for DIwater. Also the thermal resistance was found to be lower for higher concentration of the nanofluid.

Research paper thumbnail of Thermal Performance of cylindrical Heat Pipe Using Nanofluids

Journal of Thermophysics and Heat Transfer, 2010

Résumé/Abstract A cylindrical copper heat pipe with a 19.5 mm outer diameter and a 400.0 mm lengt... more Résumé/Abstract A cylindrical copper heat pipe with a 19.5 mm outer diameter and a 400.0 mm length was filled with three different working fluids and tested for different heat inputs in the range of 100-250 W. The working fluids tested were de-ionized water, silver-water colloid, and copper water. Experimental results showed that the wall temperature reduction obtained was 3-27 C. The efficiency of the heat pipe was enhanced by 14% as compared with the heat pipe filled with the base fluid. Furthermore, it was found that an increase in ...

Research paper thumbnail of Effective thermal conductivity of nanofluids – A new model taking into consideration Brownian motion

International Journal of Heat and Mass Transfer, 2016

Abstract In this study, a new analytical model for the effective thermal conductivity of liquids ... more Abstract In this study, a new analytical model for the effective thermal conductivity of liquids containing dispersed spherical and non-spherical nanometer particles was developed. In addition to heat conduction in the base fluid and the nanoparticles, we also consider convective heat transfer caused by the Brownian motion of the particles. For nanoparticle suspensions, the latter mechanism has significant influence on the effective thermal conductivity, which is reduced compared to a system in which only conduction is considered. The simple model developed allows for the prediction of the effective thermal conductivity of nanofluids as a function of volume fraction, diameter, and shape of the nanoparticles as well as temperature. Due to the inconsistency of experimental data in the literature, the model has been compared with the established Hamilton–Crosser model and other empirical models for the systems aluminum oxide (Al 2 O 3 ) and titanium dioxide (TiO 2 ) suspended in water and ethylene glycol. The theoretical estimates show no anomalous enhancement of the effective thermal conductivity and agree very well with the Hamilton–Crosser model within relative deviations of less than 8% for volume fractions of spherical particles up to 0.25. In accordance with the Hamilton–Crosser model for non-spherical particles, our model reveals that a more distinct increase in the enhancement of the effective thermal conductivity can be achieved using non-spherical nanoparticles having a larger volume-specific surface area.

Research paper thumbnail of Heat Pipe for Aerospace Applications—An Overview

Journal of Electronics Cooling and Thermal Control

Research paper thumbnail of Performance Analysis of Silica-Tiles as a Thermal Protection System

9th AIAA/ASME Joint Thermophysics and Heat Transfer Conference, 2006

Research paper thumbnail of Thermal performance analysis of silica tiles

Journal of Engineering Physics and Thermophysics, 2006

Research paper thumbnail of Steady State Perormance of a Rotating Heat Pipe

46th AIAA Aerospace Sciences Meeting and Exhibit, 2008

Research paper thumbnail of Thermal performance of heat pipe with suspended nano-particles

Heat and Mass Transfer, 2012

Research paper thumbnail of Thermal performance of heat pipe with suspended nano-particles

Heat and Mass Transfer, 2012

Research paper thumbnail of Prof.Shukla.docx

Research paper thumbnail of Indian Cryogenic Engine-State of the Art, Invention (July-August 2017).pdf

Research paper thumbnail of Effective thermal conductivity of nanofluids – A new model taking into consideration Brownian motion

