The Eucharist

Thermodynamics vs. Heat Transfer

• Thermodynamics addresses the amount of heat transfer during a process.
• Heat transfer focuses on the rate of heat transfer and temperature distribution.

Heat

• Energy transferred between systems due to temperature difference.
• Thermodynamics deals with the amount of heat transfer as a system changes equilibrium.
• Heat transfer deals with determining energy transfer rates and temperature variation.

Applications of Heat Transfer

• Relevant in power plants, automotive engineering, aerospace, electronics, and manufacturing.

Modes of Heat Transfer

• There are three modes of heat transfer: conduction, convection, and radiation.

Conduction

• It occurs in solids or stationary fluids via atomic, molecular, and/or electronic motion.
• Conduction rate depends on geometry, thickness, material, and temperature difference.

Fourier's Law

• Heat conduction rate is proportional to the temperature gradient and area, and inversely proportional to thickness.
• $\dot{Q}_{cond} = -kA\frac{dT}{dx}$
• $\dot{Q}_{cond}$: Heat conduction rate
• $A$: Area normal to heat transfer direction
• $dT/dx$: Temperature gradient
• $k$: Thermal conductivity

Thermal Conductivity

• Denotes a material's ability to conduct heat.

Convection

• Heat transfer between a surface and a moving fluid, combining conduction and fluid motion.
• Forced Convection: Requires external means like a fan or pump to force fluid flow.
• Natural Convection: Relies on buoyancy from density differences caused by temperature variations.

Newton's Law of Cooling

• $\dot{Q}{conv} = hA(T_s - T{\infty})$
• $h$: Convection heat transfer coefficient
• $A$: Surface area
• $T_s$: Surface temperature
• $T_{\infty}$: Fluid temperature away from the surface

Radiation

• Energy emission via electromagnetic waves due to changes in electronic configurations.
• It does not require a medium.

Stefan-Boltzmann Law

• Emitted energy calculation.
• $\dot{Q}_{emit} = \epsilon \sigma A T_s^4$
• $\epsilon$: Emissivity of the surface
• $\sigma$: Stefan-Boltzmann constant ($5.67 \times 10^{-8} W/m^2 \cdot K^4$)
• $A$: Surface area
• $T_s$: Absolute surface temperature

Absorptivity

• Fraction of radiation absorbed by a surface.
• $\dot{Q}{abs} = \alpha \dot{Q}{incident}$
• $\alpha$: Absorptivity
• $\dot{Q}_{incident}$: Incident radiation

Net Radiation Heat Transfer

• $\dot{Q}{rad} = \epsilon \sigma A (T_s^4 - T{surr}^4)$
• $T_{surr}$: Average temperature of surrounding surfaces

Simultaneous Heat Transfer

• Real-world situations often combine conduction and convection, conduction and radiation (in solids), and convection and radiation (from surfaces).

Problem Solving Technique Steps

• Problem Statement
• Schematic
• Assumptions and Approximations
• Physical Laws
• Properties
• Calculations
• Reasoning, Verification, and Discussion

Engineering Equation Solver (EES)

• Numerical solver for linear/non-linear algebraic/differential equations.
• Useful for complex heat transfer problems without analytical solutions.
• An engineering analysis and design tool.

What is Artificial Intelligence?

• AI is the simulation of human intelligence processes by computer systems.
• The goal is to create machines that can perform tasks that typically require human intelligence.

AI Subfields

Machine Learning (ML)

• ML involves training machines from data without explicit programming.
• Types of ML include supervised, unsupervised, and reinforcement learning.

Deep Learning (DL)

• DL is a subfield of ML that uses neural networks with multiple layers.
• It's applicable to pattern recognition and natural language processing.

Natural Language Processing (NLP)

• NLP allows computers to interact with human language.
• Tasks range from machine translation to sentiment analysis.

Computer Vision (CV)

• CV enables computers to "see" and interpret images by use of object recognition and image analysis.

Robotics

• Robotics involves designing, constructing, operating, and applying robots.
• AI is used for autonomous operation.

Machine Learning Basics

• Training data is the dataset used to train a model.
• Features are the input variables used for prediction.
• A model is a mathematical representation of relationships in data.
• Algorithms are methods used to train the model (e.g., linear regression, decision trees).

Types of Machine Learning

Supervised Learning

• Supervised learning uses labeled data (inputs and corresponding outputs).
• It can be used for classification (determining categories) and regression (predicting values).

Unsupervised Learning

• Unsupervised learning uses unlabeled data.
• It can be used for clustering (grouping data) and dimensionality reduction.

Reinforcement Learning

• Reinforcement learning trains an agent to make decisions in an environment to maximize rewards.
• It is used in games and robotics, for example, training a chess program to play better.

Model Evaluation Metrics

• Accuracy: The proportion of correct answers.
• Precision measures the correctly predicted positives out of all predicted positives.
  • $Precision = \frac{TP}{TP + FP}$
• Recall (sensitivity) measures the correctly predicted positives out of all actual positives.
  • $Recall = \frac{TP}{TP + FN}$
• F1-measure is the harmonic mean between precision and recall.
  • $F_1 = 2 \cdot \frac{Precision \cdot Recall}{Precision + Recall}$
• AUC-ROC is the area under the Receiver Operating Characteristic curve.
• MAE (Mean Absolute Error) is the average absolute error.
• MSE (Mean Squared Error) is the average squared error.
• R-squared is the coefficient of determination; it measures how well the model explains the variance in the data.

