Seeking Appropriate Equation for Linear Conductivity

AI Thread Summary
To calculate the time for a stone slab to preheat using one-dimensional steady flow conduction, the thermal conductivity, specific heat capacity, density, thickness, and temperature difference must be considered. The key challenge is the unknown area and mass, which are typically required for the calculations. The thermal conductivity is 6.4 W/mK, specific heat capacity is 0.98 J/gK, and density is 2,980 kg/m³, with a slab thickness of 3.18 cm and a temperature gradient from 260°C to 21.11°C. While textbooks provide equations, they often assume known area and mass, which complicates the solution. The discussion emphasizes the need to derive a formula that accounts for these variables or find a way to eliminate them from the calculations.
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Homework Statement



I am attempting to calculate the approximate time it takes for a stone slab to fully preheat, focusing only on one dimensional steady flow conduction. Both my area and mass are unknown.

Thermal conductivity: 6.4 W/mK
Specific heat capacity: 0.98 J/gK
Density: 2,980 kg/m³

Thickness of slab: 3.18 cm
Distance to center: 1.59 cm
T1: 260 C.
T2 (core): 21.11 C.

Homework Equations



This is what I'm looking for.

The Attempt at a Solution



I've spent hours looking through textbooks trying to find the right equation, but everything I run across seems to have additional info such as area and mass.
 
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You will have to give us the whole problem. Area and mass are needed but I suspect that they fall out in your calculation.

AM
 

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