Heat loss through insulated food container.xls

KNOWN: Dimensions and thermal conductivity of food/beverage container. Inner and outer surface temperatures.

FIND: Heat flux through container wall and total heat load.

ASSUMPTIONS: 1) Steady State conditions.

2) Negligible heat transfer through bottom wall.

3) Uniform surface temperatures and one-dimensional conduction through remaining walls.

Calculation Reference

Fundamentals of Heat and Mass Transfer - Frank P. Incropera

To calculate the heat loss through an insulated food/beverage container, considering the dimensions, thermal conductivity of the container, and the given inner and outer surface temperatures, you can follow these steps:

1. Determine the surface area of the container: Calculate the surface area of the container, including all walls.

2. Calculate the thermal resistance of the insulation: The thermal resistance (R_insulation) of the insulation material can be calculated using the formula:

   R_insulation = Thickness / (Thermal Conductivity * Area)

   Where the thickness is the thickness of the insulation material and the thermal conductivity is the thermal conductivity of the insulation.

3. Calculate the thermal resistance of the remaining walls: The thermal resistance (R_walls) of the remaining walls of the container can be calculated using the formula:

   R_walls = Thickness / (Thermal Conductivity * Area)

   Where the thickness is the thickness of the container walls (excluding the insulation) and the thermal conductivity is the thermal conductivity of the container material.

4. Calculate the total thermal resistance: The total thermal resistance (R_total) of the container can be calculated by summing the thermal resistances of the insulation and the remaining walls:

   R_total = R_insulation + R_walls

5. Calculate the heat flux: The heat flux (q) through the container wall can be calculated using Fourier's Law of heat conduction:

   q = (T_inner - T_outer) / R_total

   Where T_inner and T_outer are the inner and outer surface temperatures, respectively, and R_total is the total thermal resistance of the container.

6. Calculate the total heat load: The total heat load (Q) is the product of the heat flux and the surface area of the container:

   Q = q * Surface Area

By following these steps, you can determine the heat flux through the container wall and calculate the total heat load for the insulated food/beverage container based on the given dimensions, thermal conductivity, inner and outer surface temperatures, and the assumptions of steady-state conditions, negligible heat transfer through the bottom wall, uniform surface temperatures, and one-dimensional conduction through the remaining walls.