Main Machine Learning Algorithms

Linear Regression

• Used for regression tasks.
• Equation: $Y = aX + b$

Logistic Regression

• Used for classification tasks.
• Function: $P(Y = 1) = \frac{1}{1 + e^{-z}}$, where $z = aX + b$

Decision Trees

• Used for both classification and regression tasks.
• Builds a tree of decisions based on features.

Support Vector Machine (SVM)

• Finds the optimal boundary between classes and is used for classification and regression.

Naive Bayesian Classifier

• Based on Bayes' theorem.
• Assumes independence of features.
  • $P(A|B) = \frac{P(B|A) \cdot P(A)}{P(B)}$

K-Nearest Neighbors (KNN)

• Used for classification and regression tasks and classifies objects based on the nearest neighbors.

Principal Component Analysis (PCA)

• Used for reducing data dimensionality and finds the main components that explain the largest variance.

Neural Networks

• They use layers of neurons to model complex dependencies and are trained by backpropagation.

Machine Learning Tools and Libraries

Python

• The main language used for machine learning.

Libraries

• Scikit-learn is the primary library for ML.
• TensorFlow and Keras are libraries for deep learning.
• PyTorch is a library for deep learning.
• NumPy for array manipulation.
• Pandas for data analysis.
• Matplotlib, Seaborn for data visualization.

R

• A language and environment for statistical computing and graphics.

Machine Learning Model Development Process

1. Data collection and preparation includes gathering/cleaning/transforming data.
2. Exploratory Data Analysis consists of visualization, anomaly detection, and correlation analysis.
3. Model selection involves determining the task, choosing an algorithm and splitting data.
4. Model Training uses the training data to train the model, including hyperparameter tuning.
5. Model evaluation uses the test data to assess model performance through metrics analysis.
6. Model deployment integrates the model into a production environment, monitors performance, and retrains as necessary.

Ethical and Social Aspects of AI

• Bias: Models can reproduce and amplify existing biases in data.
• Transparency: Difficulty understanding the workings of complex models.
• Responsibility: Determining responsibility for decisions made by AI.
• Privacy: Protecting personal data used for training models.
• Automation: Impact on the job market and employment.

Heat Transfer Modes

• Conduction: Heat transfer through a solid or stationary fluid.
  • Fourier's Law: $\dot{Q} = -kA\frac{dT}{dx}$
  • $\dot{Q}$ is the heat transfer rate.
  • $k$ is the thermal conductivity of the material.
  • $A$ is the cross-sectional area.
  • $\frac{dT}{dx}$ is the temperature gradient.
• Convection: Heat transfer between a surface and a moving fluid.
  • Newton's Law of Cooling: $\dot{Q} = hA(T_s - T_{\infty})$
  • $h$ is the convection heat transfer coefficient.
  • $T_s$ is the surface temperature.
  • $T_{\infty}$ is the fluid temperature.
• Radiation: Heat transfer through electromagnetic waves.
  • Stefan-Boltzmann Law: $\dot{Q} = \epsilon \sigma A (T_s^4 - T_{surr}^4)$
  • $\epsilon$ is the emissivity of the surface.
  • $\sigma$ is the Stefan-Boltzmann constant ($5.67 \times 10^{-8} W/m^2K^4$).
  • $T_{surr}$ is the surrounding temperature.

Thermal Resistance

• Conduction Resistance: $R_{cond} = \frac{L}{kA}$
• Convection Resistance: $R_{conv} = \frac{1}{hA}$
• Radiation Resistance: $R_{rad} = \frac{1}{h_{rad}A}$
  • $h_{rad} = \epsilon \sigma (T_s + T_{surr})(T_s^2 + T_{surr}^2)$

Overall Heat Transfer Coefficient

• $U = \frac{1}{\frac{1}{h_i} + \sum R_{cond} + \frac{1}{h_o}}$
• $h_i$ inside heat transfer coefficient
• $h_o$ outside heat transfer coefficient
• $\sum R_{cond}$ is the sum of conduction resistances

Fin Efficiency

• $\eta_{fin} = \frac{Q_{actual}}{Q_{max}}$
  • $Q_{actual}$ is the actual heat transfer rate from the fin.
  • $Q_{max}$ is the ideal heat transfer rate if the entire fin were at the base temperature.

Types of Fins

• Straight Fin
• Annular Fin
• Pin Fin

Heat Exchangers

• Shell-and-Tube heat exchanger
• Plate heat exchanger
• Compact heat exchanger

Heat Exchangers Methods

LMTD (Log Mean Temperature Difference)

• $\Delta T_{lm} = \frac{\Delta T_1 - \Delta T_2}{ln(\frac{\Delta T_1}{\Delta T_2})}$
  • $\Delta T_1$ is the temperature difference at one end.
  • $\Delta T_2$ is the temperature difference at the other end.

Effectiveness-NTU Method

• $\epsilon = \frac{Q_{actual}}{Q_{max}}$
• $NTU = \frac{UA}{C_{min}}$
  • $U$ is the overall heat transfer coefficient.
  • $A$ is the heat transfer area.
  • $C_{min}$ is the minimum heat capacity rate.