Answered: 2. Consider airflow over a plate…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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$### Problem Statement 2. **Airflow Over a Plate** Consider airflow over a plate surface maintained at a temperature of 215°C. The temperature profile of the airflow is given as: \[ T(y) = T_{\infty} - (T_{\infty} - T_s) \exp\left(-\frac{V}{\alpha_{\text{fluid}}} y\right) \] **Parameters:** - $ T(y) $: Temperature at a distance $ y $ from the plate - $ T_{\infty} $: Free stream temperature - $ T_s $: Surface temperature of the plate - $ V $: Free stream velocity - $ \alpha_{\text{fluid}} $: Thermal diffusivity of the fluid - $ y $: Distance from the plate surface The airflow at 1 atm has a free stream velocity and temperature of 5 cm/s and 25°C, respectively. Determine the heat flux on the plate surface and the convection heat transfer coefficient of the airflow. ### Explanation This problem involves analyzing the heat transfer from a stationary plate to airflow passing over it. The temperature of the plate is higher than the incoming airflow, which influences the temperature gradient and consequently, the heat transfer rate. - **Equation Overview**: The provided equation describes how temperature changes with distance from the plate surface. It's an exponential decay function, indicating that the temperature change diminishes as you move further from the plate. - **Objective**: Calculate the heat flux on the plate and the convection heat transfer coefficient using the given conditions and parameters. This requires applying principles of thermodynamics and heat transfer, specifically focusing on convective heat transfer processes. ### Steps for Solution 1. **Calculate Temperature Gradient**: Use the given temperature profile equation to determine the temperature gradient at the surface. 2. **Determine Heat Flux**: Use Fourier's law of heat conduction to find the heat flux at the plate's surface. 3. **Convection Heat Transfer Coefficient**: Apply Newton’s Law of Cooling to find the convection heat transfer coefficient. These calculations offer insights into how effectively the plate transfers heat to the airflow, informing further thermal management decisions in engineering applications.$

Transcribed Image Text:### Problem Statement 2. **Airflow Over a Plate** Consider airflow over a plate surface maintained at a temperature of 215°C. The temperature profile of the airflow is given as: \[ T(y) = T_{\infty} - (T_{\infty} - T_s) \exp\left(-\frac{V}{\alpha_{\text{fluid}}} y\right) \] **Parameters:** - $ T(y) $: Temperature at a distance $ y $ from the plate - $ T_{\infty} $: Free stream temperature - $ T_s $: Surface temperature of the plate - $ V $: Free stream velocity - $ \alpha_{\text{fluid}} $: Thermal diffusivity of the fluid - $ y $: Distance from the plate surface The airflow at 1 atm has a free stream velocity and temperature of 5 cm/s and 25°C, respectively. Determine the heat flux on the plate surface and the convection heat transfer coefficient of the airflow. ### Explanation This problem involves analyzing the heat transfer from a stationary plate to airflow passing over it. The temperature of the plate is higher than the incoming airflow, which influences the temperature gradient and consequently, the heat transfer rate. - **Equation Overview**: The provided equation describes how temperature changes with distance from the plate surface. It's an exponential decay function, indicating that the temperature change diminishes as you move further from the plate. - **Objective**: Calculate the heat flux on the plate and the convection heat transfer coefficient using the given conditions and parameters. This requires applying principles of thermodynamics and heat transfer, specifically focusing on convective heat transfer processes. ### Steps for Solution 1. **Calculate Temperature Gradient**: Use the given temperature profile equation to determine the temperature gradient at the surface. 2. **Determine Heat Flux**: Use Fourier's law of heat conduction to find the heat flux at the plate's surface. 3. **Convection Heat Transfer Coefficient**: Apply Newton’s Law of Cooling to find the convection heat transfer coefficient. These calculations offer insights into how effectively the plate transfers heat to the airflow, informing further thermal management decisions in engineering applications.

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