In this study, a new analytical model for the effective thermal conductivity of liquids containin... more In this study, a new analytical model for the effective thermal conductivity of liquids containing dispersed spherical and non-spherical nanometer particles was developed. In addition to heat conduction in the base fluid and the nanoparticles, we also consider convective heat transfer caused by the Brownian motion of the particles. For nanoparticle suspensions, the latter mechanism has significant influence on the effective thermal conductivity, which is reduced compared to a system in which only conduction is considered. The simple model developed allows for the prediction of the effective thermal conductivity of nanofluids as a function of volume fraction, diameter, and shape of the nanoparticles as well as temperature. Due to the inconsistency of experimental data in the literature, the model has been compared with the established Hamilton–Crosser model and other empirical models for the systems aluminum oxide (Al 2 O 3) and titanium dioxide (TiO 2) suspended in water and ethylene glycol. The theoretical estimates show no anomalous enhancement of the effective thermal conductivity and agree very well with the Hamilton–Crosser model within relative deviations of less than 8% for volume fractions of spherical particles up to 0.25. In accordance with the Hamilton–Crosser model for non-spherical particles, our model reveals that a more distinct increase in the enhancement of the effective thermal conductivity can be achieved using non-spherical nanoparticles having a larger volume-specific surface area.

Research paper thumbnail of Thermal Convection in a Cylindrical Enclosure

42nd AIAA Aerospace Sciences Meeting and Exhibit, 2004

The paper highlights the onset of convection in a fluid layer partially filled in an axisymmetric... more The paper highlights the onset of convection in a fluid layer partially filled in an axisymmetric container. The equilibrium of the fluid is disturbed with the deformation of the interface due to residual acceleration. The general problem of deformable interface involves a dimensionless parameter, the Bond number. An analytical expression for the natural frequencies of the deformable surface is derived in terms of the Bond number, which determines the time period required for the stable location of the fluid for the propellant ...

Research paper thumbnail of Thermal Convection in a Cylindrical Enclosure

42nd AIAA Aerospace Sciences Meeting and Exhibit, 2004

The paper highlights the onset of convection in a fluid layer partially filled in an axisymmetric... more The paper highlights the onset of convection in a fluid layer partially filled in an axisymmetric container. The equilibrium of the fluid is disturbed with the deformation of the interface due to residual acceleration. The general problem of deformable interface involves a dimensionless parameter, the Bond number. An analytical expression for the natural frequencies of the deformable surface is derived in terms of the Bond number, which determines the time period required for the stable location of the fluid for the propellant ...

Research paper thumbnail of Thermal performance analysis of silica tiles

Journal of Engineering Physics and Thermophysics, 2006

The thermal response of nonablating ceramic tiles is studied by the finite-element method. A cont... more The thermal response of nonablating ceramic tiles is studied by the finite-element method. A continuum model is used to determine the thermal conductivity of porous materials. The temperature distribution for the one-dimensional model is compared with the available arc-jet result. Also presented are the 2D and 3D temperature contours and the heat-flux distributions for silica tiles. The expression for the pressure distribution in a silica tile is derived.

Research paper thumbnail of Thermal performance analysis of silica tiles

Journal of Engineering Physics and Thermophysics, 2006

The thermal response of nonablating ceramic tiles is studied by the finite-element method. A cont... more The thermal response of nonablating ceramic tiles is studied by the finite-element method. A continuum model is used to determine the thermal conductivity of porous materials. The temperature distribution for the one-dimensional model is compared with the available arc-jet result. Also presented are the 2D and 3D temperature contours and the heat-flux distributions for silica tiles. The expression for the pressure distribution in a silica tile is derived.

Research paper thumbnail of Performance Analysis of Thermal Protection System of a Solid Rocket Nozzle

Journal of Spacecraft and Rockets, 2003

A coupled approach is adopted to solve the conjugate problem of fluid flow and heat transfer in s... more A coupled approach is adopted to solve the conjugate problem of fluid flow and heat transfer in solid rocket nozzles in order to achieve an optimum thermal protection system (TPS). The computational fluid dynamics (CFD) code to solve the Navier-Stokes equations for fluid flow in a rocket nozzle is coupled with the charting material ablation code through an energy balance at the active surface of the wall material. The present analysis compares well with the test results generated in-house as well as those reported in the literature.

