This paper discusses the theory and application of single-sample uncertainty analysis in experimental research, particularly in heat transfer and fluid mechanics. It highlights the importance of uncertainty analysis in planning, evaluating, and reporting scientific experiments, emphasizing that it is often overlooked in practice. The paper introduces the concept of "zero-centered experiments," which aim to minimize fixed errors and maximize the precision of measurements. It outlines the sources of scatter in data, including fixed errors, random errors, and instrumental variations, and provides methods for estimating these uncertainties. The paper also introduces the concept of replication levels (zeroth, first, and Nth order) to help identify which variables should be included in the uncertainty analysis. Each replication level corresponds to a different level of uncertainty and is used for different purposes, such as planning, debugging, and comparing results with other experiments or theoretical values. The paper details the mathematical forms for calculating absolute and relative uncertainties and provides a step-by-step guide for implementing uncertainty analysis using computer-based data reduction programs. Finally, the paper discusses the practical challenges and implications of uncertainty analysis, such as the need for detailed calibration of instruments and the importance of reliable estimates of uncertainties for comparing experimental results with theoretical values or computational models. The paper emphasizes the value of uncertainty analysis in improving the accuracy and reliability of experimental results.This paper discusses the theory and application of single-sample uncertainty analysis in experimental research, particularly in heat transfer and fluid mechanics. It highlights the importance of uncertainty analysis in planning, evaluating, and reporting scientific experiments, emphasizing that it is often overlooked in practice. The paper introduces the concept of "zero-centered experiments," which aim to minimize fixed errors and maximize the precision of measurements. It outlines the sources of scatter in data, including fixed errors, random errors, and instrumental variations, and provides methods for estimating these uncertainties. The paper also introduces the concept of replication levels (zeroth, first, and Nth order) to help identify which variables should be included in the uncertainty analysis. Each replication level corresponds to a different level of uncertainty and is used for different purposes, such as planning, debugging, and comparing results with other experiments or theoretical values. The paper details the mathematical forms for calculating absolute and relative uncertainties and provides a step-by-step guide for implementing uncertainty analysis using computer-based data reduction programs. Finally, the paper discusses the practical challenges and implications of uncertainty analysis, such as the need for detailed calibration of instruments and the importance of reliable estimates of uncertainties for comparing experimental results with theoretical values or computational models. The paper emphasizes the value of uncertainty analysis in improving the accuracy and reliability of experimental results.