# Temperature profile of an assemblage of non-isothermic linear energy converters

## TL;DR

This paper introduces a new method to determine the temperature profile of non-isothermal linear energy converters without solving complex Riccati differential equations, simplifying analysis and enabling better understanding of their energetic behavior.

## Contribution

A novel approach using a first-order differential equation and force ratio to find temperature profiles, bypassing Riccati's equation in non-isothermal energy converters.

## Key findings

- Derived a first-order differential equation for temperature profiles.
- Provided a method to analyze heat fluxes and operational regimes.
- Enhanced understanding of energetic behavior in heat engines, coolers, and heat pumps.

## Abstract

In this paper, a proposal is presented to determine the temperature profile obtained for an assemblage of non-isothermal linear energy converters (ANLEC) published by Jimenez de Cisneros and Calvo Hernandez [1,2]. This is done without solving the Riccati's differential equation, needed by these authors to get the temperature profile. Instead of use Riccati's equation, we deduce a first order ordinary differential equation, through the introduction of the force ratio $x_{D,I}$ of an ANLEC's machine-element which operates at some optimal regime. Additionally, we used the integration constant, that comes from the solution of this differential equation, to deduce the general heat fluxes of the ANLEC and tuning the assamblage's operation as direct energy converter or inverse energy converter. The temperature profile will serve to obtain the energetic behavior of a non-isothermal energy converter as heat engine, cooler or heat pump.