Research paper thumbnail of The Linear Indeterminate Equation - a Brief Historical Account

Revista brasileira de história da matemática (RBHM), 2020

The paper presents in brief the contribution of Aryabhata in developing general solution of indet... more The paper presents in brief the contribution of Aryabhata in developing general solution of indeterminate equation of the type ax + c = by, where a, b, c are the integers. Also the contributions of Bhaskara and Brahmagupta in developing the solution of the indeterminate equations are discussed. Finally an example of Paramesvara is illustrated to solve coupled linear indeterminate equations which may be adopted to find the multiplicative inverse in a group that is of interest in cryptology, signal processing, coding and computer design.

Research paper thumbnail of The Linear Indeterminate Equation - a Brief Historical Account

Revista brasileira de história da matemática, 2015

The paper presents in brief the contribution of Aryabhata in developing general solution of indet... more The paper presents in brief the contribution of Aryabhata in developing general solution of indeterminate equation of the type ax + c = by, where a, b, c are the integers. Also the contributions of Bhaskara and Brahmagupta in developing the solution of the indeterminate equations are discussed. Finally an example of Paramesvara is illustrated to solve coupled linear indeterminate equations which may be adopted to find the multiplicative inverse in a group that is of interest in cryptology, signal processing, coding and computer design.

Research paper thumbnail of Overview of World ATW (Air to Water) Heat Pump Market and Opportunities with Respect to the Air-Conditioning Industry

Prabandhan: Indian Journal of Management, 2015

A heat pump is a device that transfers heat energy from a heat source to a heat sink against a te... more A heat pump is a device that transfers heat energy from a heat source to a heat sink against a temperature gradient. Heat pumps are designed to move thermal energy opposite to the direction of spontaneous heat flow. A heat pump uses some amount of external high-grade energy to accomplish the desired transfer of thermal energy from heat source to a heat sink. While compressor-driven air conditioners and freezers are familiar examples of heat pumps, the term "heat pump" is more general and applies to Heating Ventilation and Air Conditioning (HVAC, hereafter) devices used for space heating or space cooling. When a heat pump is used for heating, it employs the same basic refrigeration-type cycle used by an air conditioner or a refrigerator but in the opposite direction, releasing heat into the conditioned space rather than the surrounding environment. There are two types of heat pump technology, geothermal and aerothermal. Geothermal types include ground to water and water to water type heatpumps, while aerothermal heatpump technology is broadly used by the air-conditioning industry. Among the two types of aerothermal heat pumps, these are (a) Air to Air (ATA) and (b) Air to Water (ATW). Though ATA heat pumps were widely used so far in the air-conditioning industry, predominantly, there is a sudden and significant growth observed in the ATW heat pump market due to their energy efficient performance; and hence, the market is observing a technology shift. The present paper attempted to study the market segmentation of the heat pump industry with special focus on technical detailing and applications of ATW heat pumps. The research paper further described the key competitive players competing in the world market of ATW heat pump business. Secondary data analysis and review of global market for the last one decade (2004 to 2012) was carried out with a focus on leading countries or subcontinents' performance like that of Japan, China , Europe, Australia, United States, and some other small markets to draw the 'opportunities and challenges' roadmap for the ATW heat pump industry.

Research paper thumbnail of Thermal Performance of Vapor Chamber with Nanofluids

Frontiers in Heat Pipes, 2013

The paper describes experimental studies on the heat transfer performance of a wickless vapor cha... more The paper describes experimental studies on the heat transfer performance of a wickless vapor chamber with a heat sink. A vapor chamber of 78 mm length and 64 mm width was fabricated with a thickness of 5 mm and tested for two different working fluids, copper-water and aluminium-water nanofluids with the filling ratio of 30% of the vapor chamber volume. As a baseline comparison de-ionized (DI) water is considered as a working fluid. The vapor chamber was tested for heat inputs ranging from 90-150 W. The effects of heat input and metal concentration in the working fluids and the effect of particle deposition on the performance of the vapor chamber are presented. The thermal resistance of vapor chamber was decresed with the increase of the heat input for copper-water nanofluids while it remained constant for DIwater. Also the thermal resistance was found to be lower for higher concentration of the nanofluid.

