Hot air at 80^∘ C is blown over a 2-m ×4-m flat surface at 30^∘ C. If the convection heat transf

step 1 Here we have the temperature difference that the G is 80 minus 30 equals 50 degrees centigrade T

Hot air at 80^∘ C is blown over a 2-m ×4-m flat surface at...

Hot air at $80^{\circ} \mathrm{C}$ is blown over a $2-\mathrm{m} \times 4-\mathrm{m}$ flat surface at $30^{\circ} \mathrm{C}$. If the convection heat transfer coefficient is $55 \mathrm{W} / \mathrm{m}^{2} \cdot^{\circ} \mathrm{C},$ determine the rate of heat transfer from the air to the plate, in $\mathrm{kW}$

Key Concepts

Convection Heat Transfer

This concept refers to the process through which heat is transferred from one surface to a fluid (or vice versa) by the movement of that fluid. In many practical applications, such as heating or cooling processes, convection is the main mechanism by which thermal energy is exchanged, and it is typically modeled using empirical correlations and laws like Newton's Law of Cooling.

Newton's Law of Cooling

Newton's Law of Cooling, applied in the context of convection, states that the rate of heat transfer between a solid surface and a fluid is proportional to the temperature difference between them. The law is expressed mathematically as Q = hA(?T), where Q is the rate of heat transfer, h is the convection heat transfer coefficient, A is the surface area, and ?T is the temperature difference.

Convection Heat Transfer Coefficient

The convection heat transfer coefficient 'h' is a parameter that quantifies the effectiveness of heat transfer between a surface and a fluid in motion. It depends on the properties of the fluid, the nature of its motion, and the characteristics of the surface. This coefficient is crucial for predicting the rate of convective heat transfer in various engineering applications.

Surface Area Calculation

The surface area of the object in contact with the fluid is a key factor in determining the overall heat transfer rate. In problems involving flat surfaces, the area is computed by multiplying the dimensions of the surface, and it directly influences the magnitude of the heat exchange, as larger areas allow for more heat to be transferred.

Temperature Difference

The temperature difference between the hot fluid and the surface is the driving force for convective heat transfer. It indicates how much thermal energy is available to be transferred from the fluid to the surface or vice versa, and it is the term in Newton's Law of Cooling that modulates the rate of heat transfer.

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