Seeking Appropriate Equation for Linear Conductivity

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SUMMARY

The discussion focuses on calculating the time required for a stone slab to fully preheat using one-dimensional steady flow conduction principles. Key parameters include a thermal conductivity of 6.4 W/mK, specific heat capacity of 0.98 J/gK, and a density of 2,980 kg/m³. The slab has a thickness of 3.18 cm and a core temperature (T2) of 21.11 C, while the surface temperature (T1) is 260 C. The challenge lies in determining the appropriate equation without knowing the area and mass, which are typically essential for such calculations.

PREREQUISITES
  • Understanding of one-dimensional steady flow conduction principles
  • Familiarity with thermal conductivity and specific heat capacity concepts
  • Knowledge of density and its role in thermal calculations
  • Ability to manipulate equations involving temperature gradients
NEXT STEPS
  • Research the heat conduction equation for one-dimensional steady-state conditions
  • Explore the concept of thermal resistance and its application in heat transfer
  • Learn about the role of area and mass in thermal energy calculations
  • Investigate numerical methods for solving heat conduction problems without complete data
USEFUL FOR

Students studying thermal physics, engineers working with heat transfer applications, and anyone involved in material science or thermal analysis of solid objects.

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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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