Research paper thumbnail of Thermal Performance of cylindrical Heat Pipe Using Nanofluids

Journal of Thermophysics and Heat Transfer, 2010

Résumé/Abstract A cylindrical copper heat pipe with a 19.5 mm outer diameter and a 400.0 mm lengt... more Résumé/Abstract A cylindrical copper heat pipe with a 19.5 mm outer diameter and a 400.0 mm length was filled with three different working fluids and tested for different heat inputs in the range of 100-250 W. The working fluids tested were de-ionized water, silver-water colloid, and copper water. Experimental results showed that the wall temperature reduction obtained was 3-27 C. The efficiency of the heat pipe was enhanced by 14% as compared with the heat pipe filled with the base fluid. Furthermore, it was found that an increase in ...

Research paper thumbnail of Effective thermal conductivity of nanofluids – A new model taking into consideration Brownian motion

International Journal of Heat and Mass Transfer, 2016

Abstract In this study, a new analytical model for the effective thermal conductivity of liquids ... more Abstract In this study, a new analytical model for the effective thermal conductivity of liquids containing dispersed spherical and non-spherical nanometer particles was developed. In addition to heat conduction in the base fluid and the nanoparticles, we also consider convective heat transfer caused by the Brownian motion of the particles. For nanoparticle suspensions, the latter mechanism has significant influence on the effective thermal conductivity, which is reduced compared to a system in which only conduction is considered. The simple model developed allows for the prediction of the effective thermal conductivity of nanofluids as a function of volume fraction, diameter, and shape of the nanoparticles as well as temperature. Due to the inconsistency of experimental data in the literature, the model has been compared with the established Hamilton–Crosser model and other empirical models for the systems aluminum oxide (Al 2 O 3 ) and titanium dioxide (TiO 2 ) suspended in water and ethylene glycol. The theoretical estimates show no anomalous enhancement of the effective thermal conductivity and agree very well with the Hamilton–Crosser model within relative deviations of less than 8% for volume fractions of spherical particles up to 0.25. In accordance with the Hamilton–Crosser model for non-spherical particles, our model reveals that a more distinct increase in the enhancement of the effective thermal conductivity can be achieved using non-spherical nanoparticles having a larger volume-specific surface area.

Research paper thumbnail of Heat Pipe for Aerospace Applications—An Overview

Journal of Electronics Cooling and Thermal Control

Research paper thumbnail of Performance Analysis of Silica-Tiles as a Thermal Protection System

9th AIAA/ASME Joint Thermophysics and Heat Transfer Conference, 2006

Research paper thumbnail of Thermal performance analysis of silica tiles

Journal of Engineering Physics and Thermophysics, 2006

Research paper thumbnail of Steady State Perormance of a Rotating Heat Pipe

46th AIAA Aerospace Sciences Meeting and Exhibit, 2008

Research paper thumbnail of Thermal performance of heat pipe with suspended nano-particles

Heat and Mass Transfer, 2012

Research paper thumbnail of Thermal performance of heat pipe with suspended nano-particles

Heat and Mass Transfer, 2012

Research paper thumbnail of Prof.Shukla.docx

Research paper thumbnail of Indian Cryogenic Engine-State of the Art, Invention (July-August 2017).pdf

Research paper thumbnail of Effective thermal conductivity of nanofluids – A new model taking into consideration Brownian motion

In this study, a new analytical model for the effective thermal conductivity of liquids containin... more In this study, a new analytical model for the effective thermal conductivity of liquids containing dispersed spherical and non-spherical nanometer particles was developed. In addition to heat conduction in the base fluid and the nanoparticles, we also consider convective heat transfer caused by the Brownian motion of the particles. For nanoparticle suspensions, the latter mechanism has significant influence on the effective thermal conductivity, which is reduced compared to a system in which only conduction is considered. The simple model developed allows for the prediction of the effective thermal conductivity of nanofluids as a function of volume fraction, diameter, and shape of the nanoparticles as well as temperature. Due to the inconsistency of experimental data in the literature, the model has been compared with the established Hamilton–Crosser model and other empirical models for the systems aluminum oxide (Al 2 O 3) and titanium dioxide (TiO 2) suspended in water and ethylene glycol. The theoretical estimates show no anomalous enhancement of the effective thermal conductivity and agree very well with the Hamilton–Crosser model within relative deviations of less than 8% for volume fractions of spherical particles up to 0.25. In accordance with the Hamilton–Crosser model for non-spherical particles, our model reveals that a more distinct increase in the enhancement of the effective thermal conductivity can be achieved using non-spherical nanoparticles having a larger volume-specific surface area.

Research paper thumbnail of Thermal Convection in a Cylindrical Enclosure

42nd AIAA Aerospace Sciences Meeting and Exhibit, 2004

The paper highlights the onset of convection in a fluid layer partially filled in an axisymmetric... more The paper highlights the onset of convection in a fluid layer partially filled in an axisymmetric container. The equilibrium of the fluid is disturbed with the deformation of the interface due to residual acceleration. The general problem of deformable interface involves a dimensionless parameter, the Bond number. An analytical expression for the natural frequencies of the deformable surface is derived in terms of the Bond number, which determines the time period required for the stable location of the fluid for the propellant ...

Research paper thumbnail of Thermal Convection in a Cylindrical Enclosure

42nd AIAA Aerospace Sciences Meeting and Exhibit, 2004

The paper highlights the onset of convection in a fluid layer partially filled in an axisymmetric... more The paper highlights the onset of convection in a fluid layer partially filled in an axisymmetric container. The equilibrium of the fluid is disturbed with the deformation of the interface due to residual acceleration. The general problem of deformable interface involves a dimensionless parameter, the Bond number. An analytical expression for the natural frequencies of the deformable surface is derived in terms of the Bond number, which determines the time period required for the stable location of the fluid for the propellant ...

Research paper thumbnail of Thermal performance analysis of silica tiles

Journal of Engineering Physics and Thermophysics, 2006

The thermal response of nonablating ceramic tiles is studied by the finite-element method. A cont... more The thermal response of nonablating ceramic tiles is studied by the finite-element method. A continuum model is used to determine the thermal conductivity of porous materials. The temperature distribution for the one-dimensional model is compared with the available arc-jet result. Also presented are the 2D and 3D temperature contours and the heat-flux distributions for silica tiles. The expression for the pressure distribution in a silica tile is derived.

Research paper thumbnail of Thermal performance analysis of silica tiles

Journal of Engineering Physics and Thermophysics, 2006

The thermal response of nonablating ceramic tiles is studied by the finite-element method. A cont... more The thermal response of nonablating ceramic tiles is studied by the finite-element method. A continuum model is used to determine the thermal conductivity of porous materials. The temperature distribution for the one-dimensional model is compared with the available arc-jet result. Also presented are the 2D and 3D temperature contours and the heat-flux distributions for silica tiles. The expression for the pressure distribution in a silica tile is derived.

Research paper thumbnail of Performance Analysis of Thermal Protection System of a Solid Rocket Nozzle

Journal of Spacecraft and Rockets, 2003

A coupled approach is adopted to solve the conjugate problem of fluid flow and heat transfer in s... more A coupled approach is adopted to solve the conjugate problem of fluid flow and heat transfer in solid rocket nozzles in order to achieve an optimum thermal protection system (TPS). The computational fluid dynamics (CFD) code to solve the Navier-Stokes equations for fluid flow in a rocket nozzle is coupled with the charting material ablation code through an energy balance at the active surface of the wall material. The present analysis compares well with the test results generated in-house as well as those reported in the literature.